I'd like to believe Grant but I find this assault on mathematics to be dehumanizing and demoralizing. AI has destroyed a major source of "life's meaning" for many people who pursued mathematics. Imagine waking up one morning to find that an alien technology has solved the problem you had dedicated your life to (and many more to boot.) Not another mathematician but an alien technology. As a scientist, I don't want to end up as a laboratory assistant to an AI. I can take not being the smartest human in the room, but I'm pretty sure I don't want to spend my life serving a silicon master.
> Imagine waking up one morning to find that an alien technology has solved the problem you had dedicated your life to
I'm sympathetic to mathematicians but this does not paint them in a good light.
If your primary purpose is SOLVING the problem, you should be ecstatic! If your primary purpose was rent-seeking so you could play with puzzles*, you'd be very upset.
* I find this characterization overly harsh, but if you're mad about your problem being solved, maybe you weren't in it for the right reasons
Let's just say that The math problem that got solved, I was working on it for many years but some company people used my knowledge my prompts and "solved" it without giving me any credits or money.
Firstly they plagiarised the books and research papers and then they plagiarised the prompts by the mathematicians.
Yes AI can make art and has caused many artists finding work difficult but AI art is always souless and worthless, same thing will be for math it will become souless and worthless because when humans who are experts in their fields invest their ingenuity then art becomes alive but if ordinary people like me will just prompt into the machine then souless things will come out that will be very worthless and disposable.
I’m seeing this perspective expressed a lot lately, but (so far) only online.
Understand that there’s more than one way to prove something, that there’s an art to making something understandable, and that humans tend to take the most understandable paths (to humans.)
Models often don’t do that. But in solving, or claiming to solve, important problems, they nevertheless remove a lot of the excitement and incentive towards working towards a solution humans would naturally find. Plus, a lot of these problems really don’t have any critical applications at the moment. They’re done for the love of the game.
Does that bother you? That your tax dollars pay people who do math out of curiosity?
On one hand I agree. I’d also add that there will be no end of math problems to solve. That some were solved will only lead to new ones.
That said, I think what has mathematicians… upset is probably two things:
1. These are hard problems. Hard enough that solving one could take decades of work. And there’s tons of collaboration involved. Pivoting to another - and making progress - isn’t exactly something you wake up tomorrow and start doing.
2. I think motivations matter to some. And the AI companies doing this aren’t doing it for the betterment of math or even society. They are in an arms race to prove their product is superior and any careers that are damaged collaterally be dammed.
If we play a game of chess and I move the pieces to the final position on the first move and declare victory you might feel that something was missing, even if I'm right.
This is not quite like that but the feeling I get from it is much the same. Mathematicians are first and foremost busy with understanding math, not with 'solving' math though they are solving individual problems within the domain of math. The journey towards that understanding requires specialization and often lots of studying.
To quote Douglas Adams: "If 'metal nose' here is going to give you God's phone number then the philosophical question of whether there is a God becomes meaningless."
It is the journey and the questions that matter as much or more than the answer does.
And with math being a branch of natural philosophy I can see why they would be a tad upset at this shortcut because it strips the collective efforts of a large number of people of their prestige and feeling of time well spent. Imagine your life's work reduced to a short string of bits, and worse, that short string of bits was created by a machine that effectively is still a toddler.
> It is the journey and the questions that matter as much or more than the answer does.
Selfishly, as someone who enjoys programming, I feel the same way about the journey. But let's face it: for everyone else, the outcome is what actually matters. Mathematicians argue that their journey may lead to novel insights, but are those insights really valuable? Are they going to help the LLMs solve more problems? And are we sure that the LLMs can't deliver those same insights?
I think that ties in with the 'who will train the juniors' angle: if the ladder consists of nothing but the top rung because the AI combine stripped away the rest of them then a lot of fields will be looking at zero new entrants. Nobody wants to compete with a machine for their living and sense of self value. I know I don't, and obviously I can't speak for anybody else but society has pretty much programmed people to tie a good chunk of their identity, success in life and general well being to their skills and ability to put bread on the table. You can't just toss that in the bin for 3/4 of the current crop of professionals (I'm seeing the mathematicians as simply the first (and probably not even the first) of many).
I don't know if you have kids or not but I have two kids in high school and keeping them motivated through the AI revolution is a serious challenge and some of their classmates have already all but given up. The next generation down the line is going to grow up with the same kind of attitude towards thinking that you might have towards the skill of map reading. And I think we'll all be poorer because of that, not richer.
It seems like everyone presumes that the currently proofs which are difficult to parse will stay that way. LLMs are really good with language. There's no reason that the next wave of proofs won't be accompanied by very literate explanations that mathematicians can generate understanding from.
There is a difference between the process of solving a problem and a problem being solved. If I solve a problem myself, I understand it, I find out something new, I get to try lots of things. It's engaging and fun. If I tell you to go solve a problem, I can learn it afterwards but I miss out on the entire process.
Personally, I enjoy the process of solving problems. I do not enjoy wrangling unpredictable AI agents.
Why should we be estatic that some signifigant math problem was solved by machine rather of a human being in a language only the machine understands? Don't you know that problem was solved by a space alien a million light-years away a long time ago in a galaxy far far away? Makes no difference from the meatbag perspective: both claims are untestifiable.
In fact you should be estatic that in a paralell universe all math problems have been solved, so there's no reason to pursue math at all (we did it reddit!).
When your job is automated and you're living in the streets, just remember that you should be estatic that the job is finally being done more efficiently by a robot. Like, we did it. We finally did the job right. The job was never about wealth distribution, self actualization, dignity or any of that crap it was always about getting some stupid task accomplished for an industrial system that exists for... what exactly? What is the end goal of all of this? Who does the system serve in an economy of no consumers? What is the point of solving niche mathematical problems if no living person can comprehend the solution?
> The job was never about wealth distribution, self actualization, dignity or any of that crap it was always about getting some stupid task accomplished for an industrial system
There are still a whole lot of people, the vast majority of people actually, who's job involves something completely unglamorous and practical like unclogging your sewers.
To these people, it sounds like a cruel joke that people get paid 3x their salary, and after AI can do their job we learn that apparently the only purpose of their was their own self-actualization.
I don't actually believe that about math, but that's what a lot of people in this thread sound like.
I thought technology was supposed to liberate us from the fields, but it turns out that's what wealth is for, and the wealthy want us back in the fields (no more escape through special training or skill).
>There are still a whole lot of people, the vast majority of people actually, who's job involves something completely unglamorous and practical like unclogging your sewers.
I know, I have that job! And I enjoy it. But the robots are coming for me too.
You shouldn't. Maybe you should learn Hilbert Calculus so you can appreciate it.
It's like asking if what someone wrote a beautiful poem but it's in japanese. Maybe hearing about it motivates me to learn japanese, or maybe it doesn't. But as a non-speaker it makes little impression on me.
“ if you're mad about your problem being solved, maybe you weren't in it for the right reasons”, politicians/financial advisors/military members/etc… would like a word with you.
The primary value of math has never been about producing "solved problems" (is there any practical value in "solving" NS in itself?). The primary value of mathematics has always been about "machinery for thought", i.e. the abstractiosn and methods that produced the solution.
I think there is a little too much pessimism of the "math is dead" sort. As long as there is a need for humans to think there will be value in doing math.
I suggest listening to "Math Vs Machine" [1], which has a much more nuanced take. It clearly lays out two types of use of AI in math, one that helps humans have better understanding, and one just bulldozes problems without helping us get any insights. It also touches on the topic of "does it matter if the machine does things in ways humans cannot understand".
Mathematicians are saying the current papers are pretty inscrutable and use terminology unfamiliar in the math sub fields in which the models are generating proofs.
Mathematicians usually care nothing about application of their work. Working on interesting problems is their only motivation. Practical applications are almost always happy accidents.
This goes back to the hope that robots would do the laundry and the dishes and the cleaning up so we could write and play music, create art, and solve mathematical problems.
Instead the AIs are doing all of that leaving humans with only the dishes and the laundry and the cleaning up.
As of this comment you have 26 comments out of 206 total on this comment section, more than 10% basically all spreading FUD to try and make other people as miserable and pessimistic as you. I'm not sure what your motivations are but I'm glad we have people like Grant on the other side trying to keep a positive outlook on life and the future, and I hope all you eternal doomers who constantly try to bring others down with you find joy as well.
If math is nothing but solving puzzles for fun then I think a lot of people should be very pissed off that they are doing hard labor while being taxed to fund a puzzle hobby group.
Of course I don't believe that math is just fun puzzles. But if it were, then it would deserve to die as a career, AI or not.
A lot of people went into maths because they liked not only the results but the process of research and discovery. That has been taken from them. No matter how you feel about AI, I think we should all pause and at least think about this and validate those feelings.
Look at the most upvoted comment on that thread:
-----------
I feel like the point is still being missed, and it's very similar to the way software engineers are trying to cope. The argument you are making "Well yes now this part of math we will not need to do again, but now we can do this instead" however the issue with most people just don't want to do that....
Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
Imagine a leather workman who's life passion is making insanely high quality handbags, who takes joy in knowing everything he touches will last someone a lifetime and give them joy everytime they use it. And then not gradually, but almost overnight someone comes to his door and tells him we can make bags 50 times better than you at 1/tenth the price. But don't you worry, you can make more money overseeing the factory, or selling people on how good this bag is, and explaining that to them.
I mean, ok, that just is not what I wanted to do with my life. I never wanted to be a manager, I never wanted to be a salesman, I never wanted to be a writer. A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place. I enjoyed solving problems and writing code, I don't care if people say "well thats never what programming was about it was actually about becoming a manager all along" I never wanted to be a manager, I never wanted to manage, I never wanted to be a proof reader.
> Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
No, I think it's just super cool. One of the things I hate about it is that you can't really explain what you find cool about it; others just have to see for themselves (in some sense it's like a self-induced trip to sit there and work out analysis/topology proofs in your mind's eye, visualizing little nested blobs doing their things), which of course nearly no one you will ever meet has any interest in doing. I wish more people wanted to talk math/physics with me lol.
I just want to know more. There are infinite rabbit holes. Like in uni and for years after, I wanted to know why convolution should be so important. Was I disappointed that someone else had already figured that out (that it's what you get when you form the vector space over a group and define multiplication as group multiplication) long before I was born? No way! I was stoked to finally have a satisfying answer! I wish they'd find a way to stuff that into applied analysis for engineers because it's cool and engineers should get to see cool math.
But then I went into software (partly because it was a hobby of mine anyway, and partly because it pays well), and learned a long time ago to leave any notion of artisanship or nerd crap at home. Java programmers spent forever arguing against type inference, Python/Ruby programmers think static types are a hindrance, and Go programmers spent a decade saying generics make things more complicated. Metaprogramming is generally synonymous with "too clever." It's cool that the relationship C^(A+B) = C^A C^B (or generalizations) says that the way you handle an enum type is to pattern match/provide a handler for each constructor, but I'm not going to burden my coworkers with that nonsense.
AIs are currently reducing human knowledge and cognitive capabilities, replacing it with machine capabilities instead.
It’s going to destroy both academic funding for people wanting to learn more through research and salaries for people currently doing cognitive work in corporations and an irresistible crutch for students using AI to do their work for them.
It will probably reduce most people's cognitive capabilities, but most people aren't interested in learning. If you don't want that for yourself though, it's great. You now have your own personal professor available 24/7 to answer questions about whatever topic you're learning. Take a picture of a page with your phone and ask it something you're confused about, or to check your understanding. Get immediate feedback. It's awesome.
Similarly, at work, it's never been easier to have data to make decisions with. Or to just try stuff out. Really great. Gets rid of what would otherwise be massive amounts of tedious "thinking" that drains your brain but isn't actually challenging in any way.
It's early yet to see what effect it will have on research. Experimental science is full of interesting, cognitively engaging topics as well though. Or maybe they end up like me and do boring engineering work for pay, and read cool stuff that the AI has figured out in their free time. It's not all that bad.
I think it might be a result of shock to believe it’s been taken away - you have my sympathies.
Mathematicians got a new toy. It’s up to them to pick it up, play with it, and figure out what it can and cannot do.
While I cannot guarantee it will stay this way indefinitely, there is still plenty that AI cannot do that humans still can, and asking the right series of questions remains an art of its own. There is still plenty of original work to be done.
As Arnold Schoenberg stated in the 20th century, “there is still plenty of good music to be written in C major.” The search space is vast and today human judgement is still required to really navigate it usefully. No LLM has yet written anything like Shakespeare that has superseded Shakespeare in any culturally meaningful way. Although programming is supposedly just about solved, I expect to see numerous billion-dollar startups emerge over the coming decade, rather than all of the innovation running out at the speed of tokens.
I'm not entirely sure this is fair. My belief is that mathematics exists in the intersection between art and science. I don't believe in progress for its own sake, so I'm inclined to say those interested should undertake it for the art, or to "play with puzzles." The rent-seeking argument and "weren't in it for the right reasons" is the same argument as calling musicians sellouts when they start making money. Making money doesn't make you a sellout, but it can.
Mathematics is more akin to art or a sport to many — philosophy, too. I don’t see that as a bad thing.
But there’s always a risk that someone in an adjacent domain makes a breakthrough that completely reshapes the research landscape overnight. It’s happened before AI and it will happen at some point again in years to come. Grief is understandable, but this isn’t the first time or the last time.
> If your primary purpose is SOLVING the problem, you should be ecstatic! If your primary purpose was rent-seeking so you could play with puzzles*, you'd be very upset.
I'm not a mathematician but I find this framing to be rather non-pragmatic and frankly, pointed.
In the process of Leonhard Euler's "rent-seeking" so he could "play with" bridge crossings he invented a completely new branch of mathematics that is the basis for things like Google Maps today. The process of working with these problems is just as important if not more, than just solving them.
I wonder how many math professors think they were actively working on well-known unsolved problems. Is it just a small elite club, or is it every tenured / tenure-track professor in all R1 schools?
It's completely natural to be attached to the process of your job, rather than the outcome. It's not a phenomenon restricted to mathematics. We can say it shouldn't be like that, but it is.
> Imagine waking up one morning to find that an alien technology has solved the problem you had dedicated your life to
But it could be another human that did that, and the impact would be no different.
As a software engineer this is part of my life, and always has been. I may have been working on a software product for the last 3 years, and suddenly one morning I find out that another company has released a similar product, and selling it cheaper, now the value of my work is slashed by 90%. I may even have to drop my project and find something else to work on. This is a normal part of life.
In research, there is always the same risk, that some adjacent field will completely change your field overnight due to some breakthrough.
Still, I have sympathy for the people who are grieving right now.
With the software industry, you kind of know what you’re signing up for, so you have some emotional preparation. However, this might be one of the very first truly disruptive innovations many mathematicians have ever seen in their fields in their lifetimes.
Should they have better prepared emotionally for a black swan event? I’d argue that the answer is no, but even if the answer were yes, the grief that many are experiencing is still worthy of sympathy.
I am confused why this is considered a black swan event. Does AI take the joy out of mathematics research? Yes. But universities are not laying off mathematicians just because OpenAI has released some proofs. The proofs were never the point of mathematics, it is the understanding behind the proofs, and applying that understanding to solve real world problems.
Now consider a computer science major in college who knows that he won't get a job when he graduates. Consider fresh graduates who thought they would have lucrative jobs but had to take up jobs as Uber drivers. To them AI is a black swan event. That's who I have sympathy for.
Give me an argument for not having a grim outlook given current AI trajectories paired with a political apparatus incapable of action. At least in the US.
That's literally the 7.3k Upvoted top comment and I also think Grant didn't chew this one through appropriately.
I was kinda offended at 17:10, where OpenAI paper dumping proofs "takes all the wind of [mathematicians] sails". But it's so much more than that.
He did go more into it at 30:00, where he accepts that something is lost here. Or as Terence Tao said, the "age of heroes" in mathematics is has come to an end. I think Grant's points on funding and maths having a strong future are true. But I still think the dehumanizing part wasn't properly honored. But then again, this is supposed to be positive push into the future, so dwelling on it is not something Grant wanted to do.
I don't get it. I have a research degree in physics, and if AI made major progress towards the big open questions (e.g. nature of dark matter) or managed to come up with a much cheaper way (or any way at all) to test a theory of quantum gravity, I'd be super happy. At the moment the research frontier in high energy physics looks pretty bleak in that it appears like the scale of construction and energies required are too high to reasonably achieve many more big breakthroughs in my lifetime. What makes mathematics so special that the entire field is distressed when their big open questions get resolved?
I'm sympathetic to the mathematicians and don't like what AI is doing. Every other profession that relies on knowledge or thinking should be watching the mathematics community as a portent of the storm to come. OpenAI has extensively thought about and planned their disruption and chose mathematics to start with for a reason - small community, verifiable to some extent, can be used to improve model training, not seen positively by many average people etc. The AI companies are going to come for every field one by one.
I as a non maths person am not sure what you mean. Isn't AI solving lots of problems advancing the field? I understand that that maybe demoralising, but otherwise what do you mean by "assault on mathmematics"?
Solving problems and advancing the field are two related but separate endeavors.
Nobody has solved the Riemann Hypothesis, but it has been highly fertile ground for new mathematics. Answering the question is of far less value than the question itself.
1. One view of the field treats Maths as directly solving real-world problems. Under that lens, yes, solving problems is directly advantageous for the field. Even so, it's not necessarily a good thing for the participants. Suppose the incentive structures require tackling hard, long problems, the field attracts people who enjoy that sort of thing, it's hard a-priori to tell a hard problem from an aggrandized brute-force proof search, etc. Even if directly producing proofs is the desired output for the field, a capricious machine occasionally solving 40% of the big problems the field is working on is still demoralizing. On a human level, if a society has organized around producing 100yr+ problems and bestowed on you the privilege of tackling a few of them having the last 40yrs of your work solved by a fancy calculator is never going to feel good. Sure, that means that in retrospect that was a problem we could have waited to devote human effort toward, but you couldn't possibly have known that at the time. You worked hard, made locally correct decisions, and later found out that the work was worthless. Beyond that, I haven't seen any model of "Maths 2.0" produced where that issue goes away. We still want people to devote their lives to hard problems. The machine will still advance and solve a moderate fraction of them at random, killing many of the field's life's work. What motivation do you have in that environment to pursue those challenges in the first place? Why not pursue adtech or fintech and make the world a worse place instead? Solving 40% of the problems isn't +40% throughput; it's -60% as the rest of the field leaves for greener pastures, -inf when nobody's around to construct the right problems in the future..
2. "Solving problems" isn't directly the point of most of the field. That's true both from the perspective of most problems requiring many intermediate results (solving one useful thing requires solving many less useful things) and from the perspective of building the machinery capable of solving problems being much more important than the solutions themselves (a properly presented proof leveraging clever, new techniques is infinitely more valuable than whichever thing it proved -- indeed, the Millennium Prize problems were chosen precisely because it was assumed they would create such techniques, and for the human-solved ones they did -- without new techniques, eventually the field caps out at whichever frontier of knowledge we're currently stuck at).
3. A third view of the field treats it more like art. A machine producing behind your back the painting you were envisioning, or at least a close enough simile to fool the masses, doesn't advance "art" in any meaningful sense. It's extremely demoralizing when flaky cast tools are passed off for proper forged variants (your work is better, and it's sad to see people choosing a wrench they'll later snap in half instead), and when at a creative level people are accepting mediocrity instead of something objectively better.
So there's an interesting question about what mathematics is that the AI solution space is driving a wedge into and cracking wide, where previously the cracks were visible but could be ignored.
When is a problem in mathematics "solved?"
There's an old joke in math and computer science about a huge leap of logic in a proof either being flagged as "left as an exercise for the reader" or "trivially shown." The problem being that things are only trivial if you have all the context to know why they're trivial.
We can claim a problem is solved if there is one paper explaining the solution with airtight logic that is understood by five people on the planet. And that is the kind of solution that LLMs can kick out (by basically, to hand wave a lot of details that I will admit to not fully understanding, doing a search across the whole problem domain with vastly more capacity than most human beings to do the symbolic manipulation that makes up the mechanics of mathematics). But what does that really mean? To have something "proven," but only to the comprehension of five people on the planet?
3blue1brown is making the interesting argument that perhaps mathematics practice shifts from a frontier that AI might actually be better at exploring than humans, to the process of digesting the output of that exploration and making it sensible and comprehensible to the billions of mines that could take advantage of that knowledge... If it were shaped in a way that could stick in their brains.
That's a kind of creativity that AI is not likely to be good at in the near future, because AI doesn't really "understand people."
> Imagine waking up one morning to find that an alien technology has solved the problem you had dedicated your life to
That seems like a glass is half empty attitude.
For one, the problem is solved. You should be glad. That's what you wanted...
Typically every solved problem opens more doors than it shuts.
We're pretty far from knowing it all.
It's like someone saying the field of Math died when we got calculators and computers and spreadsheets to make it easier to do calculations.
Now you can use AI to help you.
Sure, if you refuse to use it, then you're screwed. That's a you choice. Not inevitable.
The only things in life that are certain is change and death.
Not any different than some Amish person being annoyed that s/he can't contribute to the field of Math because it's too hard to do all the calculations by hand on paper...
You can spend your whole life crying that one day we'll all die, or you can enjoy the time you have.
The whole point of current AI is to replace ALL human contributions, in every field. Collaborating with humans is not a consideration, as shown by OpenAI leaving practicing mathematicians completely out of their process.
The glass is a whole lot less than half empty. The pessimistic attitude is a rational response to our environment.
The only way change this situation so that it comes out positive is to enjoy being a slave, but hey thats a you choice.
>Typically every solved problem opens more doors than it shuts.
>We're pretty far from knowing it all.
Open doors to whom? AI or mankind? We have never been farther from knowing it all. The information knowable by people will become a sliver of the total relevant information in the world.
>It's like someone saying the field of Math died when we got calculators and computers and spreadsheets to make it easier to do calculations.
In that instance, the busywork was automated and challenging work remained. What we are talking about here is the reverse. It's the automation of all of the cerebral thinking.
Imagine that all of the cerebral and beautiful aspects of math were automated first, but for some reason humans were required to specialize into number crunching instead. Now open your eyes.
>Not any different than some Amish person being annoyed that s/he can't contribute to the field of Math because it's too hard to do all the calculations by hand on paper...
The thing about amish people is that they own their own land and grow their own food and are independent within a governmental system that respects their property rights. The rest of us renters and feeders operate within industrial society-work or die.
The disposition amish people have towards technology has been ahead of the curve.
>You can spend your whole life crying that one day we'll all die, or you can enjoy the time you have.
I would also encourage my peers to enjoy what little time they have left. What we are witnessing is the end of history, and I am honored to experience it. However I get the impression your nature is to go out with a wimper.
I'm not sure that's a fair summary of the situation though. If the machines understand math but humans don't, we're going to be in a bad bad bad spot.
We need humans to help guide all this, need to learn all we can.
I agree with Sanderson that the opportunity seems larger than in the past. The challenges are quite different, but if somebody loves math, loves learning about it, like I do, I see so much opportunity.
There's going to be so many more connections to evaluate, so much work needed for unification and simplification and pedagogy, and above all there's going to be intense demand for mathematical taste.
Well that's the point, there's immense value for human involvement in these skills. More now than in the past. If you can do more with math, additional funding avenues open up.
Jane Street will be using tons of AI in math, but boy are they going to need a lot of humans to try to keep it all under control.
Agency and control, the most important. Even if LLMs could somehow assimilate all the knowledge that's not available in their training datasets that's essential to all aspects of our current economy, which they can't they don't know human desires.
How is that any different than another kind of automation?
AI will make mathematics so much more approachable, comprehensible, and applicable as more problems gets solved. If the costs is a handful of PhDs tenure track, so be it. Academics didn’t much to seem to mind when that happens to blue collar workers.
Nothing stopping anyone from studying mathematics here.
I keep hearing these “AI will make this” and “AI will become that”. Boosters are always making these claims for years now, but whenever AI becomes more powerful everything just sucks more.
I don’t buy these claims anymore, and haven‘t been for a long time. I think you [as in you boosters; not you specifically] are full of shit. I don‘t think you know what AI will become, you just dream up some scenario where everything becomes better by some magic, but it won’t. It will become worse. People loose their jobs, people loose their tenures, and instead we get just more and more slop, more and more span, energy becomes more expensive, our planet becomes more polluted, our internet becomes more polluted. Our servers become overrun by bot traffic, our gaming machines become too expensive, etc. etc.
I just want you to stop making things worse. I just want you to stop training more AI. It sucks, I hate it, and I want it gone.
AI has already made mathematics better in the sense that it has greatly advanced what we know to be true (theorems).
The only way that it hasn't made mathematics better is in the sense of human mathematicians' career prospects -- and in this respect, it is identical to other forms of automation that the world, and especially computer programmers like us, have participated in in the past without complaint.
It's "worse for humans" in exactly the same way that first the Industrial Revolution and later computer programming made things "worse for humans", but the post you're referring to only notices that it's "worse" when they are the victim.
The egos of these mathematicians is not what is important here, and they should get over themselves. The goals and values should be about advancing mathematics and, by proxy, humanity. It’s not about them.
That said, change is difficult for most. Let’s give them grace and have patience as they work through the stages of grief. Once they come to accept this new reality, let’s hope they can learn to embrace this new technology to continue the work of advancing the frontier.
> AI has destroyed a major source of "life's meaning" for many people who pursued mathematics.
I studied mathematics and don't agree with this at all, for several reasons. For one the entire point of maths is that it describes a formal system in which one can 'shut up and calculate'. Mechanizing maths goes back to Leibniz and Hilbert. Nobody should surprised that the big formalism with explicit rules you invented is the first thing to yield to automation, that's why it exists.
Secondly research, including maths for a long time has been a collaboration of people, institutions, machines and processes, even maths does not consist of Faustian heroes in caves having revelations.
And thirdly just because a machine produces a 500 page proof doesn't mean your job is done. Science produces knowledge. Knowledge is information made legible to understanding by people. So there will be endless work for humans to go over machine proofs and turn it into something we understand. Just like chess computers ultimately expanded human chess.
> So there will be endless work for humans to go over machine proofs and turn it into something we understand
I'm not convinced humans will be better at this than LLMs. Frontier models are quite good at handling even deliberately lazy/ambiguous eli5 prompts on complex topics IME.
>I'm not convinced humans will be better at this than LLMs.
they don't need to be. Any scientist is already surrounded by tools that are better than they are at anything. A scientist from 200 years ago would have the same existential shock if they see how a modern scientists works.
But that's to misunderstand what science is for, which is to expand human knowledge. And a tool by definition can only ever change how you do this, not that you do it because you understanding it is the point. When people say learning to program is now useless, what they really mean is it might not make them any money, or using the AI is faster as an instrument. But if you care about programming itself, about you understanding programming, nothing has changed, it never can. And the smartest AI in the world can always assist you, but only that.
> But that's to misunderstand what science is for, which is to expand human knowledge
I agree ideologically and aspirationally but I don't believe it's the economic reality of how and why most science is actually funded (and I think you agree based on your comment about not making any money).
> But if you care about programming itself
I'm...not so sure I do any more? At least, not any more than I care about using Java over Python, or C++ over Java, or C over C++, or ASM over C, or machine code over ASM, or an abacus over machine code.
> nothing has changed, it never can
We now have programs that can write any program 100x faster and better than even the best humans and solve the hardest math problems known to humankind that have stumped the greatest minds the planet could produce for decades. That, to me, is a change with profound implications for understanding the nature of programming.
I find myself sometimes wondering if the folks on Star Trek would consider themselves laboratory assistants to an AI, seeing as how the ship computer kind of works like an LLM: interprets voice queries into actions and takes actions, queries the database for answers, can extrapolate when asked to depending on how the writers are feeling... That kind of thing.
AI solve my problem where I have to hand code all the time. I'm happier than ever. Math's analogy is they now get to find problems instead of solving them, then get LLM's to solve them or solve them together. I've been saying this, numbers go up, and LLM makes the amount of problems to solve go up, not less.
" As a scientist, I don't want to end up as a laboratory assistant to an AI."
The idea is, that the AI is your assistant.
Apart from that, I would also say get over yourself. We all have to. Arcane computer knowledge I was proud of having, that made me feel special can now be replicated by anyone with access to a LLM.
I still know how to build things and that is what I am doing. Just faster than ever before.
If you find your source of meaning in slowing down understanding and knowledge, you were never it in for the mathematics and some questionable motives. Find the solution within.
I think math will go the way of biology. Biologists enjoy untangling the infinitely complex mechanisms of life, including the brain, and win Nobel Prizes for discoveries like "how water enters a cell," rather than "constructing the first-ever cell capable of absorbing water."
No biologist has ever complained, "Gee whiz, it's so unfortunate that we already have a brain to study. It's all so meaningless! It would be so much better if we had to construct the first-ever brain from scratch."
This is an interesting perspective and maybe the most interesting argument in the thread.
But why can't a hyper-intelegent AI also do this biology-esque math work of explaining its work to feeble humans?
It is easy for a genius to have theory of mind over an idiot but not vice-versa. So it should be easier for a genius AI to explain its work to an idiot human than for an idiot human to dissect the work of an genius AI.
Also, we're not talking about solutions that are arrived though an evolutionary/statistical process like explaining the design of an organism or the weights of an LLM. We are talking about solutions that are arrived through lingual/textual/rational processes like mathematics. So it's fundamentally a different mode of thinking.
It's not that we have "a brain to study", it's like if we had an "explaination of how a brain works" to study.
The task of breaking down these AI proofs is not translating and analyzing a fuzzy real-world system into a hard logical system (like in biology), but in translating a hard logical system into a simpler hard-logical system we can understand.
I actually remember that in an old interview (that I can't find sorry) Grant Sanderson said he moved in to YouTube because he thought it was a more promising career than being mathematician, it's interesting to see his opinion change.
Hmm, that seems like a pretty cynical point to make. He still deeply is in the field of mathematics, as a math educator. He even makes this exact point in this video, that communicating math is still a hard and respectable part of the profession.
As a math educator doing what you love you requires an audience.
Its kind of in Grant's incentives to push the interest for mathematics, because without an audience he won't be able to keep doing what he loves.
Like, my old uni has a history department, and had an Egyptian history teacher. This was at some point deemed a pointless use of resources because there was no role in society except for teacher of the same subject after that, and the classes shrunk, and she ended up getting offered a role in admin. She was not happy in that role.
I remember a post in... Reddit I think it was? where I commented on an early video discussion that he should teach online full time, because that kind of intuitive education was sorely needed. He actually answered the comment, along the lines of "that would be cool but I already have my hands full in $UNIVERSITY".
I think it was relatively soon after that interaction that he started doing youtube full time. I've always wanted to think I made a teeny tiny contribution to move the needle there :)
Yeah. All due respect to Grant Sanderson, he is both great scientist and great entrepreneur, but getting an entry-career advice from a multi-millionaire is probably not quite the best idea out of all ideas in a popular discourse. Especially if the field in question was famous for producing posts discouraging people from going all-in in it, for many many years even before AI craze.
I think a lot of "mathematicians" are saddened by the sudden realization they are not even interested in it and were only in it for status and prestige. A lot of them are such pretentious tools that they willingly wasted their lives doing the absurd PhD rituals. Academia is dead.
What about the people who are in it to think deeply about mathematics questions? It's a lot harder to feel like that's worth doing when there's a black box with a crank that takes money in and spits out mathematics answers.
Like calling Lee Sedol a pretentious tool for retiring in the face of AlphaGo. If you really do mathematics for the enjoyment of doing mathematics, following a roughly unbroken line of tradition for at least a couple hundred years, an alien computer mind showing up and smashing everything would perhaps be upsetting, don't you think?
I have been feeling this way about software. Don't get me wrong, there are some things I am very interested in and would work on for recreation (macros!), but a lot of it I'm less interested in.
Frankly, despite the obvious financial worries, it's been a little freeing. I can go do something else (because, uh, I may have to).
First, "cognitive labor" is a form of labor - it's different vs. creative work, even though both use your mind. If your math theorem can be written up in partnership with an LLM, wow! You can be done with that, and go do other great work. Cognitive labor is a form of labor. Let's talk about physical labor and leverage to understand how removing labor translates to time. On your farm you buy a tractor to replace your backhoe. If it is a hobby farm you get in the tractor and you're done super fast. Or, you can take that tractor, buy a bigger farm, and spend the same amount of time you'd have spent backhoeing, but in a far more leveraged way. You can trade removed labor for time in a way that suits you.
Second; the joyful moments we get from finding generalizable abstractions and nice solutions are an adaptation. Humans can climb infinitely high conceptual hierarchies - we'll never stop climbing, using the previous ones as tools to find the next. As we do, we gain joy with each discovery because. We get so much done with brains that run on 20 watts - are we tuned to receive a neurochemical reward for finding cognitive efficiency? If AI means more concepts are discovered the tower gets taller - and we find those joyful moments more often. If there are infinite moments to be found, why not go as fast as possible!
Third; everyone else is doing it, it's a baseline skill. Knowing how to work without AI is like knowing how to ride a horse. Useful and fun! Bedsides - only 150ish years ago horses were the only viable transport. Cars were new; toys for the rich. But cars got so good so fast that we eventually reconfigured whole cities. Your homework is to consider why and how horses got disrupted.
New divisions are emerging in the lump of roles humans had at work. AI takes away roles from your job and lets us do more with less. That's identical to every mechanization before it. It's killing some roles that make up your work, even as it creates new ones.
There's so much to be excited about. Fear is a rational response to change. But so is hope :)
> If your math theorem can be written up in partnership with an LLM, wow! You can be done with that, and go do other great work.
If your painting can be painted in partnership with an LLM, wow!
If your essay can be written in partnership with an LLM, wow!
If your painting portfolio website can be written in partnership with an LLM, wow!
If your museum show can be designed in partnership with an LLM, wow!
If the placards next to each of your paintings can be written in partnership with an LLM, wow!
If the car that takes me to the gallery can be designed and driven in partnership with an LLM, wow!
If the newspaper or novel that you read on the way to the gallery can be written in partnership with an LLM, wow!
If an LLM can give tours at the gallery and answer questions asked by visitors, wow!
If an LLM can write the music that I listen to on my way out of the gallery, wow!
If an LLM can synthetically perform the music, too, wow!
> If AI means more concepts are discovered the tower gets taller - and we find those joyful moments more often. If there are infinite moments to be found, why not go as fast as possible!
I don't understand how a person can say this with a straight face. There has been so much discussion of this, and so many reasons have been given, that one can only assume that, if you're asking the question and you have thought about the issue and read what people have said, you're not only asking rhetorically but have some personal reason for insisting on a frankly pretty frustrating, borderline insensitive insistence on being positive. I'm not trying to be snotty or rude. I just want to say that to me there is something uncanny about your comment, in its total blindness to any of the reasons someone might not only disagree with you but grieve the death of, say, their academic discipline in its current form -- and in its weirdly breezy lack of empathy.
Are you suggesting that if an AI could do all of those things to your satisfaction you would not be extremely impressed.
I do have empathy for people who see the world changing and are forced to adjust. That can be uncomfortable, but it is something that is inevitable with the changing world. It has always been this way, There is very little need to make swords these days, and as anything becomes superseded there are people that are attached to the old things and there are people dependent on the old things.
I think it entirely possible to have sympathy for their position while disagreeing that the solution is to prevent change.
I don't see this as a breezy lack of empathy. I see this as a hand reaching out and saying 'Hey, you can come this way and things aren't so bad after all'
I think it would be much more of a change now, if we ban LLMs entirely and force everyone to do everything without any form of chatbot to help them. I would sympathize with the people who can’t handle this change, but it’s gonna happen, I think they should get with the times and adapt to it. I think it is wrong of you to try and prevent this change.
Actually I think we need to go further, we need to make an example out of the people who spent a trillion dollars building a product that is universally hated to try and make a buck. They need to be completely ruined financially, now that would be a real challenge, I sympathize with those adversely affected but it needs to happen if society must progress to a better place where humans flourish more.
> AI takes away work and lets us do more with less - just like every mechanization that came before!
No, it's not the same as mechanization. The fundamental difference, and why I find it illogical to argue either for "AI will open up tons of new work avenues" or "AI will kill all jobs" is that it all hinges on whether AI "caps out" at an intelligence level below humans (in at least some domains/capabilities), or if it is able to surpass human intelligence at all levels.
If the former is true, then yes, there will be a lot for humans to do. If the latter is true, then no, there will be no reasonable cognitive role for humans to play (beyond perhaps for some legal, "nostalgic" reasons or what not). So whether one decides to be optimistic or pessimistic really depends on if you think AI will stay at a level below humans. I really don't know, so I'm not "taking sides" in this debate.
On one hand it is hard to fathom not being the most intelligent thing around.
On the other hand, if we are going to survive as a species for a long time it probably depends on us learning how to not be the most intelligent thing around.
Even if it leads to our demise, I don’t think willfully holding ourselves back is the way forward
> ...hinges on whether AI "caps out" at an intelligence level below humans (in at least some domains/capabilities), or if it is able to surpass human intelligence at all levels.
I agree with you, just wondering your thought on how we will know the latter has come true? As I understand it, you're describing ASI, not AGI. The way I personally define AGI, we are already there.
I think one form of cognitive labor will remain: What do we actually want to do/build. And this is simply because AI does not know our internal world. Maybe in a few years with some kind of BCI that is extremely good. But I don't see it happening at least for a few years.
> A good precedent is mechanized agriculture. When machines effectively replaced most humans in agriculture, unemployment did not rise to 90%.
I don't consider this a good precedent to the AI situation at all.
When this happened, humans went off and started doing what we now consider "knowledge work" (well, after a brief stint in factory work, where they also got displaced by automation). They escaped massive unemployment by being smarter than the tractors and mechanical looms. But how do they escape AI job loss when AI becomes smarter than the average human? or smarter than the smartest human?
In prior displacements humans moved up the stack. There is no longer room for them at higher levels of the stack if AI beats them at cognitive labor.
And this is why we must ensure that the AIs get aligned towards humanity and crucially that they don't get aligned towards capital, which seems to be the current trajectory.
There's a better chance that a humanity-aligned AI would make sure that humans have something to do and keep us alive versus a capital-aligned one. At the same time, if AI would be the deathblow to capitalism, that'd be very, _very_ ironic.
In the essay Hackers and Painters it was mentioned that there is a project approach to learning and an academic one. The idea of pet projects is killed by language models, because what you did on weekends, a language model now does in half an hour. So you can try the other approach: maybe you should have more general knowledge right away, best practices, so more of an academic approach. In the academic approach you learn from the best reference examples, develop taste, and only then recognize what is good or bad and build your own. But here too you can see that LLMs iterate much faster, while you have to collect patterns for years, and you will also always be in the role of the one who is behind.
> The idea of pet projects is killed by language models
Only if the goal of a pet project was the end result. In my experience pet project is all about learning new things and exploring the unknowns. LLM finishing it in half and hour does not achieve any of that. Although it can be a good assistant.
Before, I would write an emulator of an old console. On weekends I would debug why the game shows garbage instead of a picture, compare opcodes with the documentation and learn from my own mistakes. And the emulator itself would be valuable as an artifact, because it holds the experience I accumulated.
Now the same thing can be done much faster. Learning from mistakes disappears, only high-level templates remain which looks similar to the academic approach.
On the other hand, you can set up an LLM so that everything goes gradually and you learn like you used to. But that's more like what I would call pet archaeology or something... Learning the tools doesn't give as much benefit anymore, it's more like a reconstruction of past events.
Like all isomorphic plagiarism, its proponents do not see how their input and markup are also obfuscated and resold to other users.
Only the IBM granite model used out-of-copyright data to build its LLM. It is the singular exception in a sea of BS arguments for pro-piracy.
While LLM do have some utility especially in search, philosophically it is wrong to scrape $9T in FOSS to be resold to naive users as tokens. The wonks think people will be compliant with being a hapless data entry caste, and are simply high on their own rhetoric. =3
I haven’t watched the video, but likely it hasn’t answered a question: why math? Why not physics, neuroscience, philosophy or history? People claim math is both philosophical and art, but is that a sufficiently good reason to pursue math as opposed to other careers?
A lot of arguments seem to try to cling to the “old” way of doing math: staring at the blackboard for hours, wrestling with papers and papers of equations, and do forth. Well, chess players went through a similar transition period: carrying books of openings and such, to chess database, to chess engine and now AI. And at no point I hear chess players complaining that we have to study chess the old way.
Ai will yield a higher demand for mathematicians, we need more people to understand the math being solved. We also need more people inventing math problems.
People who want to solve problems themselves should go on to invent them without posting them on the internet until they're solved.
Reflecting on that a year later is interesting. Agents have become REALLY good since then, and I consider the "writing code" side of my profession to be largely annihilated. Some days that's really hard to accept.
But I think Grant's conclusion about math still largely echoes what I wrote about software: don't underestimate the social aspect of these activities, and if anything AI has made the social side more important. I deliberately avoided declaring, "now is the best time to learn to write code". I suspected that skill might be going out the window. But learning systems thinking and the social skills needed to connect people's dreams to reality continues to be an important art, an art I still have the privilege to practice every day.
And if we do reach the "anything you can do I can do better" stage, then, as Grant said, that's a hard to imagine world, and one where "it can write really good code" might be the least of our problems.
At this point I'm ready to call it... LLMs aren't going to ruin my job. They're amazing, they're useful... and the problem remains that to a first approximation human beings are uninterested in spending all day talking to a computer, whether through a classic IDE or through an LLM. Specifying a problem enough for an LLM to solve it, even if we stipulate one that does it perfectly, is already more than most people want to do.
You also aren't going to get an accountant running 4 simultaneous streams of AI-driven development and working through an AWS issue when something goes wrong.
I hope you are right, but I think there will be a lot of reshuffling nevertheless if only because the shape of the work has changed so much. A lot of people who hated developing software will suddenly find a passion for it, a lot of people who were good will find they can't stand this new world.
The problem is you're focused on 1st order effects. I presume you work at some company that sells a product or provides a service - what happens if the demand for that evaporates because the clients can do it themselves or the market has been flooded by much cheaper alternatives created using AI? Or people who bought the product can't do it as they lost their jobs to automation?
Second, if "all software vendors in all spaces get wiped out" was going to happen I think we'd be seeing more of it already. Yes, there is support for some software vendors possibly getting wiped out... but, then again, you can't look at a bad vibe coded implementation of "the entire Adobe suite" that was rather overblown in the press coverage and forget that Adobe also has AIs. Instead what I'm seeing at my own workplace as we ponder the question of "should we replace this service we buy with some local vibe coding" is still remaining but we don't want to support that. Can we replace Confluence with vibe coding? Yes, but that was true five years ago too and we didn't want to do it then, either. We still don't want to do it. HN commenters have always overestimated the desire everyone in the world has to become programmers and take responsibility for everything.
One wonders what percentage of those who are certain that vibe coding is going to nuke all software vendors can't even be arsed to self-host a Jellyfin or VaultWarden install... which is way easier than vibe coding the whole of those things from scratch, and we're talking about people who are already programmers. Physician, heal thyself.
I agree. I think the days of the developer who hated talking to anyone but is still very valuable are over.
I think social skills are much more important today because one person can do so much more but this person needs to talk to many others to know what to build.
And this is why I am likely to leave software. I actually really like people, but I am autistic and not especially good at talking to them, and it's quite drianing to do so.
I will miss coding, but I had a good run. Time to learn a trade. I don't begrudge this fate.
I'm trying to think of an exception but I find it hard to disagree. Even if you know exactly what to build, it's pretty hard to get any adoption without being aggressively social. Find a good extroverted friend, maybe?
No… the person who's going to do well is the one who doesn't have to ask what to build. The one who has to ask is no better than an AI, except they start out wanting to ask, rather than starting out with no interest whatsoever until they're prompted to have one.
When everything you ask for is instant and valueless, even asking becomes meaningless, and everyone is waiting to see something they'd not thought of.
Then, a thousand thousand copies, immediately… but also, watching that person like a hawk to see if they can do it again. That's the future. A lot of people will just plain become unable to think or intend anything on their own, or even want anything.
3blue1brown has the absolute most educational and entertaining videos. Always fascinated by his animations which are custom programmed by him. I also appreciate the diversity of topics covered from deep math to software to science.
This is the same naivete that I saw in coding some time ago before most people finally accepted there is no going back and the times of writing code by hand are gone.
And the guy is not a mathematician primarily - he's a Youtube creator and entrepreneur. I liked a lot of his videos but now I usually just ask the LLM for detailed explanation and I can probe it as much as I want if something is not clear enough.
Education will also take a huge hit, you can't really beat an almost free supergenius that has all the time in the world to explain something to you in as much detail as you wish.
It is not, and for the same reason it's not over for mathematics. For anyone doing anything truly novel, and yes there are still software engineers out there doing that, it's still inept.
It's de jour to leverage formal verification as LLMs are quite good at looping it, but that's still a tool we had to invent to solve problems. It'll be truly over when we're being outpaced in the realm of invention but I have seen absolutely nothing to suggest that has meaningfully occurred at all. Coding by hand is not gone, there's just less of a reason to do so now.
I’m a cheerleader for the Khanmigo AI tutor effort. But, apparently so far they are discovering that the hard part is getting the kids motivated to actually ask the AI any questions.
3Blue1Brown does an amazing job of making math interesting to learn in itself. As opposed to the hundreds of millions of kids told “You just have to learn it or you’ll be dumb. Keep up or you’ll fall behind forever. Go!”
The vid calls out explicitly that math education is a primarily a motivation problem and I agree. One way or another, we need a lot more focus on that.
I can beat this “supergenius” - I hire a professor that knows exactly how to teach and what to teach. This professor isn’t rolling the dice every time I ask them a question. Boom.
There's never been a better time to be a professional mathematician, perhaps. Just like there's never been a better time to be a senior software engineer.
An 18 year old entering university today will retire somewhere in the 2070s. Is mathematics, or software engineering, a promising career path for the next 50 years? No, it's most certainly not, and anyone suggesting otherwise is delusional. I don't know what would be a good career path, but most certainly avoid anything that AI is having the most success at in 2026.
Yeah, there isn't anything wrong with encouraging people to get into mathematics
But recommending it as a career, might be delusional, maybe harmful? (Although people say that about artists too)
Too early to tell, but IMO unlikely. Let's see what his take will be once an AI can propose a topic, write the script, animate, and narrate a good educational math video.
He won't care because he has established position and is set. It will be just like everybody else - if the individual is at the top of the food chain then he/she is all over it how you are using it wrong and how you should use it (don't forget to follow and subscribe).
Yep, that's what I see in the CS field -- people at the top are advocating AI and don't understand why the hell the others are hesitant. I meant the top engineers, not the management. I look up to them because of their skills, but that doesn't mean I need to agree with everything they said.
But you already have Claude-directed videos that utilize OP's manim project (which he uses himself to do 3b1b) that anyone else can create. Grant open-sourced manim and now anyone can point a model at it to create their own 3b1b-like videos. They're popping up all over the place as Opus 5.5 demo videos just in the last few weeks. So... AGI?
I tried watching 3b1b over the years, really wanted to enjoy it. But I never found the way he presents things intuitive and never got a palpable intuition that helped me with math classes or work.
I saw some clearly AI slop made videos and got much better understanding of topics, since they don't do foreshadowing for an awe-inspiring connection that we'd admire together after 15 min videos, the clankers just get to the point. Not claiming those videos are too useful either, but I did however see accelerated learning gains from asking LLMs to explain (and do Bret Victor-style small interactive demos) math and algos, something I have never experienced from any of the educational STEM Youtube channels.
Even if you find them intuitive, they produce no learning gains for anyone. Take a lin alg test, watch the 'Essence of lin alg' videos, take comparable test again. I guarantee you won't see any change even if you 'understood matrices better'. They are pure mathporn.
No learning gains? I teach linear algebra. I can assure you that students who watch and study the "Essence of linear algebra" videos (which I recommend on the syllabus) do better on my tests that those who don't, because they learn stuff from them.
It's much more likely that the students who take the time to watch supplementary materials are the ones who'd do better regardless of the quality of the given material. If you have access to fresh learners, I'd say it's a good opportunity to test how good those series are.
I'm not sure anything I say can convince you, as your mind seems to be made up already, but my experience has been that those videos help my students understand the concepts of linear algebra, comparing the mastery level now vs. before the series was published on YouTube. Especially when it comes to getting a feeling for what a linear transformation is, and how the properties of matrices echo the properties of the transformation they represent.
As for "fresh learners", I can provide my own son, who watched the series before taking his first linear algebra class, and says that it helped him a lot.
This is not my experience. Having an intuitive grasp of e.g. the graphical interpretation of the determinant instantly lets you figure out most of the key determinant properties without having to memorize them. That's the primary thing you get from intuition imo, having a sense of what must be true without having to memorize or prove it.
I'm actually quite optimistic, was pointing out that, at least to to me, AI slop already produces better results than big educational content creators. For something concrete, even if not classic math, I credit direct LLM interaction highly for accelerating my understanding of CPU design and compiler tech.
fwiw the fact that brains work fundamentally differently was my big penny dropping realization after digging into what LLMs are doing. Everything (I assert) a brain does (the function between inputs and outputs) is due to training data. There is no "instinct" and there is no "ROM-driven way to think" in any brain. It's training data all the way down. As a consequence different brains do indeed think in fundamentally different ways.
I think a lot of these reactions by mathematicians are more akin to group theory than anything else. Reality is that things will naturally sort themselves out and there will be some role mathematicians play in all of it (most likely). To me it seems the timeline that some skill essentially gets retired such that if you want to keep doing it is more like "historical re-enactment" is getting quite short. Things like manually coding something is going to be a hobby. Some aspects of math are going to be a hobby, and professional math will be all about pushing up against the edge of what we can do mathematically with AI.
All these AI bros make me sick to my stomach. If you had a robot musician play better than you, would you then go tell a musician that this is the greatest time to be in music, all of you can now manage your army of robots, aren’t you excited, think of the massive quantities of music that can be played now, stop gatekeeping music from those who never bothered learning learning an instrument??
It’s all so ridiculous. The AI boosters tactic against this is to attack your character, claiming you never liked maths, you are status driven etc etc, when the truth is they never liked doing maths, they just liked the fruits of it. You actually like doing maths, which is why you hate AI. It literally is the WORST TIME to join institutional maths if you like doing maths. Get a job in finance, management and pursue maths as a hobby instead.
There is a solution to all of this, make it politically unviable to devalue human labour, which is what AI is all about, some simple political solutions that come to mind:
1. It is illegal to monetize models trained on public data (force them to be released as open weight).
2. A royalty payment when a model copies an art style, IP or ideas that it mined from human knowledge.
3. Any IP that a model trained on public data creates is de facto invalid.
If you hate what AI has done to your field, I recommend focusing your time on political solutions, just preventing construction of environmentally bad data centers is not enough and frankly the bare minimum. Move the conversation further. Prevent AI companies from profiting of the commons of human knowledge spread freely on the internet. Maybe even go as far as to ban usage of AI in certain cases, everything should be on the table, the public already hates AI, it just needs to be fanned and directed well. The worst thing you can do, is to try to gaslight yourself into believing AI has apparently made your life great.
> The worst thing you can do, is to try to gaslight yourself into believing AI has apparently made your life great.
It is make like better. You're just invested in ripping out others' tools for your own satisfaction.
> Maybe even go as far as to ban usage of AI in certain cases, everything should be on the table, the public already hates AI, it just needs to be fanned and directed well.
The difference between this & the backdrop of Dune is near 0, with its issues clearly outlined in the book: You want the system that existed in the 2010s to remain as-is & ossified for your personal enjoyment.
I suspect people who are deciding what to study will do so on the basis of a multifactor view of what interests them, how they predict their career will be after finishing said study etc.
There ought to be people watching his channel who wonder whether given all these AI advances math is even worth studying now.
Problem solving, critical thought, logic, creativity are always going to be valuable.
In a way ai is turning programming more into maths - you write a natural language description of the problem - a proof / program - and then translating that into machine code is a lot of work / abstraction. For example look how much it takes to turn relatively simple mathematical statements into lean. That I guess is going to be the future.
I would encourage everyone to learn the fundamentals still because you will need discretion and to be able to think at a more abstract level.
However its funny that its only NOW dehumanising/demoralising now when its white people losing jobs to the capitalist machine in the imperial core, and not the slave silicon miners making gpus for gamers.
In other news, there's never been a better time to be a software developer. Come to think of it, there's also never been a better time to invest in learning copy-editing and proof-reading as a side hustle. It's a Brave New World. Everything is fine, the demand just got expanded, the pie got bigger, nothing more. New doors will be opened, nothing has changed; in fact, everything improved. Stochastic parrots are no match for our carbon-based g.
I doubt demand expanded much. I mean there is just that many games/whatever apps that the whole humanity needs. Maybe ti will go up a bit, like 50%, but getting 10x (or very easily 1000x if we just vibe code them) in supply doesn't change that.
I mean if you read some history it’s not the first time complete workforces have been replaced. It doesn’t mean the same jobs stay, but usually there will be something to do.
> I feel like the point is still being missed, and it's very similar to the way software engineers are trying to cope. The argument you are making "Well yes now this part of math we will not need to do again, but now we can do this instead" however the issue with most people just don't want to do that....
> Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
> Imagine a leather workman who's life passion is making insanely high quality handbags, who takes joy in knowing everything he touches will last someone a lifetime and give them joy everytime they use it. And then not gradually, but almost overnight someone comes to his door and tells him we can make bags 50 times better than you at 1/tenth the price. But don't you worry, you can make more money overseeing the factory, or selling people on how good this bag is, and explaining that to them.
> I mean, ok, that just is not what I wanted to do with my life. I never wanted to be a manager, I never wanted to be a salesman, I never wanted to be a writer. A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place. I enjoyed solving problems and writing code, I don't care if people say "well thats never what programming was about it was actually about becoming a manager all along" I never wanted to be a manager, I never wanted to manage, I never wanted to be a proof reader.
> > But don't you worry, you can make more money overseeing the factory, or selling people on how good this bag is, and explaining that to them.
...Or you can keep working on your handbags & refine your styles & qualities, using your expertise & experience as value adds.
The existence of the factory did not wipe out the boutique craftsman.
> > A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place.
A craft wasn't ripped away from you: The process still exists as-is in its prior form, like the woodcarvers of yesteryear. Nothing that you desire (the process/journey) has been lost. It still exists.
The only step required to restore it is to ignore the contributions of others that use it. And your desire to do so will be valid & consistent.
But similarly as to how you want to be validated on your feelings of 'the craft being ripped from you', you don't get to impose that belief onto others to rip their use of LLMs away from them if they want to do so, lest you want to invalidate their feelings as a consequence.
I'm sympathetic to mathematicians but this does not paint them in a good light.
If your primary purpose is SOLVING the problem, you should be ecstatic! If your primary purpose was rent-seeking so you could play with puzzles*, you'd be very upset.
* I find this characterization overly harsh, but if you're mad about your problem being solved, maybe you weren't in it for the right reasons
Let's just say that The math problem that got solved, I was working on it for many years but some company people used my knowledge my prompts and "solved" it without giving me any credits or money. Firstly they plagiarised the books and research papers and then they plagiarised the prompts by the mathematicians. Yes AI can make art and has caused many artists finding work difficult but AI art is always souless and worthless, same thing will be for math it will become souless and worthless because when humans who are experts in their fields invest their ingenuity then art becomes alive but if ordinary people like me will just prompt into the machine then souless things will come out that will be very worthless and disposable.
Understand that there’s more than one way to prove something, that there’s an art to making something understandable, and that humans tend to take the most understandable paths (to humans.)
Models often don’t do that. But in solving, or claiming to solve, important problems, they nevertheless remove a lot of the excitement and incentive towards working towards a solution humans would naturally find. Plus, a lot of these problems really don’t have any critical applications at the moment. They’re done for the love of the game.
Does that bother you? That your tax dollars pay people who do math out of curiosity?
That said, I think what has mathematicians… upset is probably two things:
1. These are hard problems. Hard enough that solving one could take decades of work. And there’s tons of collaboration involved. Pivoting to another - and making progress - isn’t exactly something you wake up tomorrow and start doing.
2. I think motivations matter to some. And the AI companies doing this aren’t doing it for the betterment of math or even society. They are in an arms race to prove their product is superior and any careers that are damaged collaterally be dammed.
This is not quite like that but the feeling I get from it is much the same. Mathematicians are first and foremost busy with understanding math, not with 'solving' math though they are solving individual problems within the domain of math. The journey towards that understanding requires specialization and often lots of studying.
To quote Douglas Adams: "If 'metal nose' here is going to give you God's phone number then the philosophical question of whether there is a God becomes meaningless."
It is the journey and the questions that matter as much or more than the answer does.
And with math being a branch of natural philosophy I can see why they would be a tad upset at this shortcut because it strips the collective efforts of a large number of people of their prestige and feeling of time well spent. Imagine your life's work reduced to a short string of bits, and worse, that short string of bits was created by a machine that effectively is still a toddler.
Selfishly, as someone who enjoys programming, I feel the same way about the journey. But let's face it: for everyone else, the outcome is what actually matters. Mathematicians argue that their journey may lead to novel insights, but are those insights really valuable? Are they going to help the LLMs solve more problems? And are we sure that the LLMs can't deliver those same insights?
I don't know if you have kids or not but I have two kids in high school and keeping them motivated through the AI revolution is a serious challenge and some of their classmates have already all but given up. The next generation down the line is going to grow up with the same kind of attitude towards thinking that you might have towards the skill of map reading. And I think we'll all be poorer because of that, not richer.
Personally, I enjoy the process of solving problems. I do not enjoy wrangling unpredictable AI agents.
I mean the only thing that matters is the answer right?
In fact you should be estatic that in a paralell universe all math problems have been solved, so there's no reason to pursue math at all (we did it reddit!).
When your job is automated and you're living in the streets, just remember that you should be estatic that the job is finally being done more efficiently by a robot. Like, we did it. We finally did the job right. The job was never about wealth distribution, self actualization, dignity or any of that crap it was always about getting some stupid task accomplished for an industrial system that exists for... what exactly? What is the end goal of all of this? Who does the system serve in an economy of no consumers? What is the point of solving niche mathematical problems if no living person can comprehend the solution?
There are still a whole lot of people, the vast majority of people actually, who's job involves something completely unglamorous and practical like unclogging your sewers.
To these people, it sounds like a cruel joke that people get paid 3x their salary, and after AI can do their job we learn that apparently the only purpose of their was their own self-actualization.
I don't actually believe that about math, but that's what a lot of people in this thread sound like.
I know, I have that job! And I enjoy it. But the robots are coming for me too.
Why should I be ecstatic that someone solved a problem using Hilbert Calculus when I can only understand Sequent Calculus? [0]
[0] This is a joke. No 'real' mathematicians do systematic proofs. What gets posted in math journals is the equivalent of architecture diagrams.
It's like asking if what someone wrote a beautiful poem but it's in japanese. Maybe hearing about it motivates me to learn japanese, or maybe it doesn't. But as a non-speaker it makes little impression on me.
I think there is a little too much pessimism of the "math is dead" sort. As long as there is a need for humans to think there will be value in doing math.
[1] https://radiolab.org/podcast/math-vs-machine
Mathematicians are saying the current papers are pretty inscrutable and use terminology unfamiliar in the math sub fields in which the models are generating proofs.
Mathematicians usually care nothing about application of their work. Working on interesting problems is their only motivation. Practical applications are almost always happy accidents.
This goes back to the hope that robots would do the laundry and the dishes and the cleaning up so we could write and play music, create art, and solve mathematical problems.
Instead the AIs are doing all of that leaving humans with only the dishes and the laundry and the cleaning up.
Of course I don't believe that math is just fun puzzles. But if it were, then it would deserve to die as a career, AI or not.
Those people will also be pissed that people get paid to make music or art or literature or poetry and all such frivolous things.
Look at the most upvoted comment on that thread:
-----------
I feel like the point is still being missed, and it's very similar to the way software engineers are trying to cope. The argument you are making "Well yes now this part of math we will not need to do again, but now we can do this instead" however the issue with most people just don't want to do that....
Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
Imagine a leather workman who's life passion is making insanely high quality handbags, who takes joy in knowing everything he touches will last someone a lifetime and give them joy everytime they use it. And then not gradually, but almost overnight someone comes to his door and tells him we can make bags 50 times better than you at 1/tenth the price. But don't you worry, you can make more money overseeing the factory, or selling people on how good this bag is, and explaining that to them.
I mean, ok, that just is not what I wanted to do with my life. I never wanted to be a manager, I never wanted to be a salesman, I never wanted to be a writer. A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place. I enjoyed solving problems and writing code, I don't care if people say "well thats never what programming was about it was actually about becoming a manager all along" I never wanted to be a manager, I never wanted to manage, I never wanted to be a proof reader.
I just hate this existence.
No, I think it's just super cool. One of the things I hate about it is that you can't really explain what you find cool about it; others just have to see for themselves (in some sense it's like a self-induced trip to sit there and work out analysis/topology proofs in your mind's eye, visualizing little nested blobs doing their things), which of course nearly no one you will ever meet has any interest in doing. I wish more people wanted to talk math/physics with me lol.
I just want to know more. There are infinite rabbit holes. Like in uni and for years after, I wanted to know why convolution should be so important. Was I disappointed that someone else had already figured that out (that it's what you get when you form the vector space over a group and define multiplication as group multiplication) long before I was born? No way! I was stoked to finally have a satisfying answer! I wish they'd find a way to stuff that into applied analysis for engineers because it's cool and engineers should get to see cool math.
But then I went into software (partly because it was a hobby of mine anyway, and partly because it pays well), and learned a long time ago to leave any notion of artisanship or nerd crap at home. Java programmers spent forever arguing against type inference, Python/Ruby programmers think static types are a hindrance, and Go programmers spent a decade saying generics make things more complicated. Metaprogramming is generally synonymous with "too clever." It's cool that the relationship C^(A+B) = C^A C^B (or generalizations) says that the way you handle an enum type is to pattern match/provide a handler for each constructor, but I'm not going to burden my coworkers with that nonsense.
It’s going to destroy both academic funding for people wanting to learn more through research and salaries for people currently doing cognitive work in corporations and an irresistible crutch for students using AI to do their work for them.
Similarly, at work, it's never been easier to have data to make decisions with. Or to just try stuff out. Really great. Gets rid of what would otherwise be massive amounts of tedious "thinking" that drains your brain but isn't actually challenging in any way.
It's early yet to see what effect it will have on research. Experimental science is full of interesting, cognitively engaging topics as well though. Or maybe they end up like me and do boring engineering work for pay, and read cool stuff that the AI has figured out in their free time. It's not all that bad.
But if the AIs replace all the jobs?
Mathematicians got a new toy. It’s up to them to pick it up, play with it, and figure out what it can and cannot do.
While I cannot guarantee it will stay this way indefinitely, there is still plenty that AI cannot do that humans still can, and asking the right series of questions remains an art of its own. There is still plenty of original work to be done.
As Arnold Schoenberg stated in the 20th century, “there is still plenty of good music to be written in C major.” The search space is vast and today human judgement is still required to really navigate it usefully. No LLM has yet written anything like Shakespeare that has superseded Shakespeare in any culturally meaningful way. Although programming is supposedly just about solved, I expect to see numerous billion-dollar startups emerge over the coming decade, rather than all of the innovation running out at the speed of tokens.
But there’s always a risk that someone in an adjacent domain makes a breakthrough that completely reshapes the research landscape overnight. It’s happened before AI and it will happen at some point again in years to come. Grief is understandable, but this isn’t the first time or the last time.
I'm not a mathematician but I find this framing to be rather non-pragmatic and frankly, pointed.
In the process of Leonhard Euler's "rent-seeking" so he could "play with" bridge crossings he invented a completely new branch of mathematics that is the basis for things like Google Maps today. The process of working with these problems is just as important if not more, than just solving them.
There’s something here about the journey not just the destination.
Press a button and problem solved is not too fun
But it could be another human that did that, and the impact would be no different.
As a software engineer this is part of my life, and always has been. I may have been working on a software product for the last 3 years, and suddenly one morning I find out that another company has released a similar product, and selling it cheaper, now the value of my work is slashed by 90%. I may even have to drop my project and find something else to work on. This is a normal part of life.
Still, I have sympathy for the people who are grieving right now.
With the software industry, you kind of know what you’re signing up for, so you have some emotional preparation. However, this might be one of the very first truly disruptive innovations many mathematicians have ever seen in their fields in their lifetimes.
Should they have better prepared emotionally for a black swan event? I’d argue that the answer is no, but even if the answer were yes, the grief that many are experiencing is still worthy of sympathy.
Now consider a computer science major in college who knows that he won't get a job when he graduates. Consider fresh graduates who thought they would have lucrative jobs but had to take up jobs as Uber drivers. To them AI is a black swan event. That's who I have sympathy for.
For example, the original black swans who were found by the Dutch mariners neither attacked, injured, nor robbed those mariners.
That’s the nature of exponential improvement, which humans are incapable of.
Oh, nvm you made it clear 8m later: https://news.ycombinator.com/item?id=50147638
He did go more into it at 30:00, where he accepts that something is lost here. Or as Terence Tao said, the "age of heroes" in mathematics is has come to an end. I think Grant's points on funding and maths having a strong future are true. But I still think the dehumanizing part wasn't properly honored. But then again, this is supposed to be positive push into the future, so dwelling on it is not something Grant wanted to do.
Math has practical applications that hopefully will improve lives.
Nobody has solved the Riemann Hypothesis, but it has been highly fertile ground for new mathematics. Answering the question is of far less value than the question itself.
1. One view of the field treats Maths as directly solving real-world problems. Under that lens, yes, solving problems is directly advantageous for the field. Even so, it's not necessarily a good thing for the participants. Suppose the incentive structures require tackling hard, long problems, the field attracts people who enjoy that sort of thing, it's hard a-priori to tell a hard problem from an aggrandized brute-force proof search, etc. Even if directly producing proofs is the desired output for the field, a capricious machine occasionally solving 40% of the big problems the field is working on is still demoralizing. On a human level, if a society has organized around producing 100yr+ problems and bestowed on you the privilege of tackling a few of them having the last 40yrs of your work solved by a fancy calculator is never going to feel good. Sure, that means that in retrospect that was a problem we could have waited to devote human effort toward, but you couldn't possibly have known that at the time. You worked hard, made locally correct decisions, and later found out that the work was worthless. Beyond that, I haven't seen any model of "Maths 2.0" produced where that issue goes away. We still want people to devote their lives to hard problems. The machine will still advance and solve a moderate fraction of them at random, killing many of the field's life's work. What motivation do you have in that environment to pursue those challenges in the first place? Why not pursue adtech or fintech and make the world a worse place instead? Solving 40% of the problems isn't +40% throughput; it's -60% as the rest of the field leaves for greener pastures, -inf when nobody's around to construct the right problems in the future..
2. "Solving problems" isn't directly the point of most of the field. That's true both from the perspective of most problems requiring many intermediate results (solving one useful thing requires solving many less useful things) and from the perspective of building the machinery capable of solving problems being much more important than the solutions themselves (a properly presented proof leveraging clever, new techniques is infinitely more valuable than whichever thing it proved -- indeed, the Millennium Prize problems were chosen precisely because it was assumed they would create such techniques, and for the human-solved ones they did -- without new techniques, eventually the field caps out at whichever frontier of knowledge we're currently stuck at).
3. A third view of the field treats it more like art. A machine producing behind your back the painting you were envisioning, or at least a close enough simile to fool the masses, doesn't advance "art" in any meaningful sense. It's extremely demoralizing when flaky cast tools are passed off for proper forged variants (your work is better, and it's sad to see people choosing a wrench they'll later snap in half instead), and when at a creative level people are accepting mediocrity instead of something objectively better.
When is a problem in mathematics "solved?"
There's an old joke in math and computer science about a huge leap of logic in a proof either being flagged as "left as an exercise for the reader" or "trivially shown." The problem being that things are only trivial if you have all the context to know why they're trivial.
We can claim a problem is solved if there is one paper explaining the solution with airtight logic that is understood by five people on the planet. And that is the kind of solution that LLMs can kick out (by basically, to hand wave a lot of details that I will admit to not fully understanding, doing a search across the whole problem domain with vastly more capacity than most human beings to do the symbolic manipulation that makes up the mechanics of mathematics). But what does that really mean? To have something "proven," but only to the comprehension of five people on the planet?
3blue1brown is making the interesting argument that perhaps mathematics practice shifts from a frontier that AI might actually be better at exploring than humans, to the process of digesting the output of that exploration and making it sensible and comprehensible to the billions of mines that could take advantage of that knowledge... If it were shaped in a way that could stick in their brains.
That's a kind of creativity that AI is not likely to be good at in the near future, because AI doesn't really "understand people."
That seems like a glass is half empty attitude.
For one, the problem is solved. You should be glad. That's what you wanted...
Typically every solved problem opens more doors than it shuts.
We're pretty far from knowing it all.
It's like someone saying the field of Math died when we got calculators and computers and spreadsheets to make it easier to do calculations.
Now you can use AI to help you.
Sure, if you refuse to use it, then you're screwed. That's a you choice. Not inevitable.
The only things in life that are certain is change and death.
Not any different than some Amish person being annoyed that s/he can't contribute to the field of Math because it's too hard to do all the calculations by hand on paper...
You can spend your whole life crying that one day we'll all die, or you can enjoy the time you have.
The whole point of current AI is to replace ALL human contributions, in every field. Collaborating with humans is not a consideration, as shown by OpenAI leaving practicing mathematicians completely out of their process.
The only way change this situation so that it comes out positive is to enjoy being a slave, but hey thats a you choice.
>Typically every solved problem opens more doors than it shuts. >We're pretty far from knowing it all.
Open doors to whom? AI or mankind? We have never been farther from knowing it all. The information knowable by people will become a sliver of the total relevant information in the world.
>It's like someone saying the field of Math died when we got calculators and computers and spreadsheets to make it easier to do calculations.
In that instance, the busywork was automated and challenging work remained. What we are talking about here is the reverse. It's the automation of all of the cerebral thinking.
Imagine that all of the cerebral and beautiful aspects of math were automated first, but for some reason humans were required to specialize into number crunching instead. Now open your eyes.
>Not any different than some Amish person being annoyed that s/he can't contribute to the field of Math because it's too hard to do all the calculations by hand on paper...
The thing about amish people is that they own their own land and grow their own food and are independent within a governmental system that respects their property rights. The rest of us renters and feeders operate within industrial society-work or die.
The disposition amish people have towards technology has been ahead of the curve.
>You can spend your whole life crying that one day we'll all die, or you can enjoy the time you have.
I would also encourage my peers to enjoy what little time they have left. What we are witnessing is the end of history, and I am honored to experience it. However I get the impression your nature is to go out with a wimper.
We need humans to help guide all this, need to learn all we can.
I agree with Sanderson that the opportunity seems larger than in the past. The challenges are quite different, but if somebody loves math, loves learning about it, like I do, I see so much opportunity.
There's going to be so many more connections to evaluate, so much work needed for unification and simplification and pedagogy, and above all there's going to be intense demand for mathematical taste.
With potentially plummeting value for human involvement in these skills, I think that’s precisely what many people are worried about.
Jane Street will be using tons of AI in math, but boy are they going to need a lot of humans to try to keep it all under control.
The entire point of AI is to eliminate human involvement.
To generalize beyond math... how many bits of working memory do you have? How about a transformer?
AI will make mathematics so much more approachable, comprehensible, and applicable as more problems gets solved. If the costs is a handful of PhDs tenure track, so be it. Academics didn’t much to seem to mind when that happens to blue collar workers.
Nothing stopping anyone from studying mathematics here.
AIs will do all the math with zero human involvement whatsoever.
I don’t buy these claims anymore, and haven‘t been for a long time. I think you [as in you boosters; not you specifically] are full of shit. I don‘t think you know what AI will become, you just dream up some scenario where everything becomes better by some magic, but it won’t. It will become worse. People loose their jobs, people loose their tenures, and instead we get just more and more slop, more and more span, energy becomes more expensive, our planet becomes more polluted, our internet becomes more polluted. Our servers become overrun by bot traffic, our gaming machines become too expensive, etc. etc.
I just want you to stop making things worse. I just want you to stop training more AI. It sucks, I hate it, and I want it gone.
The only way that it hasn't made mathematics better is in the sense of human mathematicians' career prospects -- and in this respect, it is identical to other forms of automation that the world, and especially computer programmers like us, have participated in in the past without complaint.
— Ojibwe proverb
its not an alien technology, its a direct application of... maths.
https://www.youtube.com/watch?v=9ABLYnvpAso
That said, change is difficult for most. Let’s give them grace and have patience as they work through the stages of grief. Once they come to accept this new reality, let’s hope they can learn to embrace this new technology to continue the work of advancing the frontier.
If it is in the computer science sense of the word, or the thermodynamic one - is still to be decided.
I studied mathematics and don't agree with this at all, for several reasons. For one the entire point of maths is that it describes a formal system in which one can 'shut up and calculate'. Mechanizing maths goes back to Leibniz and Hilbert. Nobody should surprised that the big formalism with explicit rules you invented is the first thing to yield to automation, that's why it exists.
Secondly research, including maths for a long time has been a collaboration of people, institutions, machines and processes, even maths does not consist of Faustian heroes in caves having revelations.
And thirdly just because a machine produces a 500 page proof doesn't mean your job is done. Science produces knowledge. Knowledge is information made legible to understanding by people. So there will be endless work for humans to go over machine proofs and turn it into something we understand. Just like chess computers ultimately expanded human chess.
I'm not convinced humans will be better at this than LLMs. Frontier models are quite good at handling even deliberately lazy/ambiguous eli5 prompts on complex topics IME.
they don't need to be. Any scientist is already surrounded by tools that are better than they are at anything. A scientist from 200 years ago would have the same existential shock if they see how a modern scientists works.
But that's to misunderstand what science is for, which is to expand human knowledge. And a tool by definition can only ever change how you do this, not that you do it because you understanding it is the point. When people say learning to program is now useless, what they really mean is it might not make them any money, or using the AI is faster as an instrument. But if you care about programming itself, about you understanding programming, nothing has changed, it never can. And the smartest AI in the world can always assist you, but only that.
I agree ideologically and aspirationally but I don't believe it's the economic reality of how and why most science is actually funded (and I think you agree based on your comment about not making any money).
> But if you care about programming itself
I'm...not so sure I do any more? At least, not any more than I care about using Java over Python, or C++ over Java, or C over C++, or ASM over C, or machine code over ASM, or an abacus over machine code.
> nothing has changed, it never can
We now have programs that can write any program 100x faster and better than even the best humans and solve the hardest math problems known to humankind that have stumped the greatest minds the planet could produce for decades. That, to me, is a change with profound implications for understanding the nature of programming.
They had warp drives, but only starting to get human level intelligence four centuries from now in the form of Data.
I think the word you are looking for is 'peripheral'.
The idea is, that the AI is your assistant.
Apart from that, I would also say get over yourself. We all have to. Arcane computer knowledge I was proud of having, that made me feel special can now be replicated by anyone with access to a LLM.
I still know how to build things and that is what I am doing. Just faster than ever before.
No biologist has ever complained, "Gee whiz, it's so unfortunate that we already have a brain to study. It's all so meaningless! It would be so much better if we had to construct the first-ever brain from scratch."
But why can't a hyper-intelegent AI also do this biology-esque math work of explaining its work to feeble humans?
It is easy for a genius to have theory of mind over an idiot but not vice-versa. So it should be easier for a genius AI to explain its work to an idiot human than for an idiot human to dissect the work of an genius AI.
Also, we're not talking about solutions that are arrived though an evolutionary/statistical process like explaining the design of an organism or the weights of an LLM. We are talking about solutions that are arrived through lingual/textual/rational processes like mathematics. So it's fundamentally a different mode of thinking.
It's not that we have "a brain to study", it's like if we had an "explaination of how a brain works" to study.
The task of breaking down these AI proofs is not translating and analyzing a fuzzy real-world system into a hard logical system (like in biology), but in translating a hard logical system into a simpler hard-logical system we can understand.
Its kind of in Grant's incentives to push the interest for mathematics, because without an audience he won't be able to keep doing what he loves.
Like, my old uni has a history department, and had an Egyptian history teacher. This was at some point deemed a pointless use of resources because there was no role in society except for teacher of the same subject after that, and the classes shrunk, and she ended up getting offered a role in admin. She was not happy in that role.
I think it was relatively soon after that interaction that he started doing youtube full time. I've always wanted to think I made a teeny tiny contribution to move the needle there :)
Like calling Lee Sedol a pretentious tool for retiring in the face of AlphaGo. If you really do mathematics for the enjoyment of doing mathematics, following a roughly unbroken line of tradition for at least a couple hundred years, an alien computer mind showing up and smashing everything would perhaps be upsetting, don't you think?
Then I finally realized that Professors spend most of their days in meetings and management - not actual research!
Frankly, despite the obvious financial worries, it's been a little freeing. I can go do something else (because, uh, I may have to).
First, "cognitive labor" is a form of labor - it's different vs. creative work, even though both use your mind. If your math theorem can be written up in partnership with an LLM, wow! You can be done with that, and go do other great work. Cognitive labor is a form of labor. Let's talk about physical labor and leverage to understand how removing labor translates to time. On your farm you buy a tractor to replace your backhoe. If it is a hobby farm you get in the tractor and you're done super fast. Or, you can take that tractor, buy a bigger farm, and spend the same amount of time you'd have spent backhoeing, but in a far more leveraged way. You can trade removed labor for time in a way that suits you.
Second; the joyful moments we get from finding generalizable abstractions and nice solutions are an adaptation. Humans can climb infinitely high conceptual hierarchies - we'll never stop climbing, using the previous ones as tools to find the next. As we do, we gain joy with each discovery because. We get so much done with brains that run on 20 watts - are we tuned to receive a neurochemical reward for finding cognitive efficiency? If AI means more concepts are discovered the tower gets taller - and we find those joyful moments more often. If there are infinite moments to be found, why not go as fast as possible!
Third; everyone else is doing it, it's a baseline skill. Knowing how to work without AI is like knowing how to ride a horse. Useful and fun! Bedsides - only 150ish years ago horses were the only viable transport. Cars were new; toys for the rich. But cars got so good so fast that we eventually reconfigured whole cities. Your homework is to consider why and how horses got disrupted.
New divisions are emerging in the lump of roles humans had at work. AI takes away roles from your job and lets us do more with less. That's identical to every mechanization before it. It's killing some roles that make up your work, even as it creates new ones.
There's so much to be excited about. Fear is a rational response to change. But so is hope :)
Steam engines aren't very good at designing steam engines. I think this time will be different.
If your painting can be painted in partnership with an LLM, wow!
If your essay can be written in partnership with an LLM, wow!
If your painting portfolio website can be written in partnership with an LLM, wow!
If your museum show can be designed in partnership with an LLM, wow!
If the placards next to each of your paintings can be written in partnership with an LLM, wow!
If the car that takes me to the gallery can be designed and driven in partnership with an LLM, wow!
If the newspaper or novel that you read on the way to the gallery can be written in partnership with an LLM, wow!
If an LLM can give tours at the gallery and answer questions asked by visitors, wow!
If an LLM can write the music that I listen to on my way out of the gallery, wow!
If an LLM can synthetically perform the music, too, wow!
> If AI means more concepts are discovered the tower gets taller - and we find those joyful moments more often. If there are infinite moments to be found, why not go as fast as possible!
I don't understand how a person can say this with a straight face. There has been so much discussion of this, and so many reasons have been given, that one can only assume that, if you're asking the question and you have thought about the issue and read what people have said, you're not only asking rhetorically but have some personal reason for insisting on a frankly pretty frustrating, borderline insensitive insistence on being positive. I'm not trying to be snotty or rude. I just want to say that to me there is something uncanny about your comment, in its total blindness to any of the reasons someone might not only disagree with you but grieve the death of, say, their academic discipline in its current form -- and in its weirdly breezy lack of empathy.
Are you suggesting that if an AI could do all of those things to your satisfaction you would not be extremely impressed.
I do have empathy for people who see the world changing and are forced to adjust. That can be uncomfortable, but it is something that is inevitable with the changing world. It has always been this way, There is very little need to make swords these days, and as anything becomes superseded there are people that are attached to the old things and there are people dependent on the old things.
I think it entirely possible to have sympathy for their position while disagreeing that the solution is to prevent change.
I don't see this as a breezy lack of empathy. I see this as a hand reaching out and saying 'Hey, you can come this way and things aren't so bad after all'
Actually I think we need to go further, we need to make an example out of the people who spent a trillion dollars building a product that is universally hated to try and make a buck. They need to be completely ruined financially, now that would be a real challenge, I sympathize with those adversely affected but it needs to happen if society must progress to a better place where humans flourish more.
No, it's not the same as mechanization. The fundamental difference, and why I find it illogical to argue either for "AI will open up tons of new work avenues" or "AI will kill all jobs" is that it all hinges on whether AI "caps out" at an intelligence level below humans (in at least some domains/capabilities), or if it is able to surpass human intelligence at all levels.
If the former is true, then yes, there will be a lot for humans to do. If the latter is true, then no, there will be no reasonable cognitive role for humans to play (beyond perhaps for some legal, "nostalgic" reasons or what not). So whether one decides to be optimistic or pessimistic really depends on if you think AI will stay at a level below humans. I really don't know, so I'm not "taking sides" in this debate.
What would be the limiting factor?
On the other hand, if we are going to survive as a species for a long time it probably depends on us learning how to not be the most intelligent thing around.
Even if it leads to our demise, I don’t think willfully holding ourselves back is the way forward
I agree with you, just wondering your thought on how we will know the latter has come true? As I understand it, you're describing ASI, not AGI. The way I personally define AGI, we are already there.
Sure, but you don't need very many people to do that relative to the billions of workers that currently exist.
If you wipe out 90% of all jobs instead of 100% the practical implications for society as a whole are roughly exactly the same.
The Great Depression was "only" 25% unemployment.
Humans keep a few around for entertainment but that’s about it.
I don't consider this a good precedent to the AI situation at all.
When this happened, humans went off and started doing what we now consider "knowledge work" (well, after a brief stint in factory work, where they also got displaced by automation). They escaped massive unemployment by being smarter than the tractors and mechanical looms. But how do they escape AI job loss when AI becomes smarter than the average human? or smarter than the smartest human?
In prior displacements humans moved up the stack. There is no longer room for them at higher levels of the stack if AI beats them at cognitive labor.
There's a better chance that a humanity-aligned AI would make sure that humans have something to do and keep us alive versus a capital-aligned one. At the same time, if AI would be the deathblow to capitalism, that'd be very, _very_ ironic.
Only if the goal of a pet project was the end result. In my experience pet project is all about learning new things and exploring the unknowns. LLM finishing it in half and hour does not achieve any of that. Although it can be a good assistant.
On the other hand, you can set up an LLM so that everything goes gradually and you learn like you used to. But that's more like what I would call pet archaeology or something... Learning the tools doesn't give as much benefit anymore, it's more like a reconstruction of past events.
Only the IBM granite model used out-of-copyright data to build its LLM. It is the singular exception in a sea of BS arguments for pro-piracy.
While LLM do have some utility especially in search, philosophically it is wrong to scrape $9T in FOSS to be resold to naive users as tokens. The wonks think people will be compliant with being a hapless data entry caste, and are simply high on their own rhetoric. =3
A lot of arguments seem to try to cling to the “old” way of doing math: staring at the blackboard for hours, wrestling with papers and papers of equations, and do forth. Well, chess players went through a similar transition period: carrying books of openings and such, to chess database, to chess engine and now AI. And at no point I hear chess players complaining that we have to study chess the old way.
This is very much discussed in the video.
People who want to solve problems themselves should go on to invent them without posting them on the internet until they're solved.
"There's never been a better time to go into math" was the final statement of the ten minute orientation session from the Dep Chairman.
It was a great thing to do anyway.
Then.
Reflecting on that a year later is interesting. Agents have become REALLY good since then, and I consider the "writing code" side of my profession to be largely annihilated. Some days that's really hard to accept.
But I think Grant's conclusion about math still largely echoes what I wrote about software: don't underestimate the social aspect of these activities, and if anything AI has made the social side more important. I deliberately avoided declaring, "now is the best time to learn to write code". I suspected that skill might be going out the window. But learning systems thinking and the social skills needed to connect people's dreams to reality continues to be an important art, an art I still have the privilege to practice every day.
And if we do reach the "anything you can do I can do better" stage, then, as Grant said, that's a hard to imagine world, and one where "it can write really good code" might be the least of our problems.
You also aren't going to get an accountant running 4 simultaneous streams of AI-driven development and working through an AWS issue when something goes wrong.
No comment as to the next generation of AIs.
But no one has nailed that paradigm yet.
Second, if "all software vendors in all spaces get wiped out" was going to happen I think we'd be seeing more of it already. Yes, there is support for some software vendors possibly getting wiped out... but, then again, you can't look at a bad vibe coded implementation of "the entire Adobe suite" that was rather overblown in the press coverage and forget that Adobe also has AIs. Instead what I'm seeing at my own workplace as we ponder the question of "should we replace this service we buy with some local vibe coding" is still remaining but we don't want to support that. Can we replace Confluence with vibe coding? Yes, but that was true five years ago too and we didn't want to do it then, either. We still don't want to do it. HN commenters have always overestimated the desire everyone in the world has to become programmers and take responsibility for everything.
One wonders what percentage of those who are certain that vibe coding is going to nuke all software vendors can't even be arsed to self-host a Jellyfin or VaultWarden install... which is way easier than vibe coding the whole of those things from scratch, and we're talking about people who are already programmers. Physician, heal thyself.
I think social skills are much more important today because one person can do so much more but this person needs to talk to many others to know what to build.
I will miss coding, but I had a good run. Time to learn a trade. I don't begrudge this fate.
But if, somehow, you can find the right thing to build without talking to people, there is still a lot of building to do.
Good luck, I think we are all going to need it.
When everything you ask for is instant and valueless, even asking becomes meaningless, and everyone is waiting to see something they'd not thought of.
Then, a thousand thousand copies, immediately… but also, watching that person like a hawk to see if they can do it again. That's the future. A lot of people will just plain become unable to think or intend anything on their own, or even want anything.
And the guy is not a mathematician primarily - he's a Youtube creator and entrepreneur. I liked a lot of his videos but now I usually just ask the LLM for detailed explanation and I can probe it as much as I want if something is not clear enough.
Education will also take a huge hit, you can't really beat an almost free supergenius that has all the time in the world to explain something to you in as much detail as you wish.
It is not, and for the same reason it's not over for mathematics. For anyone doing anything truly novel, and yes there are still software engineers out there doing that, it's still inept.
It's de jour to leverage formal verification as LLMs are quite good at looping it, but that's still a tool we had to invent to solve problems. It'll be truly over when we're being outpaced in the realm of invention but I have seen absolutely nothing to suggest that has meaningfully occurred at all. Coding by hand is not gone, there's just less of a reason to do so now.
3Blue1Brown does an amazing job of making math interesting to learn in itself. As opposed to the hundreds of millions of kids told “You just have to learn it or you’ll be dumb. Keep up or you’ll fall behind forever. Go!”
The vid calls out explicitly that math education is a primarily a motivation problem and I agree. One way or another, we need a lot more focus on that.
There's never been a better time to be a professional mathematician, perhaps. Just like there's never been a better time to be a senior software engineer.
An 18 year old entering university today will retire somewhere in the 2070s. Is mathematics, or software engineering, a promising career path for the next 50 years? No, it's most certainly not, and anyone suggesting otherwise is delusional. I don't know what would be a good career path, but most certainly avoid anything that AI is having the most success at in 2026.
I saw some clearly AI slop made videos and got much better understanding of topics, since they don't do foreshadowing for an awe-inspiring connection that we'd admire together after 15 min videos, the clankers just get to the point. Not claiming those videos are too useful either, but I did however see accelerated learning gains from asking LLMs to explain (and do Bret Victor-style small interactive demos) math and algos, something I have never experienced from any of the educational STEM Youtube channels.
As for "fresh learners", I can provide my own son, who watched the series before taking his first linear algebra class, and says that it helped him a lot.
Uh huh, and what if the videos make me more generally interested in the topic? How would you measure that on a test?
Your view seems needlessly pessimistic and myopic. Just because something might not increase a number on a test that doesn't make it pointless.
EDIT: And don't get me wrong, I hope it doesn't happen for a long time, ideally never. But what would his arguments be if it does?
It’s all so ridiculous. The AI boosters tactic against this is to attack your character, claiming you never liked maths, you are status driven etc etc, when the truth is they never liked doing maths, they just liked the fruits of it. You actually like doing maths, which is why you hate AI. It literally is the WORST TIME to join institutional maths if you like doing maths. Get a job in finance, management and pursue maths as a hobby instead.
There is a solution to all of this, make it politically unviable to devalue human labour, which is what AI is all about, some simple political solutions that come to mind:
1. It is illegal to monetize models trained on public data (force them to be released as open weight).
2. A royalty payment when a model copies an art style, IP or ideas that it mined from human knowledge.
3. Any IP that a model trained on public data creates is de facto invalid.
If you hate what AI has done to your field, I recommend focusing your time on political solutions, just preventing construction of environmentally bad data centers is not enough and frankly the bare minimum. Move the conversation further. Prevent AI companies from profiting of the commons of human knowledge spread freely on the internet. Maybe even go as far as to ban usage of AI in certain cases, everything should be on the table, the public already hates AI, it just needs to be fanned and directed well. The worst thing you can do, is to try to gaslight yourself into believing AI has apparently made your life great.
It is make like better. You're just invested in ripping out others' tools for your own satisfaction.
> Maybe even go as far as to ban usage of AI in certain cases, everything should be on the table, the public already hates AI, it just needs to be fanned and directed well.
The difference between this & the backdrop of Dune is near 0, with its issues clearly outlined in the book: You want the system that existed in the 2010s to remain as-is & ossified for your personal enjoyment.
There ought to be people watching his channel who wonder whether given all these AI advances math is even worth studying now.
In a way ai is turning programming more into maths - you write a natural language description of the problem - a proof / program - and then translating that into machine code is a lot of work / abstraction. For example look how much it takes to turn relatively simple mathematical statements into lean. That I guess is going to be the future.
I would encourage everyone to learn the fundamentals still because you will need discretion and to be able to think at a more abstract level.
However its funny that its only NOW dehumanising/demoralising now when its white people losing jobs to the capitalist machine in the imperial core, and not the slave silicon miners making gpus for gamers.
The number of pie eaters (equivalent to workers) got bigger.
Instead, people who sell shovels win big.
> I feel like the point is still being missed, and it's very similar to the way software engineers are trying to cope. The argument you are making "Well yes now this part of math we will not need to do again, but now we can do this instead" however the issue with most people just don't want to do that....
> Like who are we kidding, the type of nerds who were attracted to math and software were into it because we saw it as an art-form, it was a craft, it was being the only one in your city to be able to solve a complicated math problem, it was immortalizing yourself because you discovered a proof and added to the ever expanding human knowledge.
> Imagine a leather workman who's life passion is making insanely high quality handbags, who takes joy in knowing everything he touches will last someone a lifetime and give them joy everytime they use it. And then not gradually, but almost overnight someone comes to his door and tells him we can make bags 50 times better than you at 1/tenth the price. But don't you worry, you can make more money overseeing the factory, or selling people on how good this bag is, and explaining that to them.
> I mean, ok, that just is not what I wanted to do with my life. I never wanted to be a manager, I never wanted to be a salesman, I never wanted to be a writer. A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place. I enjoyed solving problems and writing code, I don't care if people say "well thats never what programming was about it was actually about becoming a manager all along" I never wanted to be a manager, I never wanted to manage, I never wanted to be a proof reader.
> don't want to hear it if the cover was AI generated
https://news.ycombinator.com/item?id=49531894
...Or you can keep working on your handbags & refine your styles & qualities, using your expertise & experience as value adds.
The existence of the factory did not wipe out the boutique craftsman.
> > A craft I enjoy doing has been taken away from me, I should be allowed to mourn, I don't care that I can do something else since I never liked doing it in the first place.
A craft wasn't ripped away from you: The process still exists as-is in its prior form, like the woodcarvers of yesteryear. Nothing that you desire (the process/journey) has been lost. It still exists.
The only step required to restore it is to ignore the contributions of others that use it. And your desire to do so will be valid & consistent.
But similarly as to how you want to be validated on your feelings of 'the craft being ripped from you', you don't get to impose that belief onto others to rip their use of LLMs away from them if they want to do so, lest you want to invalidate their feelings as a consequence.