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  shubhamjain
  A very balanced perspective, and the concerns he raises are reasonable. He acknowledges that AI is going to transform mathematics, but simply dumping proofs on the math community and expecting others to do the grunt work of verifying, refining, and expanding on them is hardly a productive way to advance the field.There seems to be more interest in hitting some arbitrary benchmark (we proved X unsolved problems) than in genuinely contributing to mathematics. But what else is to be expected? It's become a maniacal race with too much money. Too much effort is being invested in proving that the exponential curve is still holding.
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  j-pb
  The authors of the proof are invited to give many talks, and meet with other experts in the area. Workshops are set up to discuss the proof, as well as other recent developments. problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is "solved", and do not understand the AI output well enough to answer questions on the result The value here seems to be the insights that the author of the proof gained, and the paths they took and maybe more importantly didn't take. Inviting only the human prompter to a talk on the paper is like inviting only the department chair, manager of the actual author.The valuable part that Tao is feeling the absence of is the insight, and you can only get that from talking to the swarm of agents that developed the original proof with all of their context.So to me it feels like we don't need Math 2.0, but Authorship 2.0. I want to "meet" the context that generated these proofs. I mean luckily these were not generated by faceless systems like a SAT solver, you can actually talk to it, but I'm not sure if we can step beyond our pride and grant the true authors of these proofs that recognition.
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  lifeisloving
  The same could be said of Software. Instead of giving up on creating novel projects and instead just taking other peoples ideas and porting them to Rust, we could be embracing AI to push software and computers farther.Im not sure how that will work, but im convinced the current paradigm of just pushing agents into codebases for not much reason other than you can is going to make building software incredibly boring and push creative people away from the field and stagnate progress.My prediction is software gets boring and building hardware projects will be the new frontier for creative engineers looking to push computing further. Which is probably a good thing.
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  devolving-dev
  Why were we doing math in the first place? We should be happy that math problems were being solved, since presumably they were blockers for other problems in science and the like. But it feels like math was really more about seeking enlightenment, like a form of mental yoga or something. If so, we can just ignore AI proofs and continue on maybe?
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  AlexAplin
  >the mere knowledge that a solution exists "contaminates" efforts by both humans and AI to find alternate routes to the problem that reveal additional insightsThis really expresses the heartburn you see across all fields, not exclusive to careerism. I certainly have friends in decomp and fan translation spaces that have been demotivated by the current rash of efforts happening there.The rush to be "first" has always been over-celebrated, but it would be nice to believe there's a way to get beyond that thinking.
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  fwlr
  I hope Terry has somewhere private where he can safely express his anger at how poorly math has been treated by these AI corps. I understand that as a recently pro-AI public figure he is limited to ambivalence, so I understand him adding caveats like “maybe math 2.0 has a place for AI”, but it can’t feel good to say stuff like that just days after OpenAI so drastically salted the earth.
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  armcat
  I think this focus on a "holistic" approach applies to everything AI is touching now, not just math. On Twitter I see people one-shotting games, or reproducing games. If the goal is to just one-shot a game using AI, it's done. But if the goal is to produce immersive medium that people can truly enjoy, admire the story and the craftsmanship, and can find entire new ways of bringing a story to life, that's something else entirely.
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  underdeserver
  Even when a problem got solved, there has always been value in publishing simpler proofs and corollaries that give better intuition into the broader field.If I understand Tao correctly, he's saying that's going to have to be the focus going forward. I just default to thinking the models are going to be much better than us at that, too.
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  InfinityByTen
  When you mechanise, you take the "meaning" out of the effort and that, in of itself, is death of human pursuit of the venture.The industrial revolution did that to battles and wars and it inspired Tolkein's lores to a considerable degree. He loathed what mechanisation had done.I feel something similar is happening to Mathematics. I shudder to think what would come of other human pursuit this mechanisation targets next.
• spuz
  I said this when OpenAI announced they had solved a Millennium prize problem: solving open problems for the sake of it will lose its cachet. AI companies will no longer benefit by making these announcements. They've proven the effectiveness of their tool. If people want to use them to advance human knowledge then let them do that. There's no benefit to humanity to turn electricity into proofs just for the sake of it.
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  koopuluri
  > But at the current time, the opposite is often occurring: problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is "solved", and do not understand the AI output well enough to answer questions on the result, give talks, or otherwise interact with the rest of the field.Sounds like Terence Tao would have said the same about Ramanujan who basically just "solved" problems without much explanation / reasoning / communication other than it just arrived from god.In the case of Ramanujan, others took on the responsibility of socializing and community building knowing that he wouldn't do it himself. Why can't the same approach happen here?There will be people who want to just "solve" math problems now that they have a new tool that lets them express themselves this way. Maybe the don't want to participate in the broader math community, etc. Why discourage them, or add friction / a barrier to them participating in their own way? Why not take on the burden of socializing, making sense of, and community building yourself?There may be valid reasons here I'm missing, but to me this seems a bit like wanting others to approach a field in a particular way even though the field can support many ways.
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  cs_throwaway
  Let us know when it is clear that UCLA does not hire the candidate with the most top-tier journal papers.It’s more likely that instead of spending a 100K/year direct grant on two PhD students, PIs will hire 1 and have the student spend 50K on AI.
• SubiculumCode
  I feel like there first will be a lot of rationalizations, hamd-wringing, and existential tummy aches, but then the eventual resigned acknowledgment (just like in Chess), that humans do math because they like to do math, not because humans will ever again be as good as computers are at math, then come to make discernments between human math proofs, and the work of an engine, maybe they'll even start start doing proofs on short time controls and stream it on Twitch.Because the other solutions are to a) quite literally become inhuman, with cyborg integrated TPUs running local models and networked interfaces to propierary models run in data centers, or b) assert dominance of human ignorance by burning civilization down, which doesn't sound pleasant.
• anon
  undefined
• ChrisMarshallNY
  A well-known MIT professor gave a presentation about the advancement of mathematics, back in 1965: https://youtu.be/W6OaYPVueW4
• anon
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• elAhmo
  It is interesting to see that we are using this term Math 2.0 so quickly, after just a few months/year of seeming progress on previously hard problems, for something that has been around for thousands of years.
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  yedhukrishnan
  This is a distilled version of what people say about the tech industry in the past year or so. Replace math with any field, and the statement is still relevant.
• MrOrelliOReilly
  Does this response properly anticipate how math will change further with the next N model generations? Exposition and exploration may fall well within the capabilities of future models.
• stared
  It is surprisingly similar to "Catching crumbs from the table" by Ted Chiang, a sci-fi perspective published in Nature in 2000, https://www.nature.com/articles/35014679
• OtherShrezzing
  I have this feeling that the frontier of maths is going to accelerate faster than humans can keep up with it, even if machines get exceptionally good at math exposition. There’ll be some event horizon of new discoveries which are so complex we’ll never understand their intermediate steps. Beyond that point, humans will revert to “Math 1.0”, where we’ll need to rediscover proofs that have already been solved by machines, and we’ll have a pair of frontiers each for the humans and the machines.
• eviks
  > placed a premium on being the first to solve an open problemWhich is a simple measurable goal requiring little bureaucracy. The mythical "all you need is a pen and paper and a lifetime of dedication"> "Math 2.0" will need to ... value mathematical progress more holisticallywhich is directionally the opposite> community building ... AI can contribute positivelywhat is this belief based on? Any other communities can illustrate?
• sanxiyn
  This is basically On proof and progress in mathematics by Thurston restated. When Thurston wrote it in 1994, many people didn't understand what he is talking about.https://arxiv.org/abs/math/9404236
• Regex777
  he put in an elegant way, that its not just about the solution it's about how we would leverage the AI for better good.Which should improve collaboration, Research and Clarity.I would really appreciate if we come up with protocols for using ai in STEM field's it might be award at first but we could regulate properly using this method.
• bluepeter
  I mean, he still seems to underestimate what future models will be able to do. The various directions he wants to reward are also things future models will do far better than humans. I suspect we're better suited to pursuing math like we do pleasure reading... it's enjoyable, can be useful in various situations, but we're clear-eyed that we're not gonna advance the field... and that's okay and doesn't mean it's not still worthwhile.
• contubernio
  Most of the problems that have been solved are problems on which a great deal of progress had already been made. Those who work on well known problems posed by famous people are those who suffer the most from this. Those who do their own thing and pose new problems, on the contrary, benefit from it. Suddenly raw technical power and great memory are not so valuable as a broad perspective, structural insight, and wild ideas. Who can be successful in this new ecosystem is different. Some of the elites are (correctly) more threatened by it than some "mid tier" mathematicians. I see lots of opportunities to overcome obstacles in my research program some of which had confounded me for years.On the other hand, it puts a premium on resources. AI is not cheap for mathematicians. Folks are fancy universities in rich countries with forward thinking ministries of science will have an advantage over the rest.What is clearly in immediate crisis is the traditional model of doctoral education. Most of the problems that were "given" to ordinary doctoral students are solvable (quickly) even by something like Claude pro. Mathematicians need to adopt training models more like what is done in experimental and laboratory sciences - collaborative and structured.Where Tao is wrong is in regards to exposition. AI already writes better lecture notes, problems, and exercises for mid level undergrad math classes than do most of my colleagues. It's exposition is generally well structured and clear and it can adjust level on request quite well. It writes research better than most professional mathematicians too.
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  adrianN
  I wonder how we could formalize the notion of „interesting“ problems in a way that would allow us to automatically generate new interesting questions from the existing corpus of mathematics.
• lubujackson
  Working heavily with LLMs for the past year has me nodding strongly with Tao's mindset.AI only take us as far as our imagination thinks to ask it. This can be exhilarating when new models drop every month and we can continually reach a new threshold, basically for free. But it is only a one time gain and ultimately short-sighted. Where I find continuous value is using LLMs to help my understanding, full stop.I use LLMs all day long as a SWE and I have tried many approaches, but the most satisfying and consistent approach is to lean heavily into understanding a problem space and a solution space. Yes, it whips up architecture and code, but I spend most of my time peppering it with questions about the design and how it handles certain situations, what about this edge case and that security concern and this future product need. I have it write a report breaking down the feature and how it integrates with existing code and if the report is too confusing I have it simplify either the report or the code until it makes sense to me, sometimes scaling back the work to a more manageable state. I do all of this before I look at any of the code it writes.The difference from this approach is that I am not suffering reading through 3000 lines of AI slop but I am reviewing a PR that I fully understand. I can eyeball it quickly for anything that doesn't fit my mental model and dig deeper or quickly revise it. Only after I am happy with the bones do I consider the meat and skin of the code.What I find most concerning is how frontier AI companies all seem to have this Math 1.0 perspective that they only want to type "solve Riemann" into the chat box and have the magic to happen. It is the same problem Google ran into, where a simple, no thinking solution serves most of the people best and most profitably, so you fully ignore or remove everything else (boolean operators, exact phrase search, verticals, filters, infinite pages of results, "nothing found" if there isn't, etc.) But that choice leads to the situation Google is in now, scrambling to stay relevant. In a different world, Google would have continuously augmented their search capabilities and eventually built a smooth, guidable AI interface.But no, we must only have an input box and a Go button.Everything looks like a nail when you build hammers, sell hammers, have infinite hammers to play with however you like and your company mission is to build a hammer starship to explore the hammerverse, whether or not that is even possible.
• rXwubXUGAm
  We go Math 2.0 before GTA 6
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  doctoboggan
  It's been very interesting watching Tao's evolution on his thinking on LLMs. Of course the LLMs have themselves evolved so that shouldn't come as a surprise.The job of professional mathematician might be the first to be completely eliminated by LLMs, save for those who can make money from a patron. I am hoping they are able to figure something out to save their profession, as other professions could use it as a blueprint as AI comes for them next.
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  vasco
  He is right if model intelligence stalls. If model intelligence continues to improve soon there's no need for the prompter to understand anything or for any workshop as a mathematician will just be able to ask the model to explain how the proof works and models will do a good job at walking them through it step by step.There will be no gap in understanding. Now there is because the models are discovering things at the edge of what they can do and so suck at explaining it. There's nothing particularly special about a newly solved problem in terms of learning it.If we accept AI can explain all of existing math nicely, why shouldn't it be able to explain new proofs?
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  bonoboTP
  I imagine doctors will also clutch their pearls when Ai starts curing disease. "But curing disease was never the point! These arbitrary dumps of AI cures for cancers is unsustainable! Who will think of the doctors and who will build their communities further? From now on progress in medicine must be redefined as what makes doctors thrive, not what generates cures!"
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  youoy
  Can we please stop reducing human activity to "taste", conferences, talks, "understanding"? I think this is a very unproductive trap.There is a world where we get to the edge of AI capabilities, and we build on top of that. As humans have always done with every new technology.There is another more pessimistic view where LLMs just replace every human capability, and our economic overlords dont need us for anything and we just eat the small pieces of bread that are left.This comes down to the fact of:is human existence/intelligence just the simbolic representations we make in our brain? Or are they just a tool?I tend to think of Godels incompleteness theorem as a proof that on the limit LLMs are useless. The real question for me is at what point approaching this limit becomes an issue, and if it has any practical consequences.
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  Chance-Device
  “doing math responsibly” is just a euphemism for “ensuring we can continue doing our paid hobby”.Take a look at this interview from two days ago: https://m.youtube.com/watch?v=oQypVVv1u1oThe interviewee is worried about the future of math research. He is not strictly worried about being replaced, instead he is worried that he will no longer be able to launder math-as-a-hobby through math-as-something-useful as is the case today. He lays out very clearly that grant proposals claim to have useful outcomes while the proposers know those claims are nonsense.Business as usual in math, and frankly in all the other sciences, is to do research that furthers the researchers careers or personal interests and pretend that it’s somehow useful. This would be absolutely fine if it were privately funded, but it’s not, this is public money.In every other endeavour, lying in order to get money is considered fraud.We have collectively wasted a huge amount of taxpayer money and human time, entire careers, on things not likely to ever matter to anyone.I look forward to science becoming automated so that we can have real progress instead of the current broken system.
• spuz
  Perhaps it's the moment that the likes of Terence Tao hand over the reins to the likes of Grant Sanderson.
• js8
  I would argue the problem is not AI, but putting value on proofs by mathematics community. They're not fully to blame, part of it is billionaires (and other elites) to appear educated, and the general status culture that sees mathematics as something that needs to be socially justified.Grigori Perelman warned about this when he refused the Millenium problem prize. He understood mathematics should be a journey, not a destination.
• ChrisArchitect
  Related:AHM Statement on OpenAI's October 6 Release of Mathematical Documentshttps://news.ycombinator.com/item?id=50000421 / https://news.ycombinator.com/item?id=49999159
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  Razengan
  I get bonked for saying this again and again, because people get annoyed with an oversimplified analogy or the use of whateverfallacy,but can someone please try to set aside their knee-jerk reactions for a while to give a good reason: WHY do humans NEED to understand the basics of something? × You don't know how to farm — That doesn't prevent you from having food or cooking good meals.× You don't know how to mine raw materials — That doesn't prevent you from using computers/phones made with aluminum, copper, glass etc.× You don't know how to fell trees and shape lumber — That doesn't prevent you from sitting in that comfy chair.× You don't know assembly language or how to write operating systems — That doesn't prevent you from using Windows or macOS or Linux.—EVERYDAY you use hundreds of things made from THOUSANDS of technologies you don't understand, because other people already MASTERED them.so YOU can go on to go do GREATER things.(but you CAN still go do farming, mining, logging, writing your own OS, if you ENJOY it — nothing's stopping you — you just won't be as good as the technology that has been specialized for that over centuries, and almost certainly you won't be bringing anything new to those fields, and it'll take time away from doing other things.)—Maybe we shouldn't be wasting time on "oshit how do we uninvent or slow down this new technology because it makes things easier than what we grew up on"and focus more on "what other greater things can we move on to"There's a whole freakin universe out there and we haven't even stepped off our home planet yet, jeez.
• patternMachine
  "Taste"
• bbor
  This is all reasonable of course, and I think you're have to be pretty cold-hearted to disagree too vociferously. What OpenAI did (opening an announcement by name-dropping the exact institution that told them not to, implying they got buy-in) is just objectively bad-faith, and more of the same from Mr. Altman.Mathematics is an academy, and academies are human assemblages for producing truth (and the tools therein); they will stop producing if we forget to repair and refine them. It's just undeniable in the abstract.(Sorry for the length, cut it as much as I could; mod(s) remove if you'd like. Talking to myself in the shadow of giants is how I'm coping with the ennui, I think.) That said, four philosophy nits on paradigms, scope, motivation, and pride:1. Paradigms | The 'Math 1.0' rhetoric is undeniably powerful, but it makes it seem like he's unaware of his standpoint[1] by lumping all of "traditional mathematics" together. At the very least we've gone through four methodological revolutions in math, each one changing how the field is done on a fundamental level: ??? => Euclidean Certainty => Aristotlean Computation (~800s) => ~Newtonian Calculation (1600s) => ~Gaussian Systems (~1850s), and perhaps one in the 20th c. I lack the expertise to even gesture at. We also have clear analogues from parts of the other two acadamies in the 20th century alone: physics becoming an arcane, inelegant group effort in the ~1920s, and mainstream philosophy adopting a cloud of Kiki ideas vaguely revolving around Wittgeinstein & Chomsky in the ~1960s.I totally understand this being distressing, especially when it's happening quickly. They, too, had people decrying the future of their fields. But we wouldn't obviously wouldn't change it, in hindsight; much of modern physics would be completely intractable without those strange, boring, unnerving methods, for example. More than intractable: unthinkable.2. Scope | This all seems overly focused on Autumn 2026. Most egregiously, this is all built on the premise that RSI never happens, and we never acheive ASI. If we do, mathematics is almost assuredly A) the first academy to be completely outmoded, and B) the least of our problems. I cut a long thing about the caveats and effects here; at this point... if you know, you know.3. Motivation | Ultimately this thread is focusing on human motivation throughout, a fact that would be more forgivable if acknowledged as an intentional tradeoff. Speculating that it'll be harder to have interest in math is just not worth withholding truth; for one thing, knowing that computers could solve a problem but it's banned to try would ruin motivation anyway, and worse. It's up to us to be motivated, and if I know us, we'll have no problem doing so as long as there's any utility there at all.In more stark terms: trading progress in the fundamental academy for the sake of its current methods of recruitment and motivation seems like something posterity will almost definitely frown upon.4. Pride | This is the common thread that weaves through all three preceeding points, I think, and is even stated in pretty blatant terms (that's Tao -- always a clear writer!): ...promising open directions are now being withheld from the public in fear that this will cause their own research to be "scooped"... "Math 1.0" placed a premium on being the first to solve an open problem, even if the solution was not initially well understood. Sure, his thesis acknowledges that some changes are welcome, but not radical ones; his tone implies tweaks to conference schedules and authorship norms rather than fundamental restructuring of what these professions are, and what it's like to dedicate one's life to the demos through them.Doing science (mathematic or otherwise) in this competitive, individualistic way is just clearly counterintuitive to me, even if it weren't a recent development. Imagine taking it to its conclusion and applying some kind of patent system to mathematics -- or even worse, copyright to combinations of symbols! Perhaps more riches would motivate some mathematicians, but it would so obviously eat away at the democratic principles that have brought us unimaginably far over the past 406 years.---TL;DR: What worked well for the past ~century is not particularly relevant, and I think Tao is missing the forest here, despite one of the best sylvan trailblazers around. On his side practically-speaking for heuristic and contingent reasons, regardless.
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  teekert
  I think we can say by now that we should not listen to the early nay-sayers and just wait a bit. With every trend, not just "AI". They still have some points (the ethics and environment etc), but the we don't hear from the Stochastic Parrot folks anymore.Of course it's good to have the discussion... So maybe, we listen to the nay-sayers, but defer judgement on the matter... That's wisdom.Edit, to be clear, I consider Tao to be the wisdom provider, not an early nay-sayer!
• anon
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  injidup
  I suspect the whole field of mathematics will simply disappear as a career path. It seems obvious that the trajectory is for the machines to be able to provide proof on demand for any solvable problem. Whether or not the proof is understandable by humans is perhaps irrelevant in the larger sense. Doing hard math will simply become another black box tool in the larger AI toolkit for goal optimisation. Is this sad and should we try to prevent it? Is it any less sad than the venerable London cabbie who spent a life time memorising every street to gain "the knowledge" and almost overnight supplanted by machine intelligence.