> 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.
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.
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 :)
"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.
People who want to solve problems themselves should go on to invent them without posting them on the internet until they're solved.
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."
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 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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
There ought to be people watching his channel who wonder whether given all these AI advances math is even worth studying now.
The number of pie eaters (equivalent to workers) got bigger.
Instead, people who sell shovels win big.
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
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. 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."
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.
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?
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.
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?
[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.
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.
Look at the most upvoted comment on that thread:
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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.
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.
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.
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.
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 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.
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."
https://www.youtube.com/watch?v=9ABLYnvpAso
— Ojibwe proverb
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.
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.
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.
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.
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.
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.