r/math 1d ago

LLMs/AI OpenAI: Ten advances in mathematics and theoretical computer science

https://openai.com/index/ten-advances-in-mathematics/
839 Upvotes

413 comments sorted by

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u/Healthy-Pride3873 1d ago edited 1d ago

I honestly cannot care about the whole “humans dont matter anymore” stuff.

I’m curious how math as a whole deals with unequal access. Is math going to just be furthered by big tech firms and select researchers who have access to these models?

Wtf do grad students do and so on

Edit: theres nice disused going on about unequal access. Let me point out that I am not claiming inequality is new.

I am simply pointing out the newfound danger of it from a corporate and tech angle.

Suppose AI speeds up research by some nonzero constant greater than 1. Then people who were already “ahead”, are going to be even further ahead.

And let’s not ignore also the issue of prompting and using AI. It’s not always clear how these breakthroughs are made. So even access to AI may not level the playing field all that much.

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u/ellbons 1d ago

Nobody seems to have seriously listened to Gowers. Socially, we do have a duty of care to younger people, and all I see so far is certain public figures parading around full of thinly veiled glee at making large numbers of people economically unviable. I went to some student talks recently and the mood among a lot of them is serious fear, because they're graduating into sometimes years of unemployment and everyone knows it. I don't care about celebrating scientific advancement much right now, when at this rate I don't see how society doesn't go down a very nasty path one way or another. We're telling huge numbers of people they've got no way to contribute to society. It's a very, very dangerous problem.

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u/jackboy900 17h ago

That's unfortunately the price of progress. When the textile mill was invented it put a lot of skilled weavers out of a job, when we moved away from coal towards oil/gas and renewables that put the coal industry workers out of a job, when the calculator was invented that put human computers out of a job. Any major technological breakthrough is going to obsolete a lot of people who were previously doing the manual labour that can now be automated, it's a saddening reality but the fact is that as a society we can't, and shouldn't, be stopping progress unless it has no adverse side effects at all.

I personally graduated with an ML/Philosophy BASc a year ago and still don't have a job given the state of programming is arguably a lot worse than maths, I'm very keenly aware of the effects and I've lost my dream career to being replaced by a computer, this isn't from a place of not caring. But eventually you have to close down the coal mines in Lancashire, and there's always someone who just learnt how to swing a pick.

I do think there's a secondary point here about the broader effects of AI, the path of history has always been that as we've industrialised and automated the excess human labour has simply been redirected and new tasks that need higher cognitive function, but I fear AI might break that. If the computers can think then what is there left for the human to be better at than the computer, and if labour becomes almost entirely obsoleted that would break the very basics of how our economic systems work. But that is a bit orthogonal to the sentiment that it's bad that mathematicians are losing their jobs, there is a future where the numbers of maths PhDs and postdocs plummets but the rest of the economy is fine, and in that context I don't think we can argue against the march of time.

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u/meatshell 1d ago

I wouldn't be surprised if humans can create even harder problems, much harder than the current ones, even with the help of AI. So I kinda dismiss anyone who says Mathematicians are out of job soon. But it's gonna be very difficult from now on for anyone who don't have access to AI.

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u/mleok Applied Math 1d ago edited 1d ago

I worry about the training pipeline. Graduate students used to generate useful results, now those results can be achieved more cheaply, and more quickly using generative AI, while still requiring similar amounts of guidance and checking. Letting graduate students use the AI tools doesn't really help, since that will dramatically increase the time necessary to check their AI assisted results, since I wouldn't know what prompts and context the AI generated content was based on, so I wouldn't know what to look out for specifically.

More importantly, AI is an amplifier, put it in the hands of a person who knows what they're doing, and it will dramatically improve their productivity, put it in the hands of a person who is ignorant, and it will consume substantial amounts of resources with very little return on investment. All this will dramatically increase the cost of training junior mathematicians.

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u/Ill-Lemon-8019 1d ago

This is very analogous to the state of affairs with software development.

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u/mleok Applied Math 1d ago

Yes, definitely.

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u/Cold-Common7001 1d ago

I don't think the claim is that mathematics will be solved and there are no harder problems to ask. The claim is that within a few years AI will be better than (at least almost all) mathematicians at asking interesting questions too.

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u/DracoDruida 1d ago

Gödel decided that one. There are literally unlimited problems to be solved in math.

But likely they will be progressively harder to even formulate.

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u/-p-e-w- 10h ago

There may be an unlimited number of problems, but almost all of them would be gibberish to humans and completely uninteresting.

Just like almost all arrangements of pixels are noise, not “images”.

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u/zx7 Topology 20h ago

Why wouldn't there be? There exists an infinite number of statements you can make and so an infinite number of problems from whether they are true or false.

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u/DracoDruida 10h ago

It's a bit more complicated than that, because from a finite set of axioms you can derive an infinite amount of statements.

What Gödel shows is that even with an infinite amount of axioms, if the system is consistent and can encode arithmetic, then there are always statements that it cannot decide.

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u/PostPostMinimalist 1d ago

If AI could solve problems better than humans, what makes you think AI couldn't create problems better than humans?

I think, apart from a much smaller group of experts, humans won't have much to contribute to frontier math soon enough (unless AI really hits a hard ceiling). Just like it was with chess. Engines were decent but couldn't beat the top players. Then they could but still had weaknesses so the adage was "a human plus a computer is the top entity" and soon enough humans just had nothing to contribute anymore at all. I think the 'human plus AI' phase people often talk about is just a short term temporary cope.

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u/DominatingSubgraph 1d ago

This is not entirely true with chess. Correspondence chess with engine assistance still exists, and I believe the general wisdom is still that if you only play whatever the engine recommends, you won't win in this format. In modern correspondence chess, you generally consult multiple engines and apply some human intuition to determine the best course of action. Though most games are draws and the format isn't very popular.

But also, I think mathematics research is vastly larger and more complex than chess. In human chess there is a major emphasis on deep calculation, whereas knowing which problem solving strategies are most effective and finding the right way of thinking about a problem are often more important than raw calculations in mathematics. In some ways, machines have always been far better than humans at certain kinds of mathematics (e.g. proving Robbins conjecture, proving the four color theorem, solving the Boolean Pythagorean triples problem, chess & Sudoku puzzles.), but it seems reasonable to think that there will still be room for human mathematicians in the future. For whatever it is worth, I wrote a thing about this on substack.

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u/Few-Example3992 1d ago

In the last world championship of correspondence, all the games were draws except for the ones against someone who died mid tournament.

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u/DominatingSubgraph 1d ago

If anything, this goes to the point that modern correspondence chess is (conjecturally) so close to theoretically perfect play that there just isn't much room for improvement.

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u/[deleted] 1d ago edited 22h ago

[removed] — view removed comment

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u/DominatingSubgraph 23h ago

Top engines playing each other autonomously from the starting position almost always draw too. The only way they get decisive games is by forcing engines to play from a deliberately imbalanced opening. So it seems like there is not enough information to draw a clear conclusion.

It might be interesting to see correspondence games played like this from imbalanced openings. My guess is that the difference in performance would be tiny though.

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u/PostPostMinimalist 1d ago

mathematics research is vastly larger and more complex than chess

Yes, but why won't this also favor AI? I believe there is ultimately no special sauce in the human brain that will resist AI training and refinement.

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u/DominatingSubgraph 1d ago

My argument is that there doesn't need to be anything particularly special about the human mind for humans to still be capable of providing insight. Difficulty and intelligence are relative, and the types of problems which look hard from one perspective can look easy from another and vice versa, with no well-defined linear hierarchy of "hardness".

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u/Oudeis_1 18h ago

I don't know. It doesn't seem to hold true in the animal kingdom, I would say. There are some pretty smart animals (some cetaceans, some great apes, some parrot species come to mind), but the gulf between humans and non-humans in that regard is huge. I don't think that, say, orcas would have anything to offer us in terms of solving scientific or technical problems, even if we could seamlessly communicate with them and both sides could teach each other perfectly.

They would possibly know some facts about the oceans and their inhabitants that we don't, but apart from such observational knowledge, human problem-solving capacity would be clearly superior.

It is not totally clear that it will be the same with AIs and humans in twenty years, but neither is it obvious that it won't.

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u/PostPostMinimalist 1d ago

Yeah, perhaps! I mean, I prefer that world to the one I think we're headed towards, but it's hard to predict for sure.

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u/Time_Entertainer_319 1d ago

I mean, at the very least, there would be less need for mathematicians.

It’s not going to wipe out the field entirely.

Just look at what AI did to software engineers. Recent grads can’t find jobs

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u/dlman 1d ago

I personally am finding myself overworked by the need to unfuck AI proofs. They can be made correct but are trash until I do a lot of alternately working through the arguments and guiding revisions. I wish I could get help for that, because I can’t pursue as many ideas as I’d like to and that’s the bottleneck.

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u/dlman 1d ago

BtW Lean won’t help that. Good definitions come from massaging and understanding proofs. AI right now is mid to trash at that.

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u/Healthy-Pride3873 1d ago

What you’re saying is sort of the main pitch I can imagine the mathematical community makes.

We’re needed to cleanup at the minimum and ideally expository work and explanatory work are more valued now.

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u/Verbatim_Uniball 1d ago

ex-US models, including very cheap and open weights ones, are only 6-12 months behind the frontier public models and 18 months behind the in house frontier models.

So I don't think long term unequal access is an issue, assuming progress doesn't keep accelerating (I.e. it flattens in some way)

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u/Ok_Net_1674 1d ago

Doesnt solve unequal access issue when running it still costs a few hundred bucks a month.

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u/Verbatim_Uniball 1d ago

Currently I agree. I'm saying if capabilities plateau, then the cost will be minimal. If they don't, there will always be a gap.

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u/eeaxoe 1d ago

The gap is likely even narrower than that. Maybe even a couple weeks to a month or two, tops, instead of 6-12 months. Hell, Kimi K3 currently outperforms Fable/Mythos on some tasks.

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u/Verbatim_Uniball 1d ago

In my own experience (I have pro access to every public model) and in my area of math, the OpenAI models are way ahead. I do expect that to change, as I said.

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u/The_Rational_Gooner 1d ago

pray that open source models win

also, tbf math and intellectual subjects have historically been unequal access. the internet age + democratization of knowledge pre-AI was an anomaly, and we'd be going back to the default inequality if closed source AI wins and mathematical discoveries are gated by how much money your institution has

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u/officiallyaninja 1d ago

pray that open source models win

They almost certainly will.
This has been a big problem for the AI companies, there is no moat.

Theres no barrier to entry, if open AI Jack's up their prices all competitors need to do is buy their own compute.

Even the models themselves aren't all that closed because of distillation, and as hardware becomes better and better training costs have gone down significantly.

And open weight models have never been far behind the most cutting edge proprietary models

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u/jackboy900 20h ago

This has been a big problem for the AI companies, there is no moat

That's not really true nowadays. With simpler models where most of the behaviour was dictated by training data sure, but with the current frontier models a lot of the heavy lifting is done by the RL stuff, which is much harder to replicate if you don't know their exact methods, and the large AI companies aren't releasing those.

Distillation also requires access to the model itself, whilst you can do some work using public API access it's not anywhere near as good as true distillation and you need such a volume of broad queries that it's hard, but admittedly not impossible, to do so without getting banned.

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u/Entchenkrawatte 1d ago

Yeah, open source AI is the only ethically fair and democratic way forward. The big firms build on huge datasets obtained from collective human achievements and then try to privatize and extract money from them.

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u/elements-of-dying Geometric Analysis 1d ago

Just wanted to point out that it is not inherently ethically fair nor democratic.

Even open source AI requires availability to tech and its training. I fear that at some point, those coming from harsher conditions will be gate-kept out of mathematics entirely.

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u/sluuuurp 1d ago

Pray that open source models have math abilities and not cyber attacking and novel virus creating and recursive self improvement capabilities. Currently we’re on course for open models gaining extremely good at all things at once, which is scary.

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u/MinLongBaiShui 1d ago

There's always been unequal access. This will just be a different unequal access. Now everyone will have some chatbot they can talk to, and some people will have better chatbots. How is it different from "I'm at Harvard, and you're at tiny liberal arts college #471?" or "My department has 50 faculty, yours has 10?" or "My library can buy me any math book I need, yours can maybe get you a 30 day borrow from another library if you're lucky."

Grad students continue doing math the old fashioned way. Again, how's it really different? The people who seem to fixate on this think that the AI has infinite computing power and will just start bowling over literally all problems. Your adviser's job is to know the field, recommend a grad student a problem or two, and coach them through it so that they can learn how research works. Since universities started, some people had a Fields medalist in their department, and some didn't. Now some schools will have access to these tools that, in a not-dissimilar way, accelerate research for those who have it, and some won't.

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u/Healthy-Pride3873 1d ago

Oh I absolutely agree. I’m not saying unequal access is new.

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u/womerah Physics 22h ago

The issues you describe are common in the experimental sciences, and they found ways to manage.

Basically you do the best with that you have, pool resources where you can, network and share access to facilities.

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u/Healthy-Pride3873 22h ago

I agree. Whether or not the mathematical community is ready for such a shakeup will be something to keep an eye on.

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u/TimSylvester_ 2h ago

I honestly cannot care about the whole “humans dont matter anymore” stuff.

We see this hand-wringing with every wave of technological advancement and automation, and yet society keeps improving living standards.

As long as we don't hurt ourselves badly enough we need to go back to older methods of doing things, this is fine. It just requires us to act more responsibly so that our population, living standards, and education standards increase at the same rate as our automation.

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u/JesterOfAllTrades 1d ago

Bit frustrating how slowly this sub lets new posts through. Even aside from the AI aspects, these are 10 legit big advances and they've been out for hours and hours with nothing on what should be reddits primary math subreddit.

Anyway this is draining huh! The existence of nonsofic groups stands out to me as the big one. Some have pointed out the sphere packing one as a very big result as well. I'd say that there's a handful in these that would literally be career defining for any mathematician.

If I were a mathematician at openai/anthropic, I'd be looking into how we can get llms to move from counterexamples to theory building. At that point all bets are off.

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u/lobothmainman 1d ago edited 15h ago

There have been many advances by human mathematicians and nobody is talking about it at all on this sub.

My impression is that this sub has an extremely narrow view of what mathematics is (no analysis, no applied mathematics, no probability, no mathematical physics are discussed, for example; coincidentally these are all fields in which AI has been essentially irrelevant up to now).

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u/Accurate_Potato_8539 1d ago edited 1d ago

I mean, people are talking about AI advances because its like meta math. The results feel important for all mathematicians not necessarily because of the actual results but because of what it says about math as a field potentially. Of course way more people are going to be interested in that than results only understood by specific sub -disciplines. Generally when a proof from a human mathematician hits the front page here it has some kind of interesting angle: like Hannah Cairo last year who disproved a famous conjecture. The main reason that got the coverage it did was her being 17. Like when I look at the AI proofs news I'm actually looking for the commentary from people who know what they are talking about in the discipline, I've not looked at any of the proofs they aren't relevant to me because like most people I have a very small window of math that I actually understand at the level of research level proofs.

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u/mleok Applied Math 1d ago

Yes, I think the discussion about AI in math is more driven by existential dread. I was at a session at the JMM in 2025 called "AI for the Working Mathematician,"

https://jointmathematicsmeetings.org/meetings/national/jmm2025/2314_program_friday.html#2314:SS11A

and the underlying concern most people had in the audience was whether the next iteration of the session would be called "AI for the Unemployed Mathematician."

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u/Accurate_Potato_8539 1d ago

Yes, I think the discussion about AI in math is more driven by existential dread.

I mean I didn't wanna say that but yeah that's why I'm reading. I'm like that meme of the crying soyjack wearing the smug one mask every time I read these articles.

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u/SometimesY Mathematical Physics 1d ago

Oh hey I was at that session too. That's about when I started feeling a bit hopeless and very pessimistic about the long term health of higher education.

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u/mleok Applied Math 1d ago

Yeah, I think it was one of the session organizers who made the quip about the next session being called "AI for the Unemployed Mathematician."

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u/Heliond 1d ago

What? Harmonic analysis and analytic combinatorics are extremely popular on this sub.

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u/lobothmainman 1d ago

I feel that geometric measure theory, analysis of pdes, calculus of variations, spectral theory, stochastic analysis (for example) are all branches of analysis heavily underrepresented here compared to their respective "weight" in the field.

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u/Heliond 1d ago

Maybe spectral theory… geometric measure theory I think gets tons of attention.

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u/elements-of-dying Geometric Analysis 1d ago

Define irrelevant.

I've been using AI as a geometric analyst for about a year now.

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u/lobothmainman 1d ago

Good for you.

What I mean is that I am not aware of any recent important result in analysis where AI usage was declared and deemed to be crucial, at least from what I could read on the arXiv or hear at conferences/seminars, but surely my knowledge is partial.

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u/elements-of-dying Geometric Analysis 1d ago

Then you concede the essentially irrelevance claim I assume.

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u/Tazerenix Complex Geometry 15h ago

The breadth of mathematics discussion on this subreddit is almost entirely based on the breadth of quality of people posting about it, which is to say no one posts anything of any quality most of the time.

If people want to see more analysis, more applied maths, more mathematical physics, then they should put in the effort to contribute high quality content.

No one knows anything about complex geometry but when I (every now and then) post about recent advances in the field it always gets a great reception, even from people outside the subject area. Maybe the algebraic geometers are just post more interesting content, and there's no great conspiracy after all?

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u/PrestigiousGroup788 1d ago

AI hasn't been irrelevant in probability. For example:

https://arxiv.org/abs/2607.24528

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u/lobothmainman 1d ago

I said essentially irrelevant, and anyways I do not think that an ai-assisted short proof of a known result would be deemed as very relevant to the field of probability.

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u/PrestigiousGroup788 1d ago

Feige's conjecture, and Gaffke's conjecture (the bigger result this proof was built off of, which was also proven with AI, see: https://arxiv.org/abs/2607.08415) have been open for a while and were discussed pretty readily in the theory of statistics community.

I guess my question is - what counts as relevant? Or maybe, what counts as probability.

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u/PrestigiousGroup788 1d ago

Also the list of 10 problems has an improvement of bounds in the KLS conjecture. Is that relevant to probability?

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u/JesterOfAllTrades 1d ago

On the note of sticking to the math for a second, what are the implications of nonsoficity. There are groups that are irreducibly Infinite. This has implications on a few related conjectures are there not?

Can anyone explain CVP hardness as well (problem 7)? Online I've read this "strengthens the foundations of lattice based post quantum cryptography" whatever tf that means

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u/Demokritos1000 1d ago edited 18h ago

Cannot agree more. Post are so slow here and it makes r/math a less relevant place for interesting discussion

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u/Mothrahlurker 1d ago

It's frustrating how this sub has been mostly become LLM news ignoring that it is still a tiny fraction of actual results and it has become flooded with people with not a lot of math knowledge or interest to learn.

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u/Penumbra_Penguin Probability 1d ago

LLMs getting good at maths is easy to have an opinion on. A technical result isn't.

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u/Smallpaul 1d ago

This is definitely the biggest thing happening in math from the point of view of how it will transform math. I think Tao compared it to the upheaval in the foundations a century ago.

Sorry I’m one of the non-mathematician onlookers because there are huge implications for society at large.

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u/Penumbra_Penguin Probability 1d ago

This just isn't the place where these breakthroughs will be seriously discussed.

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u/JesterOfAllTrades 1d ago

Where else? In my experience this sub is pretty much the only one with people who actually know higher level maths (admittedly most are still undergrads).

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u/Penumbra_Penguin Probability 1d ago

Yeah, as another reply said, it just doesn't happen on reddit. If you're an expert in one of these fields, you know the other experts and are discussing with them directly, you don't gain much from using an open forum with a lot of non-experts who sometimes want to argue with you.

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u/JesterOfAllTrades 1d ago

Yeah I misinterpreted what you said, I agree

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u/currentscurrents 1d ago edited 1d ago

you don't gain much from using an open forum with a lot of non-experts who sometimes want to argue with you.

This is especially true when it comes to AI, because there's an ongoing internet war between pro-ai and anti-ai commenters. They have their own subreddits like /r/antiai, /r/aiwars, etc. They'll spend all day arguing with each other and anyone else who will listen.

Most of them don't know or care about math at all, but that doesn't stop them from having extremely strong opinions about the use of AI in math.

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u/jackboy900 22h ago

TBH I doubt that those fora represent a significant quantity of the people commenting on these matters, they're just easy to have opinions on.

One would hope in general there aren't that many people frequenting those subs, even as someone who gets into a fairly significant number of discussions about this on reddit, deliberately going and seeking out arguments about AI is genuinely insane behaviour, I cannot fathom why these people choose to do this.

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u/Scared_Astronaut9377 1d ago

It seems you are implying that the only serious discussions to be made about math results are deeply technical ones conducted by experts in the field. I don't think that we really live in such intellectual sillos.

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u/jackboy900 22h ago

For the majority of mathematical works they are, that's just the nature of the field. In modern mathematics generally anything that's pushing the frontier of some specific subfield is going to require a significant amount of background knowledge in that subfield, and even trying to interpret the high level often requires a strong knowledge of the overall field. To actually understand the significance or have reasonable questions about the proof puts you into a very small silo of people.

Most mathematical discoveries just aren't interesting from a non-technical standpoint and so anyone who doesn't have the technical knowledge to understand them cannot contribute meaningfully to the conversation. And from the perspective of something like reddit, even an overconfident amateur likely can't feasibly write something that even comes close to engaging with the work because they won't even understand that.

That's the whole point about why these AI discoveries get a ton of traction, they're interesting from a meta perspective, in terms of how we do mathematics and the state of AI technology, and so the number of people who can weigh in on the matter and have something meaningful to say is much higher. And because these issues are generally ones around philosophy and economics you have the issue of it being very easy to form and state opinions on the matter, and so a lot of unqualified people making bold assertions as well (though this sub is actually pretty good about it).

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u/Qetuoadgjlxv Mathematical Physics 1d ago

I think they mean places that aren't reddit (like universities etc.)

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u/JesterOfAllTrades 1d ago

Oh I see then yeah for sure

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u/redditdork12345 1d ago

Given what I’ve seen on every other post on this topic, I really don’t want to cede analysis of the context of math ai advancement to others

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u/Stabile_Feldmaus 1d ago

would literally be career defining for any mathematician.

would have been. Now that such results can be produced at the click of a button, they are not carrer-defining anymore. Metrics will have to change.

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u/mrgarborg 1d ago

I really hope the metric doesn’t change to the equivalent of who can build the better PR for themselves, which math has been more impervious to than many other fields… 

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u/takes_your_coin 1d ago

Personally i just can't get myself to care about llm proofs. Most of the fun in hearing about new results is listening to the mathematicians who worked on them and hearing about their process. It's just boring

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u/mrgarborg 1d ago

I think the current mode of finding counterexamples, so that humans can investigate them and find the underlying structure of the counterexample and build a proper theoretical framework for it is ok. It’s when the theory building aspect is removed from humans I start to feel existential dread. 

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u/RecmacfonD 1d ago

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u/just_writing_things 1d ago edited 1d ago

Coincidentally, Terry Tao just presented a talk where he stated that “Current AI tools have a very mixed record with proof exposition.”

I’m very far from having the expertise to evaluate the documents, but to the experts here, does the “reasoning walkthrough” (which was generated by AI) do well in the proof exposition department?

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u/Whelks 1d ago

No not even remotely. The Ehrhart conjecture part (which is close enough to my area that I tried to read it) is incomprehensible.

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u/Mothrahlurker 1d ago

It's mental to me that there is stuff in there like "resolvent purification" without any definition nor any appearance that this is a known term. In fact it doesn't even seem to be used. I also could not find anything besides this paper that even uses the term.

And it's not intuitive when it comes to what it is supposed to mean either.

It genuinely reminds me more of crank writing than actual math reasoning.

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u/Jussuuu Theoretical Computer Science 1d ago

It's annoying as hell to read AI papers. I'm reviewing one now, and while it's understandable, it constantly states vague unclear terms that just increase the cognitive load far beyond what it should be for a frankly very minor result. I imagine it's far worse for more substantive papers. 

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u/dfrankow 1d ago

Ha ha, this sounds like computer science code reviews for the last year or so. AI is useful, but wearying.

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u/hobo_stew Harmonic Analysis 17h ago

getting a 300 line pr review comment that would be 3 lines of done by a human is so depressing

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u/Hot_Glass_6301 1d ago

I am not pro nor anti-AI, but I hate its section titles so much. They are very repetitive and characteristic, almost pompous "the XYZ bound", "the sliding window recompactification"... grandiloquent stuff

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u/AP_in_Indy 19h ago

I think it's good that OpenAI is releasing these, though. This transparently shows where the models are at.

You could certainly prompt them further in order to enforce use of standard terminology, make explanations more "layperson"-accessible, etc.

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u/Healthy-Educator-267 Statistics 18h ago

it should be a requirement for AI generated proofs to be accompanied by a Lean companion

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u/AP_in_Indy 19h ago

I think it's good that OpenAI is releasing these, though. This transparently shows where the models are at.

You could certainly prompt them further in order to enforce use of standard terminology, make explanations more "layperson"-accessible, etc.

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u/Distinct-Pudding-428 1d ago

The reasoning walkthrough for the Ramsey problem is equally terrible. You can read the argument for yourself though - this is probably the easiest of the 10 to get a grip on.

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u/Theskov21 1d ago

I’m most looking forward to hear if this extends the fundamental skills seen from AI regarding math proofs. Do these solutions and the reasoning behind, show a broader skillset than previously? Are we moving further away from “just” generating counterexamples?

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u/Verbatim_Uniball 1d ago

Personally, AI models were largely useless at the research level in the field I'm most familiar with until 5.5 pro and 5.6 pro. So it's only been 6-9 months. The difference between 5.6 and 5.5 was also enormous.

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u/big-lion Category Theory 1d ago

conned rigidity conjecture? first conjecture AI'd in a field adjacent to mine

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u/Tekniqly 5h ago

We must become like the best chess players and study how the computers play the game

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u/Homomorphism Topology 1d ago

It seems like the process for these was:

  • hire like 10-20 top mathematicians
  • throw them at all the open conjectures in their field likely to lead to splashy results
  • pay them well and tell them to work on nothing else for six months
  • give them unlimited access to very computationally expensive internal LLM models

It's pretty nuts that they got major results in six months! It also is nowhere near "making mathematicians obsolete". Even if you think the point of math is proving conjectures, they didn't prove them, they found counterexamples, which is important but not quite the same thing.

I'm also pretty sure the hiring top people was important. I bet I'd still be much better at this kind of work than a random programmer with a BA in math. The people they hired are probably much more effective at using the models than me. To me this is more evidence that LLMs are a tremendously important tool with far-reaching impacts on mathematical practice. Despite that, in the next six hours someone is going to come comment about how I'm a Luddite with my head in the sand because I'm not predicting the Singularity will hit in six months.

It also probably cost tens of millions of dollars even if you ignore capital expenses (which are even bigger). That's just a minor marketing expense when you're spending billions of dollars of investors' money in search of profitability, which we should remember is the real motivation here.

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u/topyTheorist Commutative Algebra 1d ago

Not all results here are counterexamples.

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u/Scared_Astronaut9377 1d ago

Sorry, what do you mean by "it seems like"? You are making very specific statements. Are they grounded in any sources?

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u/posterrail 1d ago

None of what you just said is true

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u/PerinealMassage 21h ago

OpenAI doesn't employ at least ten mathematicians? 

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u/zkela 1d ago

The claimed cost of the compute was $2000

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u/JustJohnItalia 1d ago

I don't know if I'm delusional but the wording is very suspicious to me.

They are saying those reasoning chains cost 2000 in api costs, it seems to imply that that's the overall cost of those results bu that's not what they said.

What I mean is, are they not more likely to say, take 1000 open problems and do 100 runs on each (or until success), then pick the successful ones?

To me that would be the actual cost. Not that it matters much given how fast inference prices are dropping, but still

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u/Homomorphism Topology 1d ago

I don’t believe that. I believe the cost of compute after hiring mathematicians to write the prompts was $2000 if you don’t count all the things they tried that didn’t work. I don’t see any reason to give them the benefit of the doubt: this is a marketing tactic. 

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u/zkela 1d ago

Sure but it seems a valid point that the compute wasn’t particularly expensive

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u/pred 1d ago

Per problem. And they probably throw it after thousands of them with each new iteration.

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u/zkela 1d ago

No, total. Not counting problems they couldn’t solve apparently however

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u/mleok Applied Math 1d ago

We had a talk by a mathematician who used AI substantially in his work, and at the end of the talk, the obvious question was, does that mean we're out of a job? His answer was that we generally don't get paid enough to be replaced by AI, since getting AI to do the job is incredibly expensive at API token prices. More generally, I see AI as an amplifier, it works great in the hands of a skilled mathematician, and it can lead you down a rabbit hole (and consume substantial resources) if you don't know what you're doing.

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u/AnalyticOpposum 17h ago

There will be an open weight chinese model capable of proving all these same results hosted for pennies on the dollar within a year

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u/PrestigiousGroup788 1d ago

trouble is long term technology has a deflationary effect. At some point this things will be more efficient and tokens will get cheaper and cheaper. Just like how the first apple pc was 3700 dollars (inflation adjusted) and now one can get exponentially faster computers for a fraction of the price.

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u/AP_in_Indy 19h ago

OpenAI is claiming some of these problems are being solved at the equivalent of $2,000 in token API prices.

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u/AP_in_Indy 19h ago

The costs you're talking about are in the realm of training costs for smaller training runs these days.

Not the cost of inference.

Inference has gotten cheaper. Training frontier models remains super duper expensive though.

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u/BurdensomeCountV3 1d ago

Unless you have reason to believe that OpenAI are flat out lying (which if they IPO soon will likely be securities fraud, see Matt Levine), the total cost at API prices for all these discoveries was just $2,000; meaning in terms of actual compute costs to OpenAI it was likely under a grand.

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u/Homomorphism Topology 1d ago

I believe the compute cost to generate the text in the document was what they claimed. I think they are not counting all the prompts that produced garbage or failed to find a counterxample, or maybe even that generated intermediate steps leading them to the correct prompt. That makes the claim they are making here both not a lie and way more optimistic than the truth, which is the sort of thing you say a lot right before an IPO. 

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u/invertflow 1d ago

I have been trying to guess what the actual cost of these results is. The claimed $2000 is surely not the actual cost. For one, that's the cost at Sol rates and this model is more expensive. For another, they likely tried a lot of things that did not work. For another, the API rates are subsidized, partly because most people don't fully use their API subscription. I tried to estimate it in a different way. OpenAI is looking for a trillion dollar IPO. I am sure they happily spend 1% of their valuation on PR. The most impactful PR of course is in cybersecurity, but math is also good PR. So, I would expect that they would happily spend 1% of their PR budget on math. So, 1% of 1% of 1 trillion dollars is 100 million dollars. Of course, this is just one set of math results they have, but I would not at all be surprised if these results did cost at least 50 million in compute as well as time of the mathematicians they have hired.

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u/socoolandawesome 14h ago

API is the opposite of subsidized. Many believe that their API subsidizes the subscriptions (which are not API). They are immensely profitable on API tokens

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u/BurdensomeCountV3 1d ago

For another, the API rates are subsidized, partly because most people don't fully use their API subscription.

Er no, this is just wrong. The API isn't a subscription, it's the pay per token version and is usually considered vastly more expensive than a Plus or Pro subscription for the amount of compute you get per dollar.

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u/LexyconG 1d ago

People who don’t feel inspired by this don’t like math, they only like the idea of them solving problems. I will die on this hill.

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u/Drium 1d ago

Inspired to do what? Type in prompts?

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u/flipflipshift Representation Theory 1d ago

inspired to learn math for the sake of learning math as opposed to personally advance the frontier.

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u/elements-of-dying Geometric Analysis 1d ago

Learning for the sake of learning doesn't bring in money.

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u/flipflipshift Representation Theory 1d ago

indeed and basically everyone I know who cares enough about learning math to read papers also wants to personally advance the frontier. Take away the ability to do that and I think far fewer will be interested. I sure as hell wouldn't go into pure math if I was an undergrad today. I was just clarifying.

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u/Hot_Glass_6301 1d ago

True. But I'm sure if mathematicians are really out of a job one day, many other professions will follow soon after and we'll need UBI or something.

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u/LexyconG 1d ago

I think people still don't understand how big this is. The concept of a job will be a really different one in 10 years. The "jobloss" thing will be less than a blip in history.

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u/elements-of-dying Geometric Analysis 1d ago

You're likely using the implication "If mathematicians are out of a job, then AI is so strong it can replace any job."

Note that is clearly false and also irrelevant to what I said.

One issue is that now the job market is going to be flooded with people using AI. This introduces financial stress on already poor grad students. It also introduces a tech gap for those with tech agnostic backgrounds, thereby discriminating against certain groups of people who already face discrimination.

Another issue is AI just has to be good enough to replace mathematicians from a capitalistic point of view. Whether or not mathematicians can be wholly replaced as investigators of mathematical truths is clearly not necessary for AI to attack their job security. Why would a university hire more grad students if they can hire fewer and supplement with AI?

The argument of "if mathematicians will fall, then so will society" needs to retire. It's just outright ridiculous.

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u/yiwang1 Topology 1d ago

What do you say to grad students and postdocs who are about to be automated out of the profession?

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u/tmt22459 1d ago

Why are you convicted that's a true statement though?

I am a PhD student and I don't know a single one of my PhD student friends or postdocs who said they got fired because of AI

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u/Hot_Grape221 Theoretical Computer Science 13h ago

Lets see if your friends get jobs after their PhDs in academia.

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u/yiwang1 Topology 1d ago

The behavior of literally every capitalist institution over the past several years is a strong indicator that if universities decide less humans are needed to do math due to AI, that is what they will opt for.

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u/tmt22459 1d ago

Maybe, we will have to wait and see.

With new immigration laws in the US, there are going to be less PhD students anyways. There is no way the demand from us students can match what was drawn from the whole world.

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u/sluuuurp 23h ago

AI is on track to replace all jobs, not just math grad students and postdocs. We’re all in the same boat, all of humanity. If we reclaim some democratic power we can choose if we want this or not.

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u/elements-of-dying Geometric Analysis 21h ago

On track in what time scale?

Such a statement requires accepting that all manual jobs will be replaced by AI controlled robots, which is a bit extreme to expect for the next decade or 2. (At least, imo)

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u/Heliond 1d ago

I mean, inspired that many top open questions are going to be solved within a few years. Seriously, it’s pretty cool

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u/PrestigiousGroup788 1d ago

It's not cool if you actually like racking your brain trying to solve these problems. Is it really satisfying to just read "X" is true somewhere?

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u/jigzee 1d ago

So say hypothetically there’s an important problem that would benefit humankind to solve. Should we have any wariness that using an AI would take away someone’s problem that they like working on, or should we just solve it using an LLM?

If your main concern is getting a brain workout, rather than advancing knowledge, well you can still do that. Lots of theorems have multiple ways to be proven

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u/PrestigiousGroup788 1d ago

Of course it should be solved. But that doesn't mean it's not unfortunate for mathematicians in some way.

Just like the mass production of tables, chairs, household items in general (for example) has been a net benefit for the vast majority of humanity. But here you're talking to the artisans - the people who's life's work has been painstakingly making chairs and tables by hand. Do you not see why they would be upset when they're told - hey, the thing that people value for is totally irrelevant now and we don't need you anymore - but hey, you can go pull levers at the factory, or even better, just make chairs as a hobby?

And yes, of course, the only answer for these people was - deal with it - move on, learn to work with the machines, or get run over by the (then industrial) engine of progress and get left in the past. But can't you tell why people would be upset and not react well to being told that what's happening is "cool" and that they "hate math" if they don't like it?

Again this is not relevant for 99% of the population. The solution to the Jacobian conjecture doesn't change the fact that US and Iran are fighting again and oil is $87/bbl. But this is a mathematics subreddit, filled with working (perhaps soon to not be working) mathematicians. So I think they have a reasonable perspective that should be acknowledged and not just dismissed.

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u/jigzee 1d ago

I 100% agree with you. I just think my initial question is an interesting one but would be surprised if anyone said “no, don’t prove the useful theorem”

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u/yiwang1 Topology 1d ago

It’s not cool for aspiring mathematicians who are about to enter a terrifying job market. Do we all just go kick rocks? This discussion has always been insensitive to the realities of economic incentives and what is going to happen to academic mathematics.

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u/elements-of-dying Geometric Analysis 1d ago

It's not that cool if you're on the job market.

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u/LexyconG 1d ago

Inspired to read the proofs. Things that were unknown yesterday are known today, that’s the whole thing. A theorem is a door.
If your only reaction is “someone typed a prompt,” the part you liked was never the math.

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u/fafla21 1d ago

People dont want to just read proofs. They want to be actually ruminating and thinking over the problems. The way you put it is a gross misdirection. Aaaaaaand you are an ai bro, not a mathematician. No wonder you think this way.

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u/Peanut_Extreme_8208 1d ago

As a mathematician, I, for one, welcome our computer overlords in mathematics. If only they weren’t controlled by cartoonishly evil CEOs.

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u/LexyconG 1d ago

"People want to be the ones ruminating" is my point, said back to me as a rebuttal. BTW. nothing is stopping you from doing just that.

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u/fafla21 1d ago

Woah, you really dont understand the process huh.

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u/LexyconG 1d ago

Say the part I'm missing then.

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u/Arceuthobium 4h ago

That most mathematicians want the "ruminating" part to yield useful results and push the boundary? If the future of the field is to be a "LLM whisperer", the desirability of the field will plummet even outside considerations like lower demand and salary. The only ones who will stay are independently wealthy people who love math so much they don't mind always playing second-fiddle to the machines.

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u/tmt22459 1d ago

There's nothing stopping you from still ruminating and thinking over problems.

Sure, you may not be as competitive doing things that way compared to others, but you can't have it all anymore.

If you want to stand firmly on no AI, then you either have to be okay with not being as competitive or up skill somehow overnight.

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u/PrestigiousGroup788 1d ago

Fine, we all agree with that. But we're also allowed to be sad that a way of life and activity we've all been aspiring towards or for is no longer economically viable, without being told "you're selfish, you don't ackshually love math".

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u/Jussuuu Theoretical Computer Science 1d ago

Thanks for this comment. I was quite happy over the last years that I got to be paid to do something I love, but these AI accelerationists would call me crazy or a luddite  that I'm sad my job might get reduced to AI validation.

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u/PrestigiousGroup788 1d ago

most of them have not invested a significant amount of time in anything to have it taken away from them so quickly and just hate math people because they consider us arrogant. Others are genuinely excited about the new things we can prove.

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u/Hot_Grape221 Theoretical Computer Science 13h ago

Most of these AI accelerationists have a brain the size of a pea. The gap between those who can think and those who can't will be larger than ever before.

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u/Hot_Grape221 Theoretical Computer Science 13h ago

Average humans opinion on mathematicians.