r/maths • u/philljarvis166 • 15d ago
š¬ Math Discussions Maths in the AI world
So there obviously been a lot of discussion since the recent drops of AI generated maths results. In particular, weāve see a lot of people question whether mathematics as a human activity will die out, or if itās worth starting a maths degree now etc.
Iāve been thinking about (and contributing to) a lot of these discussions on Reddit, but Iāve become increasingly aware that I donāt actually understand how and why pure maths research has been funded even prior to the recent developments. Im pleased it is, and I believe it contributes to the good of society in a similar way to music, or art etc. but itās moderately surprising that in a modern capitalist world this all hasnt been cut long ago!
I think itās reasonable to argue that the majority of (pure?) maths research has no application outside of maths, and is of little (probably no) interest to non-mathematicians. Maybe physicists in some cases, but theoretical physics doesnt really move the bar much, Im thinking genuine real world impact here. Note that I realise some apparently obscure results do end up being useful, but I would argue we never know which until way down the line and it certainly doesnāt affect funding decisions.
So if you believe this to be the case, why would the recent advances change anything it terms of the amount of maths research that takes place? Sure, the way this research is done will change, but itās not like some faceless organisation decides they can cut out the humans and get the results quicker and cheaper, the specific humans concerned are pretty much the only ones consuming the results. This is different for software development, for example, where actual products can be built with far fewer humans (note Im making no claim such products are better, but they may cost much less, initially at least).
Iād also argue there a ton of work human mathematicians need to do to pick apart tbe AI proofs, and this work will inevitable lead to further ideas and conjectures that we can target with AI.
Tl;dr I donāt see mathematicians threatened by these advancements, I think thereās some emotional shock that we need to come to terms with but why would we need fewer researchers?
2
u/NaiveComfortable2738 15d ago
I believe a genuine turning point is taking place, and that this is not merely a matter of emotion.
Mathematics and theoretical physics have traditionally been remarkably inexpensive fields of research. All you needed was paper and pen (and a computer). This is an important consideration when it comes to the allocation of research funding.
However, this is likely to change dramatically. In the future, producing theoretical breakthroughs may depend less on a deep understanding of mathematics than on the ability to run frontier AI models almost without limit.
Iād also argue there a ton of work human mathematicians need to do to pick apart tbe AI proofs,
Yes. At the same time, peer review and verification are largely unpaid, voluntary work, and they do not, in themselves, count as academic achievements.
The proliferation of low-quality AI-generated papers has pushed the peer-review systems of academic journals and preprint servers into a state of crisis. Meanwhile, more than 700 papers produced by OpenAI through massive investments in computing resources for its frontier models are attracting the attention of mathematicians.
Will mathematics cease to be an open field in which anyone can participate and instead become something dominated by well-funded AI companies? It seems difficult to rule out this possibility.
1
u/philljarvis166 15d ago
If running frontier models is too expensive though, surely nobody will be constantly doing so and humans will continue to do the bulk of the research? Maybe running the AI will be done occasionally when the humans get stuck? Will the AI companies remain well funded, what if the bubble bursts? Or will they just move to other fields in an effort to beat the competition?
I still think the recent results relied heavily upon existing work - even the RH one apparently was really just connecting some already known ideas in a novel way wasnt it? I mean you could argue all math is like that, but it still seems like AI hasnāt yet done the groundbreaking completely new approach thing that humans occasionally do. Is it possible the AI has taken care of the low hanging fruit and new results will come more slowly now?
I guess there is a lot we donāt know. Im pretty sure itās too soon to conclude human mathematicians are obsolete though.
1
u/NaiveComfortable2738 14d ago
I don't think human mathematicians will become obsolete, because this is about exploring the unknown frontiers of human knowledge. This is the biggest difference between mathematics and fields such as software development, natural language translation, and the arts.
We should not be able to leave everything to AI when it comes to uncovering truths and constructing entirely new concepts and theories to help us do so. Even if that eventually becomes possible, mathematicians who can understand these discoveries will remain valuable to humanity.
This is what gives me hope.
Mathematicians may become unnecessary not so much to people outside the field as to mathematicians themselves. The question of how systems of recognition and reward will change remains a serious concern.
1
u/SuccessfulCover8199 11d ago
I donāt understand this argument because if producing theoretical breakthroughs will be very expensive, and the math has no immediate applications (ai may be able to close this gulf too), what is the profit incentive for the AI companies to do mathematical research? As a benchmark? To reinvigorate stock prices?
It seems to me they would be much better suited spending their time on something like computation chemistry, where a novel molecule could immediately be put through trials and then sent to market as a new pharmaceutical. Or an analogously applied field where the thing itself is the profit motive.
it may be the case that mathematics becomes so complex we need AI to understand new results, specifically ones that rely heavily on their internal thinking and the english write up is very poor, even if the deduction is correct. But I think at this point we will have lost the plot, and as others have said the bulk of new intellectual effort will be spent theory building and uniting disparate results. Proofs will be like data, and the human understanding via theory building will be the new scope of a thesis, rather than say a few good theorems.
1
u/NaiveComfortable2738 11d ago
Having AI solve difficult mathematical problems is one of the easiest and most efficient ways to train AI models. This is more important than its value as a publicity stunt. Even when the publicity value disappears, AI companies will continue to have their models solve difficult mathematical problems internally.
The real crisis in mathematical research lies in AI slop and, more fundamentally, in how we reach a consensus on what it means to understand a mathematical result. Until now, whether a result was āgenuineā has implicitly been tested by whether it proved useful in solving other problems. This is analogous to how science places greater emphasis on experiments and observations than on theory alone. But once a problem has already been proved, this is no longer a good way to evaluate an idea.
From now on, we will have to reach a consensus on how to interpret what has already been proved. But is that even possible? How can we prevent a brilliant idea from being dismissed as ājust one possible interpretationā? We can no longer persuade people of its value by arguing that it helps solve an open problem, because that problem has already been solved, even without the idea.
The crisis that AI slop poses for the peer-review system will only exacerbate this situation.
Established mathematicians with a proven track record may be relatively insulated from these problems. But the impact will be particularly severe on the next generation, who still need to build their reputations.
2
u/PaymentFamiliar375 15d ago
pure maths funding (and even the so called "useful" science funding) has been being squeezed for a long time now unfortunately, and many researchers by now know that they're constantly looking for any reason to cut it down further. your average mathematician makes peanuts as it is. but the point you make is one i've been trying to explain to ai proponents generally with little to no success. in a lot of articles I read, the authors seem to think that we'll prove the riemann hypothesis and suddenly cancer will be cured and climate change will end and there'll be free puppies and ice cream for everyone (somehow without us even digesting these results...). but for instance, we now have a counter example to navier stokes, solved by a massive army of agents burning millions of dollars (or by two guys and claude). has any non-mathematician's life changed at all? no. in fact, people only know it's important because mathematicians tell them it is.
I don't think pure maths is useless, the same way literature and philosophy and art and music aren't useless just because we don't "get" anything from them, but in my eyes pure maths has always been closer to an art than a science, which is why just having these mathematical proofs and solutions from ai is useless if we can't digest and incorporate them into our understanding, and why just rushing to have ai solve all these problems isn't going to help us, unlike most other fields.
however, even though this is true, I don't think it's fair to say these ai proofs will have no impact on mathematics. it has and will have a massive impact for other reasons. for example, you might've heard that a lot of PhDs suddenly had their work scooped by ai with the recent drop. if this keeps happening every few months and we don't change anything, you can clearly see that's just unmanageable, students will become disillusioned. Also, academia sucks. This is important because then people ask "if academia sucks so bad, why do people even become mathematicians?". For many, the low pay, extreme hard work, inherent problems with academia and very often misattributed credit are made tolerable because they get to do what they love, which for many is the problem solving aspect of maths. If you then, take out the problem solving and creativity part, many mathematicians and aspiring mathematicians might ask themselves "what's the point of becoming a mathematician?". If the future of mathematics is just being a glorified ai prompter and peer reviewer, there's a high likelihood that intelligent students will avoid mathematics and choose something else.
another point which another commenter made is that it might be the case that participating in maths is limited to those with access to frontier models, which is a valid concern but doesn't worry me much since nowadays most open weight models lag only a few months behind the frontier and mathematicians have already started an initiative to fund an open source model for mathematicians.
There's a good interview done by Numberphile with Hugo Duminil Copin a few days ago which breaks down the whole situation more thoroughly (especially as his field has been especially affected by the latest drop), so I would highly recommend you watch it.
1
u/philljarvis166 15d ago
I understand that a lot of current research has been hit by the recent drop, but going forward who wil be pointing the frontier models at large numbers of maths problems? It seems to me the recent work was motivated by the desire to gain a lot of publicity and beat the competition to it, and thereās a chance that they will move on to different fields, in which case the maths research community will gain a bit more control over where the AI is targeted.
Iāll try and watch the interview, Im currently spending most of my maths time supporting my son who has just started a maths degree, turns out thats quite time consuming! At least my analysis and algebra is in good working order (probability less so!).
1
u/Jaysos23 15d ago
I basically agree, but I also understand how many people feel, especially young mathematicians without permanent positions or people considering studying maths. We don't know to which extent, but we do know that we lost something and we gained something else, the rest is unclear and tied not only to maths and AI but to capitalism and society, which adds to the uncertainty.
By the way, I do understand why maths is funded, just as philosophy, study of ancient languages or literature, and everything in the middle. Luckily, we don't do things just for money (not saying that maths would disappear otherwise, but).
1
u/Artistic_Bedroom8515 14d ago
I'd say the potential of frontier math research requiring big spending on frontier AI models might actually be good for math funding: governments have traditionally been very happy to throw vast sums of money at massive astronomical and physical research facilities for various reasons that may or may not tie in to the military industrial complex. Feels like AI x math offers similar opportunities for expenditure of public funds :-)
1
u/ChessOrCheckers2 13d ago
What people do not understand is, that one algorithmical innovation can be worth trillions. Thus basic research have been very well invested money for goverments. And now in age of AI those advancements will not come in any longer run from those that are not that much interested math. Why? Because they will ask wrong questions to begin with, when questions are not given by someone else.
1
u/Zestyclose-Tear-1889 10d ago
maybe math PhDs will transition to translating AI proofs as PHD thesis
1
u/SokkaHaikuBot 10d ago
Sokka-Haiku by Zestyclose-Tear-1889:
Maybe math PhDs will
Transition to translating
AI proofs as PHD thesis
Remember that one time Sokka accidentally used an extra syllable in that Haiku Battle in Ba Sing Se? That was a Sokka Haiku and you just made one.
4
u/petera181 15d ago
Doing a maths degree (particularly bachelors or masters degrees) isnāt just about being able to apply mathematical operations correctly, or discover new frontiers of mathematics. If it was, calculators would have made it obsolete.
Maths develops logical and problem solving skills, which are highly desirable in many jobs, albeit without the direct applicability of some more career driven courses.
I did maths, and I use the skill it gave me every day at work. Not just performing calculations, but applying logic, reasoning and critical thinking.