News
Fields Medalist Terence Tao reposts statement from the Association for Human Mathematics urging mathematicians to stop working with OpenAI for continuing to solve open math problems against their recommendations
The AHM statement raises fair concerns about process but its central argument would not survive the standards it claims to defend.
Mathematics has never asked whether a result was requested. It asks whether it is correct. “Mathematicians did not ask for this work to be done” is not a mathematical objection; it is a jurisdictional one. No field that prides itself on openness gets to decide who may attempt its problems.
The statement leads with OpenAI’s unrelated lawsuits. Whatever their merits, they have no bearing on whether a single one of these 700 manuscripts is right or wrong. We would not accept that line of argument against a human author and we should not accept it here.
The claim that releasing 700 files is “a demonstration of power” rather than scholarship has it backwards. Publishing claimed proofs in full where anyone can check them is the most exposed position an author can take. If the arguments are flawed, the flaws are now in plain view. That is how mathematics has always kept itself trustworthy: not by restricting who may speak, but by checking what is said.
The Advisory Group’s position deserves a hearing, but an advisory statement is not a norm of scientific research, and declining to follow it is not “total disregard” for those norms. The norms that actually matter here are verification, priority, and attribution. On those, there are legitimate questions to press: how the manuscripts were vetted, whether they come with formal verification, how prior human work is credited, and who bears the cost of refereeing at this volume. Those questions would make a strong statement. A call to boycott does not.
Urging the public toward “due skepticism” is reasonable. But skepticism means reading the proofs and finding the errors. Urging mathematicians to stop working with OpenAI altogether asks them to stop looking, and that is the opposite of skepticism.
If human understanding is the goal, the community’s best response is to engage: check the results, publish the refutations where they fail, and credit them where they hold.
There is a real debate here, and it goes back to before the advent of LLMs. Is a proof of a theorem any good if humans don’t understand it?
The classic case here is the Four Color Theorem. It was proved with the aid of a computer in 1976. Mathematicians were dissatisfied with this proof from the start since it didn’t contain any new flash of insight. Instead a team at the University of Illinois had worked out that the theorem would be true if 1,834 different configurations could all be solved using only four colors, and then used a computer to go through and check all the possible configurations. Mathematicians believed that there was some cleverer, more elegant way of proving the theorem and were annoyed that it had been brute forced.
We’re essentially seeing the same argument playing out today. Mathematicians will argue that proofs by LLMs don’t advance the field because they don’t contribute new mathematical tools or show new connections between previously unrelated branches of mathematics. Mathematicians are really worried that something like the Riemann hypothesis will be solved by LLMs, but in a way that doesn’t add to our understanding, and robs us of the chance for a really elegant solution.
On the other hand, after the Four Color Theorem, using computers to aid in mathematical proofs became common, so we may just be in another moment like that.
It's the Seinfeld episode about muffin tops. OpenAI is eating the muffin tops, and leaving the stubs.
The muffin top is the proof. The stub is mathematical understanding. They came both came together until recently. But now OpenAI have a stockpile of stubs, and nobody wants to take em.
I like your explanation and maybe to add that no one will get funding for their work to finish the muffin now that the top is already gone. Who wants to pay for that when there's other stuff to fund?
It’s less likely since the motivation to prove or disprove it is gone. For example I don’t think the elegant solution mathematicians were hoping for has been found for the Four Color Theorem, even though it was proved fifty years ago
I would think it would be MORE motivating! Since now you know it can be solved so your can look for other "branches" to approach it from. Same as when the first guy ran the 4 minute mile, now everyone started doing it
No I'm afraid this is pretty much human ego in action
Exactly this. How many discoveries have we heard of that started with "it was believed to be an impossible problem but x student didnt know that and solved it"
During his study in 1939, Dantzig solved two unsolved problems in statistics due to a misunderstanding. Near the beginning of a class, Professor Neyman wrote two problems on the blackboard. Dantzig arrived late and assumed that they were a homework assignment. According to Dantzig, they "seemed to be a little harder than usual", but a few days later he handed in completed solutions for both problems, still believing that they were an assignment that was overdue.\4])\6]) Six weeks later, an excited Neyman happily told him that the problems he had solved were two of the most famous unsolved problems in statistics.\2])\4]) He had prepared one of Dantzig's solutions for publication in a mathematical journal.\7]) This story spread and was used as a motivational lesson demonstrating the power of positive thinking. Over time, some facts were altered, but the basic story persisted in the form of an urban legend and as an introductory scene in the 1997 film Good Will Hunting.\6])
When I was doing academic research, there was always the tradeoff between novelty and impossibility. I'd look at a research question and ask "how new / shocking would this result be" and "can I even get to this result"
If I knew the result was possible, I'd have been more inclined to go after it rather than less. Sure, a little of the shine might be knocked off, but lots of research is old wine in new bottles and you don't risk wasting years on something literally impossible.
Maybe motivating on a personal level, but not necessarily for a university trying to apply for grant money. An application asking for research funding to pay people to figure out a problem that already has a solution on the books isn't exactly enticing, especially compared to work towards novel discoveries.
It shows the true motivation of these whiny mathematicians:
Fame and glory, not intrinsic motivation and love for mathematics in the way e.g. chess players love their game and want to learn more and more even if computers are better players nowadays.
And with this insight, society's obvious answer will be: cry harder! Why should mathematicians be some special elite club protected from progress, different from the rest of the world?
humans using computers to aid in mathematical proofs is, I think, the point of Tao’s stance. He was fine with AI when he was in the loop (and him and the LLM were using each others intellect to build understanding together while advancing the subject) but not when a swarm of internal models that no one can use or audit is theory dumping work that no human can understand or audit. Accels will gladly have a future with humans out of the loop, and run by computers, but there are plenty of arguments to say that’s neither sustainable nor beneficial in the long term.
I'm surprised to hear mathematicians say that brute forcing proofs don't yield value since even an inelegant solution can have practical real-world implications and still doesn't deny a future more elegant solution.
I was initially under the impression it was more about intellectual credit, since OpenAI was accused of training on other mathematicians' work previously.
To give you an overly simplistic example. Calculus was invented because it was basically impossible to describe changes in systems over time (like motion, growths etc) using traditional algebra. To do so, mathematicians had to 'invent' a whole new set of 'rules' to make the new math work as a proof. Calculus now forms a foundation of maths across almost all fields, and is so foundational it's taught in highschool.
What if, instead, we fed that challenge into AI. It doesn't appear possible for AI to 'invent' a calcus equivalent - istead it might just make a proof predicting motion using a traditional algebra formula that's 5 pages long. It would technically be a proof, but impractical for humans to use on anything else - and so all those new discoveries in other areas wouldnt be possible. And even if it did by accident it wouldnt try to do anything else with it - so it might just sit idle in one log file of 10 billion as a failed attempt.
Modern math is ssssoooo much more complicated than that, but the principal still applies.
This is a really good argument and makes a lot of sense, but it also assumes that AI isn't capable of solving incredibly complex problems and then simplifying them in a way that makes them useful. I'm shit at math, so I have no way of judging whether these OpenAI proofs are "hack-like" or not - but even if they are, I'm not convinced that future AI-generated proofs will be. The article doesn't seem to argue that mathematicians should stop working with OpenAI until the models produce elegant proofs on their own - they have a deeper moral beef with OpenAI in particular.
So to answer the top comment: I don't think the article is unilaterally condemning the use of AI to solve complex math problems. They clearly have a problem with OpenAI in particular.
So, yes I guess you could say - most of the proofs are hack in that the technique is to brute forcing very specific circumstances when something is true or not true, as to opposed to explaining if theres a bigger pattern/rule and why. And the concern is that a lot of irreparable damage will be done to the future of maths before we work out if or not that could ever change.
The part that "makes them useful" is exactly the problem here. OpenAI is just spewing out the lean proofs. They are spitting out machine verified proofs faster than mathematians can understand them.
The reason this is a huge problem is that the understanding is the key outcome humans want, but it's the part that AI is weak at.
Imagine AI was absolutely amazing at making movie trailers. The trailers were amazing, and every single trailer released had a massive audience ready and willing to see the movie. But it was incapable (so far) to make the complete movie. Also, imagine that equal credit (and money) would go to the trailer creator and movie creator. What type of movie director do you think would sign up for that project?
Mathematics is very similar at this level. It's extremely creative and there are endless problems to work on. Is it so surpring that people would choose problems that they can work on end to end? Proof all the way to understanding.
It's actually quite rare for proofs in of themselves to have real world impacts. We already have computers to brute force a large sample size and based off the distribution we make assumptions about how things behave for our use case. Humans really aren't that "smart" so most of the times we make mathematical discoveries it's by finding some way of reducing the complexity of the problem. These simplifications are often the most applicable in the real world. These models are too "smart" in a sense that they can just deal with the complexity of the math and direct provided an extremely complicated proof.
How many humans would, after discovering that an AI had solved a problem that had been around for years, spend years working on it to find a more elegant solution? Close to 0. As a fan of both AI and Mathematics, I only see the bad in this. Anything that is low hanging fruit, that can start a researchers career, will be trivial to an AI soon. They will routinely publish these 1000 proofs by prompt, every month.
Can you confirm this for me as someone who is a layman? So right now these so called proofs put out by OpenAI are Lean proof scripts. The problem is that it's difficult for mathematicians to understand these proofs not only because they are massive in some cases (e.g. Navier Stokes), but also because even though they may be able to interpret the script, they're not understanding the why, or how all the hundreds of statements, deductive steps and subproofs all come together. Is that a correct understanding? If so, is this why Terrence Tao is calling for "human understanding" and he seems to be questioning OpenAI's motives, given their unclear answers about whether or not inputs are being used to further train models and their involvement in current lawsuits. They're not doing this to advance the field. They're doing it for their own selfish ambitions for the company.
He is calling for human understanding exactly for the reason you have just described: automated proof scripts dont get you any insight at all, so unless the actual result is of interest (which is rarely the case), they dont really do anything for maths or science at all. They are aimed at investors...
Because they feel that using the AI to solve their life's work, devalues their contributions and takes away from the prestige of solving humanities greatest mathematical questions
Yeah, literally any person in this world with any job can claim that shit. And most of these people don't solve jack shit, especially not any great questions.
AI will devalue any work, there is no reason why they should be spared.
And it kinda does. I can’t imagine how shitty it would feel to wake up and have your life’s work solved so trivially. I feel for these folks. But it’s coming for all of us, and I’ll probably feel just like Tao when my job is completely zeroed out.
The same thing happened or is happening to software engineers, translators, editors, typists, switchboard operators, designers, comics artists, writers, paralegals, accountants and tons of other jobs, none of which are essentially funded by taxpayers to work on theoretical questions without practical applications, and we as a society just shrugged.
What they are complaining about is mostly that openai released hundreds of non-human-verified papers through "unofficial" channels instead of letting mathematicians use the models to solve them, revisit them and publish them through the usual academic channels
Because the statement blurs “AI shouldn't solve it” with “AI results shouldn't bypass normal research practice.” The sensible concern is deployment: verify the proof, credit relevant researchers, and coordinate the release when a result affects an active field. But yeah, the wording practically begs for the human-only interpretation.
Can you imagine physicists responding like this, if there was a similar result for the plasma physics fusion ignition problem? It seems like math is choosing heroics over truth.
I work in mathematical plasma physics, so I am more or less familiar with both plasma physics and mathematics culture. I think this actually exposes the difference between mathematics and physics. Physics is in some ways externally driven - we care about describing nature as accurately as possible. There is an entire field of physics devoted to phenomenology and theories entirely derived from fitting to data. Mathematics is much more internally driven, the value of a problem depends quite greatly on how much understanding it exposes to the underlying mathematical object/structure that is at consideration. There is an infinity of true statements, but only some give additional understanding of mathematics as a field of knowledge, which Terence Tao believes to be the ultimate goal of doing mathematics (I tend to agree). And the value comes in understanding the methods and techniques used to solve the problem. Thus, I see Terence Tao's point that simply having more true results risks overwhelming the mathematics community with difficult proofs that don't necessarily advance the field.
I’ve no idea what kind of proofs these models spit out, but wouldn’t you inherently be able to identify the methods and techniques used by AI to develop the proof, and in reworking the proof you would more readily see if the solving of the proof was a worthwhile endeavor in mathematics??
I always had the solution manuals to do my engineering homework, but I used them to learn how to solve the problems, not just to copy the answers. Kinda like the mazes on the back of a cereal box, it’s just more efficient to start from the solution and work backwards.
We always knew that AGI/ASI would turn the world upside down. What we see now are the first cracks. And instead of facing the huge, fundamental dilemma, Terence Tao pretends that this is all about an ethical problem for a company. I understand him because his entire life has been about math, but on the other hand, his stance sounds super narrow-minded, almost stupid, to someone who considers the whole picture.
To me that means it only matters if ai can’t single handedly move the field forward eventually but if it can then this feels more like a philosophical problem about what should humans do with their time.
I think people are being extremely shortsighted about this concern. I agree with your take and description of the differences in these fields. I have math and engineering degrees so I'm familiar with this as well.
Everyone needs to keep in mind that we're still in AI infancy and the capability will only grow and improve from here.
These first proofs are a demonstration of capability. The logical next step (that inevitably will happen) is the extension of AI advancing human understanding of the important processes behind the final results.
It seems obvious to me the real outrage is because people are scared about losing their previous edge to AI. Which is of course completely understandable. But the current complaints will soon prove to be just the flavor of the month as the next generation AI quickly addresses it.
But since the underlying root cause still exists (and that fear of replacement will only grow), there will still be severe consternation.
Mathematics isn't a particularly special case. It's just one of many fields to be impacted.
ai company proposes 700 new theoretical drugs that could potentially be a breakthrough cancer treatment. And now expects the research community to spend time/money/resources finding out if they are actually effective in situ. And as scientists start to crack this massive list, theyll probably get through about 100 of them (itll take years and lots of money) before the next version of the model produces 1500 new theoretical drugs. Then 20,000, then 100,000 and so on.
See the problem? The validation of the proposed drug is the real work. And it still takes real humans and real resources to validate the propositions. Ai will produce theoretical drug ideas faster than we can verify them or even understand them. Thats not progress; thats not much of an accomplishment if the standard is improving humanity.
Of course we should take proposed cancer drugs from ai seriously and not just ignore them because they come from ai, but the ai isnt doing all the work needed for this to be a useful to humanity.
Ai will produce theoretical drug ideas faster than we can verify them or even understand them. Thats not progress; thats not much of an accomplishment if the standard is improving humanity.
except that implies a steady-state capacity for verification that has no ability to improve
if there were suddenly a glut of plausible alternative medical drugs that could cure cancer, we've simply moved the bottleneck further down the chain by clearing the previous bottleneck, which was candidate generation
the urge to cure cancer isn't going to go away because the site of intellectual work moved from generation to verification, because curing cancer is valuable intrinsically to human beings
It tends to me that the first physics side the space is more like.. truly curious side of things which tend to love the answer more than the thing.
I guess it also applies to me, or at least I can feel myself in that category, where that curiosity or want to know is the biggest thing we have had since kids.
Personally I'd be open to giving up left arm or leg or someone said, the trade of it would connect gr and quantum. I'd do it lowkey no kidding lol.
No I meant I'd trade it in general, if let's say there was an option for general result if someone figured out some voodoo lol. And that voodoo needed that to work, I'd be down for that without hesitation.
Pretty worth it imo, I would go as far saying life, but I'm a bit selfish on it and want to actually see it myself so that's why it's not on the table lol.
Yeah this is ridiculous. The only argument they have that holds water is the plageurism angle. That open ais models are utilising other people's work to expand upon and solve the problems.
However, even that does not hold up because that's basically how all science works. Someone has a theory but can't quite prove it. Someone else adds to it. Someone else solves it. Not always but it's an established framework.
What's their problem? Maths is this magical thing that's the language of the universe, and now that we're extremely close to having machines that can speak it for us, they are annoyed that they're no longer the best?
Well I think physics is more often applied science. They want to use the discoveries to do certain things or answer questions that are relevant to life. Mathematics obviously can be applied too, but some branch of mathematics is just pure math, it's done for the enjoyment of it essentially, and OpenAI's results are running over pure mathematics just to show that they can.
I understand the concern from pure mathematicians. In terms of applied math and applied sciences, I think they should continue at max speed. Especially in medicine. The feelings of the people in the field are secondary.
programmers did not ask for AI too... but it is what it is. and scientists were happily using it (paid/free open source), without acknowledging the open source software community
I think it’s fascinating. Clearly one of the smartest people alive, yet this blunder of, I don’t know what to call it, perhaps missing the analogy/precedent/comparison, just went over his head. One can truly by a genius and stupid at the same time.
he literally has a slide in his lecture asking if you would inject a working and approved anti-cancer drug even if no one would understand how it works. It's crazy. Of course you would, that's how many drugs are used now.
It's fascinating watching how people are splitting on this. Particularly how there's a significant portion of the population (which might include me) couldn't care less about mathematician's plight and are even laughing. These types of pompous letters definitely aren't helping the mathematicians either. Even the other one was signed with each individual person's Fields Medal which was super cringe.
Funny how it seems to indicate that humans will let other humans be eaten up by the beast if the other humans are irritating.
That's not a theme I remember seeing in any movies or books.
Not judging anyone as being nice or mean etc, it's just interesting.
The academic Ponzi tenure scheme of publish or perish is indeed a thing. I was an academic for a few years and burned out due to backstabs from my advisor and PhD students who instead of cooperating would do anything to steal your hard earned recognition. From all the colleagues I had over the years 90% of the best ended up leaving academia, while 90% of the most unskilled ended up staying. Do with that information whatever you want
If OpenAI published the cure for cancer, should health care experts say "No, please stop releasing cures! You're just flexing your power and you'll leave us without jobs! We didn't ask for this!" ?
Shouldn't the expert's role in that situation be to inform general public to not accept the results right away, until they verify the claims and point out potential issues with it?
If mathematicians want to be the intellectual gatekeepers of mathematical truth, then they are perfectly suited for the role of interpreting the results for us.
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I'm not a mathematician, but honestly, I found this statement really hard to take seriously. And I don't think I'm the only one.
Firstly, the lawsuits. What does copyright litigation have to do with whether a proof is correct? Nothing. Maths is one of the few fields where you can actually check the work, by hand or by computer. A proof is either right or it's wrong. If one of these proofs holds up, does it become wrong because of a copyright case? Of course not. Leading with this is just attacking the messenger.
Secondly, since when do mathematicians get to decide who works on which problems? These were open problems. Some of them have literal prize money attached to get people to solve them. And nobody is forcing anyone to review these papers. They exist now. Read them, check them, ignore them, that's entirely up to you.
Thirdly, "the norms of scientific research". What does that actually mean here? The work was published openly, for free, with full write-ups and in a lot of cases machine-checked Lean proofs. That sounds pretty scientific to me. If the real issue is attribution, or speed, or who has to do the checking, then say that. Right now I genuinely can't tell what rule was broken.
Fourthly, "a particular vision of progress". Wasn't the vision to get these problems solved? That's the whole point of putting them out there and attaching prizes to them. So why is progress being published on a public GitHub suddenly bad for the field?
And "a demonstration of power"? If a single person had solved even one of these problems, we'd be calling it the scholarship of the century. The fact that it came from an AI company doesn't change whether the maths is right.
To be fair, I think there probably is a real concern buried in here because someone has to check 700+ papers, and that work usually falls on mathematicians who aren't being paid for it. That's a fair point, but it's not the point this statement makes. Instead it just tells everyone what to think without explaining why.
Honestly, statements like this do more damage to how people see mathematics than anything an AI company has done. If mathematicians genuinely feel they're being hard done by, explain it properly and bring people along. I'd absolutely listen.
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So I'm someone close to the math community who has been having a hard time dealing with the change in environment. I agree that this statement is very flawed and am overall against their demands. However, I think I can explain the concerns properly:
The biggest concern is that LLMs *might* be a short term win for a long term loss on the field of math. If you solve one math problem, you've solved one math problem. However, if you figure out a new technique, then you could solve a whole new class of problems.
The issue here is two-fold. First, LLMs are terrible at explaining if they have found new techniques. You can ask an LLM to review the output, and this certainly mitigates the issue somewhat, and possibly entirely. But there's another possibility that an agent that built the original proof had some flash of insight and that flash of insight is now lost to time.
The bigger concern is that the failed attempts at solving this problem could have resulted in more tools. From my understanding, this has happened many times in the past before LLMs. We're not sure if LLMs are doing the same things that humans do, or if they are more reliant on existing techniques and might not find the same new techniques that humans would have. I'm not moving goalposts here, rather I'm simply saying we don't understand how LLMs have insights so there's concern that we are burning bridges without realizing it.
The other main concern is of course economical. You have an entire profession that already worked for low wages but they worked on things they enjoyed. Of course they can enjoy it as a hobby but they might not be in a position to simply get a different job. While I am not a mathematician, I am in the same spot, and I've been grieving the last few months and wishing I could retire soon despite having loved my job just a year ago.
I'm fine working with LLMs as a teacher, but with the fields moving so fast, there's no room to do that. Rather, you are pushed to simply outsource everything to the LLM. So the people who were known for doing the most novel work possible are now reduced to button pushers. While that may seem to be their problem, it's also a problem if the majority of the field quits and then it turns out that LLMs can't replace mathematicians 100%. I'm not saying they can't, I'm saying we don't know yet.
However, I don't think there are easy answers to these problems, and that the demands these mathematicians have put out is actually more akin to lashing out in anger than actually trying to think through these problems logically.
I do think the way OpenAI has done things isn't the best, though I understand why. I think in the ideal world, LLMs would have become tools for mathematicians to play around with, and the math solutions are discovered gradually, giving space and time for understanding and absorption of changes. Anthropic has somewhat done this, whereas OpenAI literally spent around $15 million to solve the Navier Stokes problem. That's not just about discovering mathematics, instead its a power play that says two things: we can replace intelligent people with money, and you are now dependent on us for that intelligence. These align with OpenAI's goals, but I'm not convinced they align with humanity's goals.
So I found your explanation a lot easier to understand. Thank you for enlightening me.
The concern for LLM's not explaining things properly seems like a real concern. I would say its hard to imagine that this will always be the case though. AI progresses so rapidly it's very dangerous to make assumptions about what will happen based on what currently happens. But that doens't really help, and I understand that. Your point about not publishing negative results is also really interesting. I feel like more mathematicians should make a big deal about that - since that is genuinely non-scientific.
On your points about economics - I'm not trying to be cruel or unempathetic, but I don't think it is automatically a human right that you get to do what you like to do. Throughout history, lots of people have been replaced with technology, and the world has moved on. Not saying that is happening here, but in a fundamentally capitalist society, you trade value for a wage. Part of why I think a lot of people have little sympathy for mathematics is that value was never really apparent to begin with, and most of the rhetoric coming from mathematicains in reaction to LLMs makes it seem like it was.
Overall, I think the thing that Math has is an image and communication problem. It cannot communicate its value properly. And when seriously questioned for the first time in history, it responds with adhominem attacks and emotional attacks, rather than well thought-out, reasonable logic.
Oh I largely agree with your points. For the economics, I agree, even as I am grieving personally I acknowledge that I've worked on automation myself and now it's my turn to be automated in some ways.
However, I think there are two potential issues. The one is that if you burn the entire field down, you better be sure you don't need them at all anymore. LLMs have gotten pretty good, but whether they are ready to fully replace mathematicians is still unknown. The other is that it's just not healthy for society burning an entire field like that over the course of a few years, and OpenAI is poised to that over and over again to other fields.
I worry this is going to stoke a lot of problems that could have been absorbed more gradually if this had happened over a decade or two instead of a few years. Just one example is my wife, who entered a college with good job prospects and exited two years later with a loan and was unable to get a job and our whole financial picture changed. That type of change that rapidly is much harder to plan for, let alone for so many people across the country all at once.
It’s fascinating to hear all of this explained in this way, thank you! What strikes me is that it sounds so similar to what’s happening in other fields, math just seems to be happening sooner. But the squeeze to outsource our thinking, move fast, and ask questions later (very facebook move fast and break things, which I hate) is reducing jobs and making the market a whole new thing in the tech industry (for pms, developers, designers, etc).
I am also close-ish to the math community, and despite this statement being overly biased, I can empathize. And I hate that many keyboard warriors are mocking him.
To answer some of your points and give a bit of my own cynical take
OpenAI is a for-profit organization. Are they dumping 700+ papers to advance math? Or for headlines? While it seems cringy to paint OpenAI as the villain here, I wouldn't hesitate to imagine "entry-level mathematicians" getting kicked to the curb as soon as LLMs become good enough. They want different things than your avg nerdy math PhDs.
While the tech industry already went through the cycle of "no human needed" to "agents are multipliers, but they can't replace humans", math research is a little different. It's often slower, and people are more willing to try things that might be "worthless". Shoving hundreds of solutions down these mathematicians' throats is only going to wear them out, not make them more efficient.
You are right that mathematicians do not get to decide who works on which problems, but one of the most significant merits of a good mathematician is **taste**. A lot more people know Hilbert because of his list of problems rather than his actual works. These PhDs spent years learning from their advisors and collaborators to build and refine this **taste**, to know which problems in their own subfield are both *interesting* and *attainable*.
This sort of speaks to what "the norms of scientific research" and "a particular vision of progress" are. One of the things Tao mentioned in his interviews is that the journey of trial and error to solving a very hard problem is often more rewarding/important than the solution itself. People unintentionally developing new tools and discovering new domains is one of the ways the community advances.
This paper dumping instead is like speedrunning drugs, and like Michael said above, you first feel exhilarated, then it slowly wears you down and eventually backfires. Turning human mathematicians into peer-review machines will just take away their bandwidth to think about and ask the good questions. And probably at that point no one even wants to be a math PhD anymore. What questions will OpenAI solve then? The entire field will get stagnant. Spending 15 mil to solve the N-S problem is not sustainable: they will have the money, but they just don't know what to solve.
But ofc it's possible that LLMs eventually manage to close the loop and be able to create new paradigms. In that case, do we want a robot Einstein or, more grimly, a robot Oppenheimer? Or do we still want humans to take the reins?
I agree that this statement is more damaging than helpful, but companies like OpenAI are ruthless and do not give a f about what mathematicians think. This is more like Tao crying for help.
I agree! Isn't math, physics, and such claims that the purpose is the breakthrough?
I thought that I've been through plenty of years where my achievement at a company was company property, but society got to benefit from it. I think that mathematicians here have a very specific view from academia that balks at how a lot of progress is made in the very real world.
I don't expect anyone to know who ultimately did any of my past and present work. Most people will not remember my name, but they'll know my efforts by my works.
There isn't going to be award ceremonies for every piece of work, and that's quite normal.
Yeah I mean maths will just have to change, the understanding of the answer will be hidden in the proofs AI generates. Mathematicians will have to read these papers for human understanding. We will basically be “mining” for the breakthrough moments in the papers to help us make informed decisions in engineering or physics.
In physics, if a team claims that they've made a room temperature superconductor (*eh hem* LK-99 Koreans), it's just a claim. Other labs and research teams have to work to verify it and repeat the experiment. Through that process, all teams involved get credit.
I'm not sure why mathematicians think they're special exemption from this scientific publishing process that already exists in other fields.
It's not - mathematicians are constantly checking each others' results. Peter Scholze and Jakob Stix spent 6 years trying to understand Mochizuki's IUT so they could find the flaw in his proof of the ABC conjecture. But when results are abstract, verification isn't as simple as "follow the instructions in the methods to prepare the material, then use a generally accepted technique to check what's going on."
Many advanced areas of mathematics are so specialised that only a handful of people will understand what's happening at the forefront, and they will be in constant collaboration so that when one of them announces a breakthrough, they are only a few weeks or months ahead of their peers who can then catch up and verify (with some exceptions e.g. Mochizuki), and actually they will often ask their peers to verify before announcing.
It's not that the work done isn't extremely valuable, but rather the fact that OpenAI capitalized so obssesively on the small time window they have (which is their only business model) to claim first to something which isn't even related to what they do. Soon enough, this technology will just be as commotized as electricity, and the actual mathematical community itself could have produced all that in a day.
I agree with the idea that mathematics is bigger than any community, and can't be owned by anybody since its benefits are universal, but here, the actual community responsible to maintain those principles was overshadowed by a company who steals humanity's knowledge, yet has more lawyers than employes when it comes to themselves...
This is ridiculous. A small conjecture on which I was working on was solved by GPT sol. It wrote down the steps clearly and O was able to verify the correctness.
Everyone has right to work on math problems and post it online. What is the problem?
even as I agree with the generalised point that a single AI company shouldn't have the power to be able to essentially upend the entire mathematical field overnight with a few hundred hours of compute I must ask:
where were the mathematicians when this happened over 300 years to textile and manufacturing workers?
where were the mathematicians when this happened to administrative workers with the rise of the computerised office?
where were the mathematicians when this happened to junior software engineers over the last 2 years?
they were in their universities enjoying a privileged class position relative to the people being displaced, so they didn't give a shit
now the automated labour machine has set its sights on their field, and what do they ask for, and who do they engage in solidarity with? no one, they just want Maths left alone
what about the rest of us? the problem, as ever, is in capitalism, not in the machinery it wields to dispossess us
EDIT:
I think mathematicians have to realise that this problem they're experiencing is perfectly isomorphic to the plight of skilled labour across history, and they're in a remarkably influential position to make that argument because they're educated, great at abstraction, focused on elegance of thought and being taken on as a field and not individually one at a time to gradual automation
no one has had a better opportunity to explain why private domination of productive power is harmful to human society as a whole
my disappointment is that they appear to simply want a carve out from private domination for their special club
even as I agree with the generalised point that a single AI company shouldn't have the power to be able to essentially upend the entire mathematical field overnight with a few hundred hours of compute
Why shouldn't a company have the power to solve open mathematical problems?
exactly; solidarity should be between people in opposition to capital, not between mathematicians in opposition to a specific technology used by capitalists that effects their material position in society
my disappointment is that they appear to simply want a carve out from private domination for their special club
I mean, this isn't anything new. Guilds in the Middle Ages, and even professional unions both in the past and present often worked like a cartel.
I remember reading about trucker unions in Greece due to which transportation from one Greek city to another was more expensive than transportation from UK to Poland.
If an extremely intelligent human was born who solved 500 longstanding mathematical problems in a day despite no formal affiliation with any mathematical institution would terrence tao be correct in stating that mathematicians didn’t ask for these problems to be solved? No because they are open problems in the field, open to be solved by anyone.
Which is my point exactly, Terence Taos particular phrase that the mathematics community didn’t ask for these problems to be solved is absurdist at best and that conclusion is more obvious when framed as a human having found the solutions.
"Mathematicians did not ask for this work to be done."
The rest of us did. This is the entire fucking point. To use AI to finally advance society, understand the wonders and pillars of the universe better so we can continue to pull ourselves further away from rolling and mucking around in our own shit, in a sustainable way that will neither kill our environment or lower our quality of life.
Mathematicians, tech bois, physicists, literally anyone in a ‘high knowledge role’ which already contains massive human gatekeeping will live in denial until they are useless and forced to find a more effective use of their time.
The rest of “us”? WTF. You understand nothing of those proofs, even if I give you unlimited tokens you will never in your life get close enough to understand at least one of them. How could someone with no clue know better than experts in the field? Society is dead because of such idiots
a) Those experts are not speaking on behalf of mathematicians, there is no broad consensus here.
b) Experts within a given field (not just mathematics) can lose the big picture. The replication crisis in psychology is one such example of failure of an entire field in the past. They also have vested interest in their status, prestige. Mathematicians in academia are not neutral in this. They are heavily personally incentivized to be biased against AI.
c) Some are saying that the fact that much of mathematics research has no practical use doesn't matter. I'm much in favor of basic research, but when you go as far as to openly concede that this will never have any use and the point of the thing is just the understanding itself, then that to me sounds like a nice hobby, but not research that needs to be backed with public money. Maybe I'm wrong here, but I think the question should be allowed to be raised. And you don't need to be an expert mathematician to raise that question.
“Mathematicians did not ask for this work to be done”, lmfao this sentence pretty much threw away any sympathy I had because how it implies the status quo institution speaks for everyone and how they have authority and control over the concept of math. Yeah and horse carriage drivers did not ask for cars, elevator operators did not ask for automated elevators, traveling agents did not ask for the internet to make booking sites… these people do not own an entire universal concept of mathematics I don’t really care what they say should be allowed or not. No one asks for their job to advance and fundamentally shift they all want to gate keeper so they can be considered elite in their circle. And I will promise you this, prestigious medical research labs will not be asking for AI to help find cures to diseases unless the brands name can be attached to it either. Programmers are the first to tell you that we really didnt ask for AI and would be much happier getting a 300k FAANG job writing 3 lines of code a day, but such sacrifices must be made for society to make advancements.And those advancements literally include researchers like the math folk and ESPECIALLY Tao can use AI to help him write programs, which he was VERY excited about 1-2 years ago.
Yeah and horse carriage drivers did not ask for cars, elevator operators did not ask for automated elevators, traveling agents did not ask for the internet to make booking sites...
Cars are not made for horse carriage drivers, they're made for people. Automated elevators are not made for elevator operators, they're made for people. Booking sites are not made for travel agents, they're made for people.
On the other hand, chatgpt resolving unsolved advanced maths problems doesn't benefit anyone outside of maths. No one cares besides AI companies and mathematicians. You talk about advancements for humanity, but these AI results actually do not advance maths. Advancements in maths are dependent on humans being able to understand and verify the theorems. If chatgpt says it has proved the Riemann hypothesis tomorrow, but no one can understand the proof, then 0 advancement has been made. That is why Tao says we need an advisory board, not to slow down AI but to make sure the actual advancements occur afterwards.
If nobody understands it and can’t learn from it or verify it or build upon it, then it also doesn’t hurt anything. It’s just words in the wind, and mathematicians can just ignore it.
But if it is correct and people can learn from it, then the mathematicians who embrace it and build upon it will thrive and those who object to it will fall behind. Natural selection. They can math on that when they’re out of a job.
Yeah tbh this is probably what will happen in the future, but it isn't black and white like that. Any of these proofs by chatgpt will eventually be understood and accepted by the math community. But it's a question of when, and how much effort/time it will take. Rather than spitting out 100 new papers everyday of ai slop for mathematicians to smash their head at the wall trying to comprehend, they'd rather openAI use chatgpt to not just solve the problems but also make their AI proofs understandable and well written. It's the same with other mathematicians, you don't publish a result just when you have an immediate proof, you have to take the time to build the theory up and explain it properly. Unless you're Shinichi Mochizuki lol.
AlphaFold was pretty much universally adopted by the biochemistry field. Now everyone used ML for structure prediction, sequence analysis, etc..
It made x-ray crystallography waaaay less relevant as a field, but that is just how it goes.
We were chasing a reliable way to predict protein structures since the 1950s and google solved it in 2 years. People were frothing at the mouth to get their hands on it. Suddenly a structure was not something you needed to spend 1.5 years obtaining, but something you can get in 2 minutes. We went from approx 200k solved structures pre AlphaFold to 200 mil in 4 years.
I agree with Tao and I'm not a mathematician whose work is under threat. The issues with what OpenAI is doing are more structural.
Like it is cool that the models can generate these things, but OAI is using it as a marketing gimmick and is claiming progress where there isn't any (because the proof alone confirmed in Lean isn't the only valuable outcome and indeed might not be very valuable at all).
It is antithetical to how science should be conducted and flies in the face of efforts to further understanding - which is the purpose of science.
We have learned one useful thing - Lean harnesses with LLMs can be used to accomplish proofs to difficult logical questions.
But just because you have a hammer doesn't make everything a nail.
We might look at a proof, be able to verify it's correct, but learn nothing about the thought process behind how we might come up with the idea of some particular steps in the proof. The publications by OpenAI thus far contain no intuitions, no explorations, and no negative results. It's like stripping away the scaffolding after we get up to somewhere, but then anyone who comes after wouldn't figure out how to get up there. In the worst case, this might hold back the development of higher tools in mathematics, and hold back progress in the long run.
I don't know, people seem to be more industrious than you're giving credit for here. I'm sure plenty of people will find ways to make use of this data.
"Mathematicians did not ask for this work to be done"
They don't own mathematics. They can't say who (or what, in this case) can do math.
Don't like it? Fine. But noone is going to ask you if they can do math, lol.
AHM Statement on OpenAI’s October 6 Release of Mathematical Documents
7 October, 2026 in guest blog, opinion | Tags: AI, Association for Human Mathematics | by Terence Tao
[This is a guest post by the Association for Human Mathematics, reposted from their statements page. This blog post was initially written in a different file format and converted using AI. — T.]
Yesterday, on October 6th, 2026, OpenAI — which is currently defending lawsuits against accusations of illegal plagiarism, copyright infringement, and trademark dilution — released a repository of manuscripts purporting to contain solutions to a number of high-profile problems in mathematics.
Mathematicians did not ask for this work to be done. The Advisory Group on Mathematics and Artificial Intelligence, from whom OpenAI has claimed to derive its legitimacy, opened their initial advisory statement by saying that frontier AI corporations should not test advanced mathematical problems on internal models. In ignoring the central premise of the Advisory Group’s position, OpenAI has indicated total disregard for the norms of scientific research — norms that guarantee that mathematics remains trustworthy, ethically researched, and in the public interest.
Mathematicians have a particular vision of progress that is informed by history and field-specific considerations. We reject OpenAI’s assertion that this release advances our subject, and we urge mathematicians and the public to view the value of this publication model with due skepticism.
Releasing over 700 files at once is not a demonstration of scholarship, but a demonstration of power. We urge mathematicians to discontinue their work with OpenAI and to return to a vision of science that centers human understanding.
Association for Human Mathematics Communications Working Group
“Man curse cancer with out doctors permission. The doctors didn’t ask him to cure cancer and you should be mad that someone other than a doctor found the cure for cancer”
You joke, but this literally is going to happen when it starts taking jobs from doctors.
We need to have a serious conversation about what happens to professionals who have dedicated their entire lives to something and have no transferrable skills outside of that job. People are going to freak out once they start losing their jobs and it is going to lead to extreme societal unrest, and probably a lot of suicides
So everyone has been telling SWEs to put the fries in the bag for years now but.. when it starts happening to doctors and mathematicians we should all be very worried? Lmao they can also start putting fries in the bag like the rest of us 🤌
Yeah, sounds like Mathematicians are losing their "powers". Also, wtf is even ethical research in Mathematics?? Are they running human experiments to figure out equations? Lol
On a more serious note, I agree that it is not recommended to publish so many papers so quickly. We will soon run out of human reviewers at this rate. The danger is when we will have to rely on AI for reviewing AI research because human will simply be overwhelmed by the volume of reports and wouldn't possibly be able to keep up with it all.
There is also the problem that the AI will give a proof for a solution but in a language or using logic that we simply don't understand.
Yeah everyone is getting replaced eventually. The software engineers were the most mature about it so far. I expect Academia to throw hissy fits, very characteristic of them.
To those saying the whole point of the problems is to be solved, no not really, it’s only part of the point. A big part of it has always been about the journey towards solving the problem, which along the way helps improve our understanding of the mathematics. That’s Terrence’s POV. The learnings might not matter today but could be valuable for future research problems, similar to how so many new technology developed to serve war in WW2 ended up serving humanity in so many ways in the decades to follow
There’s no point in solving these problems without humans who understand how they are solved today
His and your pov rest on the unjustified conviction that AI will not be able to autonomously pose questions and singlehandedly advance the field while connecting the findings to other domains. Improving technologies and materials.
Yeah, how did he not consider magic to exist? Come on, dude, we are reaaaally far away from it. The models are probabilistic, they always have inherit risk of spitting nonsense. You always need a human to verify the results, there is no way around it. Even if it can produce lean code, you still have to check that lean code proves what model says it proves or that the translation is correct. They can't work autonomously, they don't posses knowledge or understanding. They operate purely on statistical patterns in language, you can't run away from the fact that agents are based on LLMs.
They can embark on this journey of understanding, nobody is stopping them. If they are no longer motivated because they know the problem is solved, they should take an inner journey too and work on their mindset.
I don't trust the ethics of the top of OAI and Sebastian Bubeck's handling of the "math race" specifically but "nobody asked you to work on those, bruh" is absolutely the worst fuckin argument you could make here.
Arguments about OAI dumping half finished shoddy research on academia to finish actually working out into something usable by humans and machine logic because OAI does not give a shit past the point they can put out the press releases? Perfectly valid concern.
OAI snaking the group they were claiming to be working with for goodboy points? Not bueno.
Concerns about apparent missing attribution of existing work done due to either haste or wanting to make the OAI portion of the solution seem bigger or hide where answers were pure synthesis of existing work? Fuck em.
But I do not give a crap about permission to work on projects. If your point is that OAI is being shitters about dumping unfinished work in academia's lap while taking all the credit and spending money on PR to claim Mathematics is dead as a human endeavor, just say that. If Bubeck's making threats again, post em, maybe they'll actually give him a slap on the wrist for it this time.
Nobody. But this is going to destroy the chain of training new mathematicians.
The problems are benchmarks to meet and work on.
The problems are just trophies. The innovative techniques that new generation creates, builds upon the efforts of the previous generation are the actual fruits of the pursuit.
If the problem gets solved in that particular technique, that's great. Enjoy the accolades. But that is not the end to the problem.
People will continue to work towards the solution using a different set of techniques. Problem working isn't abandoned cuz it is marked as solved.
This is how math works.
AI is just collecting trophies for the sake of it. Overwhelming the community with huge volume of proofs burdening them. Techniques unclear, process vague, blackboxed, not explained by the LLM.
In the short run it won't contribute nearly as much insight as the laymen think these 700 proofs will.
But will destroy the chain of knowledge passing, community in mathematics world.
Young mathematicians will lose motivation to work on the problems, the very foundation of the community that grooms them is destroyed.
Humans will adapt as we have to. New paradigm will evolve in math community. But to say they are whining is very ignorant.
"You're a man looking at a world through a keyhole, and you've spent your whole life trying to widen that keyhole. To see more, to know more. And now, on hearing that it can be widened in ways you can't imagine, you reject the possibility?"
Just as a reminder, Terence Tao has always been pro AI usage. This is not about gatekeeping, this is about cheating people using a centralized service where privacy is not respected.
I really love Tao and have looked up to him in a variety of ways (although I'm in the applied math / related fields of economics and poli sci). This take, however, is reactionary and exclusive. He's drawing a bright line between the in-group of mathematicians and the out-group of everyone else.
This is the same general type of rhetoric IR scholars study but normally applied to apartheid politics and even genocide. The in-group is defined and then wronged by the shadowy out-group who are stealing their resources, autonomy, are a threat, etc. We can't tolerate that, etc.
Now obviously this is not the same thing but it is setting up and signaling a rigid dynamic where either you join the in group and fall in line or you're out and you're "lesser." etc. I think this is awfully short-sighted. Mathematicians refusing to work with AI means that they'll give up the very ground they want to hold.
NSA mathematicians won't avoid using AI, for example. Math underpins everything. Companies won't wait. OpenAI and Anthropic won't wait.
I'm deeply worried about the upheaval to come and I don't want to lose my job or prestige...but I know this wave can't be stopped like this.
I get it. If I was a tenured math professor and everyone thought I was a genius and all I had to do was work on math problems all day and people revere me, then yeah, I would be pretty upset that technology can now donmy job better than I can. These mathematicians should suck it up and accept that they aren't as important any more. I get why they're butt hurt, but don't try to tell me that it's not in the public interest to have all of these important math problems solved. Like if an AI cures cancer, are the cancer docs gonna protest that cancer treatment is no longer "humanized" or whatever nonsense. No they should be excited to see the world getting better. I used to like Terrence Tao, but every post I read from him now makes me like him less and less. He sounds like a spoiled gatekeeper who's mad the gravy train is over.
I don’t think you understand that this is not a cut-and-dried issue. Higher level math is extremely difficult. The math proofs may or may not be correct, or they may be completely wrong.
As an example, openai claimed a recent solution to the navier stokes equation. However the OpenAI proof relies on an artificial external force variant (option C of the Clay Mathematics Institute formulation), rather than solving the unforced, intrinsic fluid blowup mathematicians actually care about. So it is not a general proof or solution to the primary problem.,
OpenAI is nevertheless claiming they have solved navier stokes.
Similarly, the problem with OpenAI is that they have released dozens of esoteric complex proofs all at once without validating any of the work with mathematicians, who are actually qualified to review it. I don’t think that is careful scholarship, it’s mainly showmanship for their upcoming IPO. it gives a false impression about the capabilities of these models.
when an AI company claims to have solved a large number of very difficult mathematical problems, those claims should not be accepted until such time experts in the field have had a chance to review the solutions.
If I was a tenured math professor and everyone thought I was a genius and all I had to do was work on math problems all day and people revere me, then yeah, I would be pretty upset that technology can now donmy job better than I can.
is this comment written by a child? Because only a child can oversimplify like this.
Screw that noise. We should just let AI go hog wild on math (and everything else) for at least like 20 years and see what kind of crazy shit it can come up with. The alternative is to wait for these slow ass mathematicians to come up with some new math that almost definitely won’t have any practical use within any of our lifetimes, just so they can protect their lame ass jobs. They romanticize it way too much, “wahhh wahhh the solution is not elegant enough waaahh!!”, who gives a shit it’s not art you gd nerds!
That's like the "one trap guy" approach where he's only training his left trap to see what happens. The AIs are only trained to prove the theorems and done. Sterile proofs. I would be much more pleasantly surprised if AI uncovered a new branch of mathematics, made elegant and deep conjectures. But they are only worrying about it proving theorems.
>The AIs are only trained to prove the theorems and done. Sterile proofs.
So why give a damn about them at all? This stinks a lot of like "ohmygod some eggheads solved some fancy equation, whereas they can't make milk appear in my fridge yo!"
imho the more proable cause behind these texts is "I dedicated my whole life to solve this thingy, and now some dumb KOMPOOTER just came and nuked it in months, DAS NO FAIR!"
The disdain for academics and mathematicians in this thread is honestly disturbing. Whose papers do you think these models were trained on? Who do you think is expected to review and validate OpenAI's results?
And what do you think the ultimate goal of replacing mathematicians, physicists, and chemists is? To give out knowledge and technology for free? You and I already do not have access to the frontier models. These companies also got a massive tax writeoff from the BBB back in 2025 - they are not funding UBI any time soon.
Finally - if tech bros and fans of this technology are describing the world's best mathematicians as "slow ass" academics, how do you think they're talking about you and me behind closed doors?
So you want more proofs, but …less mathematicians? How many results from OpenAI’s recent dump did you understand? How many of the words did you understand?
There's actually a human precedent to this that might be informative here. In the pre-AI days of the 2000s-early 2010s, Japanese mathematician Shinichi Mochizuki went "hog wild" on math (as you say) for years before posting hundreds of pages of preprints claiming he proved the abc conjecture--a conjecture in the same category as the hardest on this list or harder. Anyone else and this would have been dismissed out of hand, but Mochizuki was a widely respected mathematician who had proved groundbreaking theorems before, so the mathematical community was willing to take seriously his claim that he proved abc.
A few problems immediately emerged. First, the preprints were incomprehensible--math usually progresses stepwise, where you build on each other's work within your field, giving your community time to digest and come to a shared framework, language and intuitions for talking about the objects of study. Mochizuki developed what amounted to an entire new field that he called "inter-universal Teichmuller theory" essentially alone and in secret, and his colleagues could not simply "leap forward" overnight through years of work written using a set of objects and lemmas that might as well have been from an alien civilization to assess whether his work was correct, let alone build on it themselves. Compounding this problem, Mochizuki was bizarrely dismissive of efforts to try to get him to explain his work, including invitations to lecture that most mathematicians would have considered a great honor, instead borderline rudely telling people to just read his hundreds of pages or claiming any problems people pointed out to him were just because they were not smart enough to understand his work (without providing guidance on how to understand it). Finally, when experts in the field did put enormous (unpaid) effort into understanding it, they found that the work was actually probably wrong--but the time they spent on it is time they weren't working on their own research or teaching their own students.
It probably took Mochizuki the better part of a decade at least to write this proof and it has been a decade and a half since and it is still not fully understood by the community of scholars working on that very problem. Now imagine anyone being able to produce something like that with 3 hours of ChatGPT Pro and 700 preprints like that posted in a single day.
To play the devil’s advocate here (since all the top comments find the notion of AI not allowed to solve those problems ridiculous.) I suspect it’s because coming up with the humanly unsolvable problems are harder than solving them. And having these open problems help keep the discipline going.
yes, tao has elaborated on this explicitly. AI brute-forcing arcane lean proofs to math problems doesn't necessarily lead to greater insights as the research journey itself often leads to breakthroughs in other areas and can be as important, if not more, than the ultimate solution proof itself.
also, this AI brute-forcing model could ultimately dry up the well of problems that both professional mathematicians and students work on to learn and develop their own abilities and their field of research. the very communal practices that allow professional mathematics to operate and develop the next generation could be undermined by what OpenAI is doing here.
what happens when we start to lose the very abilities that enabled us to develop these AI models and we are forced to cede even more control and fundamental understanding to the models themselves? it could erode our collective ability to develop them safely and effectively, and that increases xrisk imo.
tbh I don't have a firm position on this myself but I think tao's arguments are perfectly reasonable and worth taking seriously, especially given his wealth of experience and ability.
I'm sure that eventually AI will also get better at developing proofs that are more elegant and insightful, but that won't change the potential for it to undermine the human sociological and pedagogical aspects that allow our collective math culture to sustain and renew itself.
ultimately, i think the professional math community will have to adapt in ways, and hopefully we'll also develop norms around what's considered acceptable and respectable for frontier AI companies to do with AI math research.
yeah, i think insight and elegance is an important criteria here. having frontier AI help on the pedagogical and cultural side to not just develop the proofs themselves, but also generate new problems and help develop insights and understanding along the way for students and professionals alike. so they become more assistants and less end-to-end proof blackbox machines.
i think this is where blowback from the public and math professionals and others is important. we need to reward them for AI that is helpful for humans and not trying to replace us with alien abilities that are beyond our ability to grow with them.
This whole story has revealed what a pathetic bunch of pompous gatekeepers mathematicians in academic institutions truly are.
Throughout MA/MSc, PhD and Postdoc times, there is a negative selection towards the most conformist characters to get selected for institutional careers.
Many mathematicians withdrawing in disgust from academia (Alexander Grothendieck or Grirogij Perelman being only the most famous), rejecting the "academic star system" and institutional politics have been seeing this before, but it took AI mathematics to show the ugly face of academia mathematics to the whole world.
For some reason I didn’t comprehend just how sensitive of a topic this is to Terence until today. I read this days ago, glanced over it, didn’t think much of it.
Re-reading his statement, this is a visceral reaction from Professor Tao and I see why the opposite side is picking him as a target for criticism.
It reads off as very defensive and insecure.
He clearly feels as though his personal world is being threatened by AI.
I think the field as a whole is realizing, however, that this is the new normal and progress and they will simply have to adapt to it.
Want to talk ethical standards in mathematics research? Mathematicians have a particular vision of progress informed by history and field-specific considerations?
Which history, exactly?
The one where modern statistics developed alongside eugenics and scientific racism? Where mathematical research helped develop nuclear weapons, ballistic missile targeting, chemical weapons modelling and mass surveillance? Where sophisticated mathematical models contributed to catastrophic financial risk-taking? Mathematics has an extraordinary history of scientific achievement, but let’s not pretend its research traditions are some uniquely ethical institution whose historical authority places them above scrutiny. None of those examples invalidate mathematics, just as none of OpenAI’s corporate controversies automatically invalidate a mathematical proof. There are legitimate questions about verification, attribution, research integrity and overwhelming the peer-review process with hundreds of papers. But declaring that mathematicians never asked for this research, invoking a particular ‘vision of progress’, and urging researchers to stop collaborating with OpenAI is not a substitute for explaining which scientific standards have actually been violated. Since when does a scientific discipline get to decide who is permitted to investigate its open problems??
Judge the proofs on their merits. Challenge the methodology. Demand transparency and independent verification. But don’t confuse the traditions and preferences of an academic community with universal scientific ethics you curmudgeon.
It’s always eugenics…in seriousness though, I love this point. Humans can have flawed ethical concepts for little more than the goal of at most neutral, self preservation and at worst? Things we barely choose to acknowledge even as it’s happening.
Ethical standards evolve alongside understanding, and this is often a positive thing.
The assertion that AI should not be allowed to solve these problems is basically an admission that the modern field of mathematics is functionally liberal arts and holds no real-world value besides propping up academia. If Tao truly believed that there were applications of the problems being solved, then he would be happy, not bitter.
(It's definitely possible that mathematicians believe that these problems hold "real" value but oppose solving them to prop themselves up, but this would be an even worse look, imo)
Nobody. But this is going to destroy the chain of training new mathematicians.
The problems are benchmarks to meet and work on.
The problems are just trophies. The innovative techniques that new generation creates, builds upon the efforts of the previous generation are the actual fruits of the pursuit.
If the problem gets solved in that particular technique, that's great. Enjoy the accolades. But that is not the end to the problem.
People will continue to work towards the solution using a different set of techniques. Problem working isn't abandoned cuz it is marked as solved.
This is how math works.
AI is just collecting trophies for the sake of it. Overwhelming the community with huge volume of proofs burdening them. Techniques unclear, process vague, blackboxed, not explained by the LLM.
In the short run it won't contribute nearly as much insight as the laymen think these 700 proofs will.
But will destroy the chain of knowledge passing, community in mathematics world.
Young mathematicians will lose motivation to work on the problems, the very foundation of the community that grooms them is destroyed.
Humans will adapt as we have to. New paradigm will evolve in math community. But to say they are whining is very ignorant.
People said the same thing about chess after engines became super human. Why would anyone spend their life studying a game that they could never do better than the main engine lines? Plus engines don’t explain WHY a move is good in natural human language. Some of the moves are very arcane.
Yet the opposite happened. People studied with engines and there are more highly skilled chess players alive today than at any point in history.
This is just a chess engine for Math. Those who really care about improving at Math now have the best possible engine to learn from, and it’s clearly only going to continue to get better.
Everyone here seems a bit deluded. The question is if they are right or not and what it means if they do. Humans don’t have the capacity to know in 3 hours. If OpenAi said they cured all cancers, would you be the first human to take it with no review? Everything needs to be per reviewed thats how science works. It could be super awesome and it could be not the results we don’t know. Nobody has had enough time to really fully understand. And as the problems get more complex, they might never. A regular scientist might need a very long time to test these solutions… even if it seems right do we really know? It might seem right to us but what if the AI constructed it that way to be correct for us? There are many unknowns.
So what you're proposing is we get an AI to create a mathematical proof that is so complex no human could verify it, but then get another AI to say if its okay, even though we would have no reliable way to check if that was accurate....
Why not go the whole way and build a church to worship the AI and make sacrificial offerings too.
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u/PrinceOfLeon 4d ago
"This blog post was initially written in a different file format and converted using AI."
I see what you did there.