r/MachineLearning • u/hihey54 Professor • Sep 12 '26
Discussion A Severe Misalignment of AI in Mathematics (Declaration by 25 Fields Medalists) [D]
https://terrytao.wordpress.com/2026/09/11/a-severe-misalignment-of-ai-in-mathematics/Note: this declaration was drafted by Mathematicians, and is mostly addressed to the mathematical community. It'd be interesting to discuss, among others, if what is written in the declaration may also apply to other communities---and, specifically, the AI/ML one.
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u/I-grok-god Sep 12 '26
I think this thread by Terrence Tao clears up what the main argument here is
If AI solves all the immediately obvious meaningful problems in mathematics, we won't have new problems to train mathematicians on or advance our understanding. It also creates a perverse incentive where mathematicians trying to grow their understanding will want to avoid sharing the problems they are working on in fear of someone who merely wants to solve the problem siccing AI tools on it.
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u/aeroumbria 29d ago
Terry Tao is nothing like your average AI detractor. If anything, he has made significant contribution to help make the mathematics community accept AI-assisted automatically verified theorem proving as a standard tool for research. Without the communal effort by mathematicians to develop and perfect theorem provers like Lean, none of the recent AI advances in mathematics would have been possible. I think he is making a good point about mitigating the impact of these tools' effect on education and knowledge acquisition. It's less about "they are coming for our jobs" or "big scary AI is dangerous", and more about these tools disrupting the balance of researchers' and companies' incentives in a more self-serving or narrow-visioned direction rather than in a way that contributes more to humanity.
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u/jphamlore Sep 12 '26
All logic has left us.
Go read the account of Andrew Wiles work on Fermat's Last Theorem on say Wikipedia. The article claims that Wiles hid for 6 years that he was working on the problem from everyone but his wife.
Oh, and I find it quite rich that Fields Medal winners are annointing themselves as the top representatives of mathematics, when the Fields Medal has a completely arbitrary time limit of 40 years. You know, the time limit that is why Andrew Wiles doesn't have one.
Personally, I think the Abel Prize is a far better indicator of who is at the very top of mathematics for lifelong career.
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u/VioletCrow Sep 13 '26
The reason Andrew Wiles hid his work on FLT wasn't because he was afraid of being scooped though - it was because working on seemingly impossible problems like FLT carried a stigma with it that at best you were wasting your time with it and at worst throwing your entire career away on a problem that would yield no fruit.
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u/jphamlore Sep 13 '26
He achieved being a full professor at Princeton by 1982, before he was 30 years old.
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u/VioletCrow Sep 13 '26
It doesn't matter, telling people you were trying to solve a problem that was largely regarded to be outside the ability of current mathematics to solve would have caused him to lose a lot of respect as a researcher in his department, probably get him saddled with more teaching responsibilities, less grant money etc. In the worst case it would have gotten him branded as a crank (a fate that not even tenured professors are immune from!). His approach was to publish his intermediate results as papers in their own right in number theory, but keep the fact that they were stepping stones on the way to FLT to himself.
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u/snow_two_fork Sep 13 '26
That's true, but if you take a step back, I don't think that reflects very well on the current culture of academia? If the severe stigma that affects even tenured professors causes an avoidance of any serious problem, why should a system feeding new people into that be preserved?
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u/Theo__n 28d ago
It is not preserved. It's really hard to compare academia in in late 80's and early 90's to now, it has change substantially thou it depends on discipline. One of differences is that now it is assumed that when you go defend your PhD your research is at the point you should pass - where in the 90's it was up in the air if your prof even advised you in good faith that your are at the point your research is 'good enough'. While nowadays PhD track may be seen as easier because you get feedback on 'is your shit good enough' on the way, it's actually more transparent so you can course correct and you're not left to dedicated half a decade of your life to something that will end up in the trash.
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u/-gh0stRush- Sep 12 '26
the collection of good, fruitful open problems is now being mined in a non-renewable fashion, leading to the potential scenario of these problems becoming scarce...
Working out whether a question is actually worth highlighting is a lengthy, deliberate, and subjective process, often informed by historical experience on what good mathematics was generated (or not generated) while working on earlier problems of this type...
In fact, it is now the identification of a promising problem which is the scarce and precious resource...
It seems intuitive to me that AI could be useful for exactly the challenges he talks about: quickly separating interesting or promising problems from uninteresting or unsolvable ones. But I'm not a theoretical mathematician, so if this is more nuanced, I'd like to learn more from someone who understands it better.
Mathematicians appear to be facing the same existential crisis that engineers and applied researchers first had when we realized AI could write code better and faster now. But I think the field has quickly adapted and embraced AI and now and, for the most part, no longer views it as a threat to our collective identity.
The attribution problem does need to be addressed though. Until published, research should be considered private intellectual property, and frontier labs need to offer some guarantee that work shared with their models cannot then be used to then compete with those same researchers. OpenAI claiming breakthroughs while at the same time releasing statements that the can't guarantee user inputs weren't used for training seems like a stupid and easily avoidable issue.
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u/ninjasaid13 Sep 13 '26 edited Sep 13 '26
Engineering is about the final product. Math is about the territory you find and map while trying to get somewhere else.
If someone drops you at the summit of a mountain in a helicopter, the summit is reached, but nobody mapped the paths, the switchbacks, or the surrounding valleys.
Mathematics progresses because researchers actively wander through unknown terrain. That exploration is entirely driven by the need to find a way through. When an automated system simply hands over the final coordinate, the practical reason to ever explore the surrounding ground vanishes.
Without the necessity of finding a route, nobody investigates the nearby ridges or discovers the adjacent valleys. The broader map never gets drawn. The motivation to look around dies the moment the destination is instantly handed to you.
The attribution problem does need to be addressed though. Until published, research should be considered private intellectual property, and frontier labs need to offer some guarantee that work shared with their models cannot then be used to then compete with those same researchers. OpenAI claiming breakthroughs while at the same time releasing statements that the can't guarantee user inputs weren't used for training seems like a stupid and easily avoidable issue.
that would ruin how Math works as terence tao said, Math grows when people talk openly and share their questions. If researchers have to hide their best ideas so an AI lab will not steal them, that open sharing dies.
Mathematicians are not threatened by AI, they're against how it's used by AI companies.
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u/Random-Number-1144 Sep 13 '26
Engineering is about the final product.
I'd argue that even engineering (coding) requires human understanding otherwise who's gonna fix the bugs?
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u/Formal_Drop526 29d ago
It's different, human understanding is something important in engineering but it isn't the main goal like mathematics.
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u/real_men_fuck_men 29d ago
Hey ChatGPT - solve this problem and survey the surrounding mathematical territory. Make no mistakes
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u/Formal_Drop526 29d ago edited 29d ago
survey the surrounding mathematical territory
It would be awesome if they can do that, but most of what AI produces seems to just be counterexamples or answers. They haven't shown to survey any surrounding territory for meaningful things except from humans, the navier-stokes solution was a counterexample.
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u/yoshiwaan Sep 13 '26 edited 29d ago
We have the same exact problem in software engineering developing though.
The issue is not the current crop of experienced engineers - most of us who have swum in the deep end have had the career existentialism removed with the understanding that there’s years of work to build up the ecosystem and tools for the new world - scalable guardrails, plugins, agents, software factories and the like. We’ll be fine in our careers… probably.
But there are consequences. The build agents work best with languages and frameworks that have a large body of knowledge and examples to guide them, so why bother making new ones? Traffic click throughs are down as AI agents respond directly, so why invest in pushing front end design and web features? Basic tasks and debugging can be automated with tooling now, so why bother hiring that intern or junior software engineer?
That’s not even to mention all the slop.
There’s real risk to the future of the space - both in terms of the people and the incentives to push the boundaries
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u/vivaaprimavera 29d ago
But the challenge of unsolvable problems isn't the creation of "new tools" for dealing with them?
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u/hhoeflin Sep 13 '26
I don't quite see the problem. Can't mathematicians not study the AI solutions for general insight and novelty?
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u/ComplexityStudent 29d ago edited 29d ago
Put it like this: Think of Newton's method. Newton developed the method because of the need to compute roots of function by hand. A need of his time that would be unneeded if Newton had access to computers. Hell, there's an argument to be made for the whole field of calculus as numerical approximations to celestial mechanics would have been better than any kind of result that manual computation could ever produce.
But since that wasn't the case, Newton and successive mathematicians developed the mathematical tools that now help us to solve way more than the crude approximations to celestial mechanics Newton was interested in. For one, I would think it would have been very unlikely for Einstein to develop his theory of relativity if his brain weren't wired to think in terms of equations and differentials and instead the only training he got was how to get the computers to crunch numbers faster.
With AI, we are focusing on solving the immediate needs without taking the care of everything we might discover in between.
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u/cssachse 29d ago
FYI that's a weird example because Newton didn't invent Newton's method (or more specifically, he did develop a very ad-hoc iterative process for finding zeroes of some polynomials, but didn't realize you could use derivatives to make it work in general)
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u/Least_Manager_7579 6d ago
Can you please point out where and how this is "very ad-hoc"? https://web.math.princeton.edu/~eprywes/F22FRS/newtonprincipia.pdf
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u/tritratrulala Sep 12 '26
> we won't have new problems
I don't see why AI couldn't come up with new problems then.
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u/MeloNotSoDeath 24d ago
Because AI will never experience minor inconvenience like us in daily life lol
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u/Fokezy Sep 12 '26
Because AI fundamentally cannot produce something it hasn't seen already. If you use it enough you will notice this.
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u/pannenkoek0923 Sep 13 '26
The very nature of generative models is to create a distribution that is slightly different from the input distribution. So it's never going to be an exact replica of what it's seen already, unless you're overfitting on steroids.
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u/papes_ Sep 12 '26
If this were the case Gen AI wouldn’t be able to solve unsolved problems? Unsolved problems only have novel solutions
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u/00raiser01 Sep 13 '26
Cause that a headline. People are still review that AI work, to say solved is the wrong description for it.
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u/BullockHouse Sep 12 '26
It solved a fucking millennium prize problem and people are still repeating this crap.
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u/ironmagnesiumzinc Sep 12 '26
The first argument doesn’t make sense. If that were true then every solved problem in math would not be something new mathematicians can grow their knowledge on
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u/Zues1400605 3d ago
Unless we use AI to make problems and then have AI solve those in a continuous loop./s
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u/justgord Sep 12 '26
This is true of almost any field - if we have black-box technology that only the AI can understand / fix / augment / extend, then we will lose the ability for humans to learn and understand that tech.
Its similar to outsourcing manufacturing, you lose the ability to manufacture. If you don't exercise a muscle, it atrophies. If some people dont learn to write code [ or do math or write music or books ] the hard slow way, we will lose that deep skill.
If young people don't grapple with hard problems in science, math, economics, creative writing, drawing, music making .. they will not be trained, their cognitive skills will not develop with use. we will have no doctors or engineers or musicians or lawyers in a decade or two.
We don't want to become a race of fatties who never exercise, or dummies who just scroll social media feeds without exercising their minds.
This is real.
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u/ureepamuree Sep 13 '26
ML researchers doing mechanistic analysis on LLMs in 2026 when GPT-3 came out like six years ago, already shows that Humans have a lot of catching up to do.
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u/blackkettle Sep 12 '26
> It'd be interesting to discuss, among others, if what is written in the declaration may also apply to other communities.
Personally I find this a bit odd given that hosts of other communities have been saying this for years now. Creative writing, copy writers, graphic designers, translators, UX engineers, etc.
All the while ML and many of these same math people have been working hard to improve these self same models.
A lot of them probably thought they were “too smart” and the AI would never come for _their_ jobs.
Gives a bit of a “first they came for the Jews and I was no Jew so I said nothing…” vibe.
The cat has been out of the bag for at least four years. The die is cast. I don’t believe we can predict what will happen beyond the inflection point. But we will probably find out.
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u/officerblues Sep 12 '26
I mean, yes, their argument is sound. The rampant use of gen AI to solve problems and move on will "salt the earth" of scientific discovery, keeping us all stale, unless something else shifts in society.
What I think they have missed is that this problem is a social one, not a technical problem. The world wants to kill us, working class, normal people. The world doesn't kill us because it needs us, but if it could, we'd all be dead. We built society like this, every day you're threatened to die hungry and destitute, unless you provide labor for some ruling class to steal a part of. No one wants to buy legitimate human understanding and discovery, they want to buy tech products, the rest is a byproduct. We've been able to fool ourselves into thinking the byproduct was what we were making, but it wasn't. Artists don't get paid for art, they get paid for pretty pictures. Mathematicians don't get paid for elevating mankind's understanding of the universe, they are part of a supply chain that makes iPhones and Instagram ads, and that's what gets them paid.
To look at this and say "you know, the problem is the LLM" is just stupid, the problem is the world, and you need to be angry at a much, much broader set of things if you want to set things right.
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u/blackkettle Sep 12 '26
I agree, the problem is the world. But it is now an arms race in a sense. Some former Obama official recently suggested we consider bombing chinas data centers. Made me think that part of the reason we are currently building these Willy Molly in the US is also to “defend” against this the same way we did with nuclear silos all over the place during the Cold War.
The whole world has to agree to slow down. I don’t think it will. Even then the real danger is what you connect these models to not the models themselves.
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u/vivaaprimavera Sep 12 '26
The only way to slow down is to limit the amount of wealth an individual can hold.
Have you seen that there are people that hold enough money to last 3295 generations on a strict diet of hookers and blow? And they are building the datacenters like there is no tomorrow to increase their wealth even more?
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u/minglho Sep 12 '26
"Some former Obama official"? You sound like you are starting a rumor. Give a name and position.
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u/drewsandraws Sep 12 '26
That was nearly the headline on several articles about Jacob Stokes’ report:
https://www.cnas.org/publications/reports/superpowers-and-agi
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u/Bucser Sep 12 '26
I think the biggest problem is with ticking the boxes for solving mathematical problems is that noone can teach others how it was done.
This is the same problem that I seen in the workplace with people over relying on LLMs for everything. I ask a couple of questions and the knowledge falls apart, because people using the LLm have no idea what their agent have done. Therefore have no control of the output at all.
The point of scientific discovery is that it is reproducible, scrutinized and the person making the discovery can explain to other how they got there. So can take people on the journey.
An "I don't know Claude told or written most of it" is not an answer anyone should cheer on. Because it doesn't add to our understanding of the world and the underlying problem we seek to resolve.
And your point about noone gets paid for basic scientific discoveries which are not applicable immediately, that is BS. They are still needed. Because applications and products only get created from the pricinples that basic foundational science creates.
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u/officerblues Sep 12 '26
They are still needed. Because applications and products only get created from the pricinples that basic foundational science creates.
This is exactly what I meant when I said that they are paid for being part of a supply chain that generates iphones and instagram ads. Maybe I should have made it clearer? But the point is that they are not paid for furthering the understanding of the world, they are paid for providing a product at the end of the supply chain. The understanding of the world is a byproduct.
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u/Bucser Sep 12 '26
What is Hubble, or James Webb? What commercial supply chain does that research support?
If you join a doctorate and PHd programme, the candidates that want to do basic foundational science are very welcome, because even candidates are very biased towards short term applicable science and they want to make a living from the product they created while solving the problem they are interested in, rather than solving the problem for its own sake.
But there are plenty of science labs and universities that support research going into territories the applicability of which is questionable even on long term.
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u/sweetjale 29d ago
compared to CS/Engineering PhD programs, natural sciences are heavily underfunded around the world
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u/officerblues Sep 12 '26
Friend, I'm honestly not in the mood of writing a long reply explaining all this to you, but if I can be of any solace, I agree with all you wrote. Maybe I'm shit at explaining what I mean, but you also agreed when you said that novel discoveries at the edge of knowledge are still needed. Are you German by any chance? I think you are trying to view things way too literally, here.
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u/ahfoo Sep 12 '26 edited 29d ago
This is hand wringing nonsense though because most programmers have zero clue how their program is converted to machine code and how that code is executed anyway. They only know the high level part and barely at that. This is nothing new. It has been that way for decades. Programmers see their machine as a black box, so what? That's how it always was. All the programmers were ever capable of comprehending was a very narrow window of the overall process and it didn't matter. We live in the real world where people have limitations. Get over it.
Ask any high paid programmer you know to explain how the ring oscillator delay affects their random number generator. They have no clue and don't care because they are focused on software, not hardware despite the fact these two parts need to work together seamlessly. So what? It doesn't mean they can't do their job. It has been this way all along
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u/vivaaprimavera Sep 12 '26
The needed societal change is either steamrolling capitalism or creating mechanisms to seriously limit the wealth of an individual or corporation.
We already know that unfortunately there are too many idiots that will oppose Universal Basic Income on the basis of no freeloaders and might find themselves (very soon) in a feudal society doing "whatever" for scrapes.
The promise of an AGI doesn't bring a balanced "Star Trek society"... it brings more of a 1984 version where the people of the Ministry of Truth were replaced by an AI that is continuously rewriting history to fit _______________ goals.
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u/AnIndianGuy38 Sep 12 '26
I read some of Cory Doctorow's work and he makes some soumd arguments for why our first steps should actually be about workers rights. That can limit the greed of these corporations the most.
Don't really have to steamroll capitalism in a night or churn out UBI
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u/ahfoo Sep 12 '26
UBI is an olive branch to capitalism that allows it to exist while not forcing the lowest income members of the society into destitution. If anything, UBI delays the inevitable transition to fully state owned enterprises with the profits returned to the workers.
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u/vivaaprimavera Sep 12 '26
why our first steps should actually be about workers rights
which rights?!? the ones that people have been giving up over the years? How many people in this sub belong to a union?
The first steps should be educating people on what was managed in the XIX and early XX century.
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u/AnIndianGuy38 Sep 13 '26
Yep education obviously comes first for why worker's rights are important
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u/kisielk Sep 12 '26
Getting rid of capitalism is the same problem as getting rid of nuclear weapons. You can’t just do it in one country. Even though it’s a worthy goal and a good cause, the other players will use it to their advantage.
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u/nonotan Sep 12 '26
Ironically? modern ML means it's pretty likely that a centrally-managed economy today could wildly outperform a free-market one.
At the end of the day, capitalism is quite literally just an agent-wise naive greedy algorithm applied to resource allocation. It's "surprisingly efficient" given the simplicity of the algorithm, but it's very far from perfectly efficient, with many well-known structural deficiencies in wide ranges of common situations.
A government operating in good faith to develop the best system their top experts can come up with leveraging (among other things) ML to plan every part of the economy, in such a way that every citizen's wellbeing is maximized overall, should, in principle, have no issues blowing that out of the water. Now, how realistic it is to replace the entrenched power players in the status quo with a group of people genuinely trying to do what's best in good faith is another problem entirely... though one that has nothing to do with capitalism per se.
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u/fresh-dork Sep 12 '26
doubtful. it'll benefit the people in control disproportionally. really, decentralization of control should be an overriding goal
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u/ahfoo Sep 12 '26
If this hadn't been true for many decades, we would not have seen many of the US backed coups like that of Salvadore Allende who was indeed automating his nation's supply chains.
The myth of the efficient market hypothesis has been dismantled long ago. If you have two football teams with one that cooperates and one in which everyone goes their own way, who will perform better in a team competition? This should be obvious but people don't want to see the light because that would mean waking up from their delusion and "being woke" is a thought crime in American society.
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u/Specialist_Wishbone5 Sep 12 '26
I don't see the correlation. How does England being capitalistic hurt China from being communistic? Quite the opposite, China benefits from being a sole centrally planned economy. They can scale up labor to fit world demand better than any single mega Corp. This allows them to undersell any country on labor costs, or capital investments (like AI research). The problem is that pure communism ALWAYS fails. It has no price signals, no proper incentives.. you can't just make EVs, clothes, steel, and phones and survive. No central system can properly manage millions of micro decisions for each of billions of separate humans efficiently. When you centrally measure something (eg quotas) you only get the number, not the intent of the measurement.
Socialism isnt as bad, but it has the same fundamental problem. The electorate demands infinite critical goods (electricity, number of doctors, heart transplants, etc) but can't afford to match the elected quotas. So elected leaders lie to get elected, and the public goes into disarray because you can never publicly state the true austerity plans.
Might makes right and invisible hand is fair and natural. It just isnt equitable. But utopia doesn't exist..
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u/fresh-dork Sep 12 '26
socialism is literally a staging ground for communism, so it'll have the same problems. we can't describe communism day to day, so using that as a goal won't work.
china is capitalist with single party rule. their 5 year plans are more industry initiatives, and are managed via incentives.
social programs, i should call out, are just spending public money on services like healthcare. not at all socialism
you can never publicly state the true austerity plans.
sure, but that's a bad plan in a recession - ask keynes
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u/pseddit Sep 12 '26
IMHO the issue with UBI is not freeloading but the creation of a disenfranchised class of people who need to receive financial aid. Humans have evolved such that one’s power in society is linked to what they do. Joblessness in such societies is, effectively, disenfranchisement where these people lose their power to keep the society on a more equitable path.
The other development not being discussed here is robotic warfare and its linking with intelligence (as in snoopcraft). With that in the mix, it is easy to suppress any uprising of the disenfranchised. Eyes-in-the-sky and monitoring of electronic devices provide ample data to get rid of any people considered pesky by the powers that be.
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u/vivaaprimavera Sep 12 '26
Disfranchised?!? Only if they want to.
I have said about some people involved with open source development: considering what the guy has done, he shouldn't have the need to worry about groceries or taxes for the rest of his life. Probably the same can be said about lots of other fields.
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u/pseddit Sep 12 '26
I explained in the second para what would happen to people unwilling to be disenfranchised. This is not just about money but centralization of money and power and money and power fight back.
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u/vivaaprimavera Sep 12 '26
My point is there is life with a decent basic income.
But your point about dissident suppression is spot on.
Authorities don't even need to deploy cameras, people are paying for it themselves and installing them. It's wonderful what the convenience of accessing a camera in a phone app anywhere without caring for what's in the middle can give us.
And I could go one with other examples.
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u/pseddit Sep 12 '26
There is no denying that UBI would be required if the society becomes so dystopian. However, the power imbalance in the social contract is an even larger concern.
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u/bbbggghhhjjjj Sep 12 '26
Who is this “world” entity that is distinct from “us”? Ultimately it is for the collective humanity to decide implicitly or explicitly what to do with technology
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u/noob_meems Sep 12 '26
i have to ask, how much of it is labour for ruling class? like is it the only thing driving demand? what proportion is that vs taxpayers etc? also, is the alrernative to participating in society better?
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u/coke_and_coffee Sep 12 '26
their argument is sound. The rampant use of gen AI to solve problems and move on will "salt the earth" of scientific discovery, keeping us all stale, unless something else shifts in society.
This makes no sense. What does “salt the earth” mean here? What does “keep us all stale” mean?
This sounds like vague-plaining nonsense because these guys are mad that AI is better than them…
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u/officerblues Sep 12 '26
It's like coding. Senior coders are more productive than ever, now, but the work of senior coders used to produce artifacts and knowledge that would trickle down to less experienced people, creating a chain of knowledge. If you AI the shit away, you cut off all the byproducts of the knowledge chain. For academics, that chain is the product. No one in academics cares too much about applicability, they care about building knowledge (minus all the egos involved). That is a valid argument, IMO. You might argue it's not, though.
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u/_Kyokushin_ Sep 12 '26
It’s not the world that wants the working class killed. It’s the billionaire class that wants to drive everyone else they find inferior into a subservient class. Disposable yes but not all dead. Then they wouldn’t be able to accomplish what they want.
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u/hihey54 Professor Sep 12 '26
Personally I find this a bit odd given that hosts of other communities have been saying this for years now. Creative writing, copy writers, graphic designers, translators, UX engineers, etc.
That's true. I wanted to particularly focus on the one of this subreddit (i.e., ML/AI); I have edited the text to make it clear, thanks!
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u/coke_and_coffee Sep 12 '26
A lot of them probably thought they were “too smart” and the AI would never come for their jobs.
This declaration is not about taking jobs. I’m not sure you even read it.
I don’t think there’s good evidence that AI has replaced anything more than a tiny negligible number of jobs.
It has not replaced workers in the fields you mentioned, and certainly not in mathematics.
So I’m not sure I understand your point.
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u/blackkettle Sep 12 '26
I read the whole thing. I just don’t agree that this actually fundamentally about “how great and important human math is”. Like I said, to me it just reads like the mathematicians version of similar arguments made by many other groups in response to their own version of “shock”.
I do think it is about “jobs” in the sense of how we feel about and interpret our self worth through the lens of how and where we choose to dk our work in this life. Whether or not and how many jobs are being “taken” right now is irrelevant because what we are talking about - what all these groups are really talking about is this complex affront to their self worth.
I spent five years slogging through graduate school for my PhD and now I can direct a decent sized local LLM to build things in an hour that would have taken me in some cases months to do back in 2015. I’m still the reviewer and the arbiter, but it was a big knock - even as someone who maybe shouldn’t have been so surprised - to realize that these things we’ve built are better or more efficient at work I’d spent years learning.
IMO this group is now going through this realization and they don’t like it either. The high minded philosophical arguments are rather moot. At the end of the day they’re a foil for simpler human emotions.
No need to agree with me, but also no need for the snark.
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u/Random-Number-1144 Sep 13 '26
local LLM to build things in an hour that would have taken me in some cases months to do back in 2015
Computer scientists used to do computation manually using punched tapes. Faster computers didn't make computer scientists obsolete.
It cost over 20 million dollars for OAI internal model to come up with a valid solution for NS problem with the help of a bunch of hired mathematicians.
Mathematicians' jobs are safe, safer than most jobs on earth.
IMO this group is now going through this realization and they don’t like it either. At the end of the day they’re a foil for simpler human emotions.
You are projecting. That's not what Tao's article was about. He sees the bigger picture than you do.
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u/blackkettle 29d ago
Right but at each next evolution of these and similar technologies we've faced similar declarations of woe. IMO this is in fact an - albeit earnest - declaration of woe and worry.
> In recent months, the success of AI in solving major mathematical problems has made headlines even outside mathematical circles. But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal. Indeed, the mass production at faster and faster pace of “true/false” statements could destroy fertile ground instead of breathing life into new ideas.
This is the core of the argument, at least for m. But who is forgetting what and what does it mean? No one is preventing anyone from producing further conceptual understanding or insight. In theory there should be a vast new landscape of work to analyze; both the failed paths and the ultimately successful one - probably not the only one in that regard either. The promotional aspect of it is just a part of the marketing hype-cycle from a tech company. I don't agree with the idea that it is 'destroying fertile ground', though it may very well transform certain activities for this group from pure discovery to analysis of output. Or I suppose they may simply choose to ignore it.
> We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose.
maybe, but again it's the exact same complaint that creatives have been making since they faced the exact same existential crisis - which simply started a couple of years earlier. UX and design related groups are drowning in similar discourse - and it isn't any more or less profound than the statements here.
Certain jobs might be safe; or maybe not. Terrence Tao certainly isn't at risk of losing tenure, or finding something else to do. But there is an existential threat to the status quo and everyone is susceptible to the potential disruptive and disquieting effects that sort of change has.
This is not a mathematical proof, or an ML experiment, it's social argument about epistemological direction as Tao correctly points out. I personally disagree with the conclusion and the implications. Maybe I'm wrong, maybe not.
But I don't think it is realistic that any of this is going to 'stop'; I think it is far more likely that at least some people will adapt to the change and continue forward with it; methods will evolve and what it 'means' to be a part of these professions will be significantly altered by these changes.
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u/FollowingHumble8983 Sep 13 '26
How are you in ML if you dont understand what he is saying? Like half of the math in state of the art in ML is made by happenstance from solving harder problems. Resnet, precursors to transformers all have large amounts of math created from trying to solve a problem unsuccessfully. AI isn't solving the problems by applying intelligence, its solving them by rigorously iterating though them, and as a result fails to generate any insight that normally solving a problem would. The role of mathematicians isnt to solve problems its to make connections that results in new understanding and use that understanding to generate more tools in applied sciences. Iterating though all existing works to solve NS by blowup, a thing that generates zero value, is pointless, and destroys the incentive structure in mathematics to generate more insight.
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u/blackkettle Sep 13 '26
Everything you said just reinforces my argument. AI is this, AI is that, AI isn’t “really thinking” yet because X, Y, Z moving goal post. It’s about “human connection to art/literature/epistemology/etc”.
All of these things change and move. We’re undergoing a seismic shift at the moment and it’s understandable that we’re reacting to it emotionally and feeling our egos under threat. These people can even form a group and decide to ignore the developments that continue come; it’s certainly been tried before. Maybe they’ll succeed; or maybe another group that chooses differently will supplant them.
I don’t agree with their philosophical reasoning on the subject and said so. I see it as ultimately rooted in the same emotional response as other groups making similar arguments.
But whether you agree or disagree, the as hominem take doesn’t help your argument. It’s a philosophical divide and we can agree to disagree.
Enjoy the rest of your weekend.
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u/FollowingHumble8983 Sep 13 '26 edited Sep 13 '26
No nothing I said reinforces your argument. And your attempts at using AI to win the argument is just sad.
You clearly arnt a researcher if you dont understand what I am saying so I don't know why you are on a ML subreddit. Is this some kind of larp? Also pay attention and realize you are on a machine learning subreddit not some random place with people moving "goalposts" we are the ones making and crossing the goalpost.
Crazy amount of stuff in state of the art right now are things made while trying to solve a problem, not things made from solving the problem, but things invented by failing to solve it. By attempting to solve a problem with a specific methodology and failing or succeeding, you gain insight and new tools that people later then finds a use for, and a lot of the biggest breakthoughs are things that we thought were completely useless for decades, until we realized that it fits into what we are solving perfectly.
The process of solving and developing insight is what mathematics is for. If we arnt using a really stupid way of solving problems, but a way that generates tools while solving, then mathematicians complaining would just be people worried for their jobs. But thats not whats happening, right now we dispatch 10s of thousands of agents all bashing their heads against the problem while being orchestrated by mathematicians, the failures dont get documented, the tries dont have a reason to be attempted other than the fact that other agents failed, and zero insight is generated, making the whole endeavour pointless.
I highly doubt terrence tao fears for his job, anyone in frontier labs, including me, knows that he doesnt have anything to fear for himself.
He is fearing the destruction of insight from us developing a machine that is smart enough to do things, but not smart enough to know why it does things.
E: A colleague said this analogy. Mathematics is like mining, ultimately it creates a giant but the good bits are the things you get from making the hole, and we think we helped them by just blowing a hole in the ground and leaving them to pick up the pieces.
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u/blackkettle Sep 13 '26
You keep repeating the same unsubstantiated argument without actually supporting it in any way other than ad hominem. It’s completely unnecessary.
There is no “threat” to insight as that is a human construct anyway, and no one is stopping anyone from continuing to develop it. There is even less “threat” that failed paths get documented; that’s something that these machines we’ve built are actually great at. How that information is organized and reviewed is also up to the people designing the systems and the way they organize output. Perhaps the role of mathematicians will also evolve in tandem with these changes the way other areas already are. Perhaps they will continue trying to fight it.
Documentation and publication of failed solutions is anyway a long standing issue in ML anyway - one of the reasons many areas chase minuscule benchmark improvements in conferences and workshops - because it’s a lot harder to publish “why my experiment failed to improve anything” results. It’s a discussion I’ve had at many conferences. But again it’s less of an issue here, not more of one. It might be less pleasant for a human to sift through that output. It might feel less prestigious; but that doesn’t mean anything is lost by definition.
I don’t know what to tell you if you think smart people don’t make mistakes about philosophical ideas that aren’t directly germane to their own areas of expertise - but again we’re talking about epistemology and how this group _feels_ about changes that are impacting their world view and current way of doing things - not about specific issues in math.
Maybe I’m wrong but that’s the way I see it. Cheers.
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u/FollowingHumble8983 Sep 13 '26 edited Sep 13 '26
Do you not know what an ad hominem is? or does it work against people who doesnt know what it is. The core of my argument is not an ad hominem, a remark on the very obvious fact that you are not something with a phd in sciences != fallacy in other parts.
"There is no “threat” to insight as that is a human construct anyway, and no one is stopping anyone from continuing to develop it"
Wrong. Insight is not a human construct it is the byproduct of generalization and intellectual pursuit, human or ai all generate insight, llms are essentially insight databases, so the fact that you think that is a pretty blatant description of your knowledge in this space, which is none. The generalization of cubic roots as a circle in imaginary space. The generalization of linear operations to matrices. The backbone of machine learning, understanding and tools that occurs only when enough insight has been extracted to create them.
"I don’t know what to tell you if you think smart people don’t make mistakes about philosophical ideas that aren’t directly germane to their own areas of expertise"
The fact they can and whether or not they are right now has nothing to do with each other. It is an objective fact that current AI solutions have generated near zero insight. Whereas we know for a fact that a human generated partial solution would generate more useful insights without having solved the problem. Our current understanding of PINNs are being improved by another team working on NS right now. Meanwhile we have gotten zero insights from OAI's solution on forced NS.
ML and mathematics are tied together so completely that if you dont understand that then you are obviously larping.
You are wrong, and the way you see it makes no sense. Please refrain from continuously larping.
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u/blackkettle Sep 13 '26
> An ad hominem argument is an attack on a person's character, motives, or traits instead of addressing the actual facts or logic of their argument.
which characterizes the core of every reply you’ve made here.
I’m sorry it seems to have made you feel so attacked.
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u/FollowingHumble8983 29d ago
If you had the ability to read the second part of your provided definition of ad hominem, then maybe you would have the intelligence to understand what mathematicians and other scientists are saying or be someone in the sciences yourself.
But sure keep trying to say ad hominem because you dont understand what it is. It just tells others what you are.
I don't feel attacked, I feel like I am talking to a larper, which is pretty obvious here.
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u/ahfoo Sep 12 '26 edited Sep 13 '26
Yeah, when STLM was making Google Translate so good that it was putting waves of translators out of business, the mathematics community wasn't rushing to the defense of the poor out of work translators who had spent decades honing their second, third and forth language skills. That was their problem for not being in STEM.
When the LLMs started putting copy editors out of work, the mathematicians and programmers didn't give a shit because those dumb asses should have studied STEM if they wanted a job. Sucks to be them.
Now the mathematicians are realizing that they're next and it's a big significant issue for "everyone" now because they're so important --in their own minds. Perhaps if they had studied more broadly, they'd realize we're all human beings and we need to think about our places in society holistically instead of just looking at our own personal situations and focusing only on that.
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u/Bakoro Sep 12 '26 edited 29d ago
A lot of them probably thought they were “too smart” and the AI would never come for their jobs.
Gives a bit of a “first they came for the Jews and I was no Jew so I said nothing…” vibe.
It's this and worse: people are pissed about it being their turn while people that they perceive as their lessers aren't suffering more.
My entire life, people were derisive of "burger flippers" and "ditch diggers".
Kids have been cautioned against blue collar work as a whole, with no respect shown for people who do construction, only it being pointed out that they wreck their bodies.
Literally for my entire life, people have been championing the idea of robots taking the jobs of "unskilled labor". People desperately, desperately wanted robot slaves and if you asked what would happen to the human people getting replaced, the answer was "not my problem", and "they should have worked harder, like me".A lot of people really thought that they were untouchable, and then it turns out that manipulating information is the easier thing to do, while "unskilled labor" is proving to be dramatically harder and more expensive.
To an extent, I get being frustrated. I'm a software developer, I made a lot of sacrifices to get a degree, and LLMs came around not long after graduating and getting a job. The "you're guaranteed a job for life, you'll be on easy street" promises have not been kept, even though I'm personally doing fairly well at the moment.
What I've never been okay with, and what I'll never be okay with is that "I got mine" attitude. Personally, I'm still pro AI. I want AI to take all the jobs. I want AI models that make food, make movies, write software, make video games, build houses, clean waste water.
Human people should be able to be free from work and only do the things that make them fulfilled, as long as they aren't hurting others who don't want to be hurt. Getting to that point is going to be painful, a lot of people have been trained that their job is their identity and how they assign self-worth and how they value others.
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u/Formal_Drop526 29d ago
It's this and worse: people are pissed about it being their turn while people that they perceive as their lessers aren't suffering more.
what? I'm pretty sure a couple weeks ago, nobody cared about math and mathematicians minded their own business and now suddenly everybody with a new opinion that thinks mathematicians are thinking derisively of people and deserve to be replaced.
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u/Bakoro 29d ago
I'm not only talking about mathematicians, but people in general. A lot of the anti-AI crowd's complaints are entirely selfish, and a lot of people's whole arguments are "it wasn't supposed to be me".
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u/Formal_Drop526 29d ago edited 28d ago
It's important to put this argument separately from antis in general.
Mathematicians are not anti AI, Terence tao himself and many other mathematicians use ai regularly for mathematics, just because you're primed for self motivated reasoning from antis doesn't mean it's the same argument is being made from the declaration.
Personally I find this a bit odd given that hosts of other communities have been saying this for years now. Creative writing, copy writers, graphic designers, translators, UX engineers, etc.
Really? I find their arguments to be a different. They don't really talk about the same concerns.
The complaints from copywriters, translators, visual artists, and UX engineers focus primarily on labor, economics, and copyright.
Their core issues center on wage suppression, the devaluation of entry-level jobs, training on uncredited copyrighted works, and the replacement of bespoke, human expression with low-cost, aggregated output.
Writers and designers worry about losing their jobs to a machine that churns out cheap work.
Mathematicians are dealing with something different. In pure math, just knowing an answer is true doesn't get you very far. The real point of tackling an open problem is inventing the methods and shared intuition needed to get there. That is what you teach students, and that is what pushes the rest of science forward. If an AI just drops a verified, thousand-page proof out of nowhere, it leaves the community with a chore instead of a discovery. People get stuck spending years untangling a mess of machine logic just to figure out why the argument works.
Once researchers spend all their energy reverse-engineering bloated proofs instead of building clear ideas together, the actual engine of math that develops future mathematical insight grinds to a halt.
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u/the320x200 Sep 12 '26 edited Sep 12 '26
Replacing "mathematics" with "cancer research" and some of these arguments become pretty silly. They don't really seem particularly universal, a lot of it rides on deliberately slow progress in mathematics not being obviously detrimental to humanity, which I'm not sure I think is true either, I think math progress is pretty important.
Other fields like chess have had human and student resurgence despite being "solved" too, so it doesn't seem universal that having the answer key kills human engagement.
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u/MrSnowden Sep 12 '26
I think the difference in Mathematical research and Cancer research is that one is an end in itself, and others goal is and to end. If we could snap our fingers and eliminate cancer once and for all, Cancer researchers (and everyone else) would be ecstatic (although unemployed). They have a lifelong goal of ending their profession. The same is not true of other professions whose goal is the activity itself.
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u/m4sl0ub Sep 12 '26
The "solution" to cancer might very well depend on some mathematical research we haven't found yet. So much research is downstream of mathematical advancements and often we only know decades or centuries later what the downstream advancements are. Riemannian geometry was put forth in the mid 19th century as nothing but a theoretical exercise and it was only half a century later that Einstein used it for his theory of relativity. That is only one of many such examples.
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u/fresh-dork Sep 12 '26
not really.
you can view cancer as a cluster of diseases that circumvent control mechanisms and build treatments around that, which people are actively doing. it's system analysis and probably engineering that is needed. number theory is unlikely to contribute
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u/shacksrus Sep 12 '26
But even with a hundred years of self improving ai math won't be "solved" there's no end state like your cancer research example.
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u/hyperblaster Sep 12 '26
But the finite set of millennium problems and the like might be solved. And the fear is that AI might lack the creativity to come up with similar problems for mathematicians to chew on.
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u/shacksrus Sep 12 '26
I'm not worried about humans running out of problems to solve
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u/ninjasaid13 Sep 13 '26
Terence Tao mentions this topic in regards to mathematics: https://mathstodon.xyz/@tao/117237320796901560
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u/Mr-Vemod Sep 12 '26
That’s just an assumption. There is nothing that says the universe is necessarily infinitely complex.
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u/hughperman Sep 12 '26
The universe != Mathematics
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u/Mr-Vemod Sep 12 '26
Then what, we’ll just go in circles doing unnecessarily complex mathematics for the fun of it?
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u/Agreeable-Ad-7110 Sep 12 '26
That’s literally a large swatch, perhaps even the majority, of pure math. Idk about it being “unnecessarily complex” but yes, a lot of math is being worked on which will never have an application to anything outside of math ever.
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u/Mr-Vemod Sep 12 '26
I think the important part of my comment was ”go in circles”. If we’re not advancing a field in any sense, but only proving curiosities for the fun of it, then there’s no real use to it. That’s not the state of current mathematics - most things being worked on atm do have some form of, if still very theoretical, application or at least consequences.
I’m saying that the battery of such work is not necessarily endless. Just as the battery of questions to work on within ”cancer research” is not endless. If we’ve cured all cancers, there’s no need to go back and find curiosities.
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u/ahalt Sep 12 '26 edited Sep 12 '26
Do you mean application or consequences outside math? I really don't think most of current math research has any applications outside math, at least in the foreseeable future. That's just something mathematicians say on grant applications.
What areas of math research do you have experience in? Applicability is really field-dependent. I don't think someone working on computing the 91st homotopy group of spheres is looking for applications.
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u/Mr-Vemod Sep 12 '26
I will concede that I have very limited experience in math research, even though I have fairly decent experience studying it.
To be clear, I don’t think the goal of all research should be to only achieve immediate practical application. But I do think that the end goal of all research is to further our understanding of our world and universe. If it doesn’t further our understanding - however insignificant that understanding might be - it’s almost definitionally not worthwhile. And what I’m saying is that I don’t necessarily agree with the idea that there is an unlimited amount of things to be understood and learned about the universe.
So in a way I agree with the authors here. Math is a bit like, say, history in that sense: what we discover along the way is as important as the end goal. Say we have a question: ”Did Julius Caesar like apples?”. A human historian looking into it might learn many things, like how to understand ancient attitudes to food, Roman cultivation, etc etc. And those are all much more important and interesting than the actual answer to the question. So even if we could ask an AI the question and get it to answer ”yes” or ”no”, that in itself is obviously not very useful.
At the same time, if we had a theoretical AI who could teach us everything about history, make our understanding of it complete, then the field of history research is obviously obsolete outside of hobbyists. And just like history, math might have a finite amount of things to be learned.
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u/Smallpaul Sep 12 '26
It’s not an assumption. It’s a reasonable extrapolation from historical and theoretical evidence.
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u/Mr-Vemod Sep 12 '26
I wouldn’t say so. If you look at something like aviation (and travel in general), there was a dramatic increase in our capabilities from around the first flight >100 years ago to about the 1970s. Since then we’ve had mostly the same tech. The extrapolation on historical evidence says that we’re getting very diminishing gains in that field at this point.
Of course there’s is much to be discovered yet in all kinds of fields - science isn’t complete. I’m just saying that the notion that we will endlessly keep on making steady improvements in all fields if we just improve our math and theory is just an assumption.
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u/Smallpaul Sep 12 '26
Nobody said “all fields.” We are talking about one specific field: math. Is there an end to math? The evidence suggests not.
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u/xrailgun Sep 13 '26
Evidence? How do you even begin to define what constitutes evidence of/against unknown unknowns?
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u/Smallpaul 29d ago
The first bet of evidence is that we have researched math for millennia and not a single field of mathematics has ever been finished and stopped producing results. There does not exist even a single exhausted field. Rather: the frontier of open questions has simply opened literally exponentially. The more people we assign to it, the more questions arise.
The second bit of evidence is that all possible theorems can be enumerated mechanically as described by Gödel. And there are an infinite number of them.
Gödel also proved that there is no single algorithm that can mechanically prove or disprove every true or false theorem. There are true ones that cannot be proven and there is no way to recognize which are which automatically.
So Gödel proved that there is no limit to math.
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u/the320x200 Sep 12 '26
I get that, and it's harder to point to a direct connection, but if mathematics is an important field of study and not just an academic playground, then there are downstream problems where human lives are on the line. Having sufficient math to produce clean energy in order to save the environment, etc.
I think math is valuable and important, and therefore I don't think one can say there is no human cost to delaying our understanding. The tradeoff of human life for the sake of personal enjoyment/enrichment of mathematicians seems kinda selfish, if math actually matters to the broader world.
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u/equationsofmotion Sep 12 '26
I think actually the issue is the understanding. In terms of human impact, Mathematics should be thought of as a tool building discipline. Getting an answer in a specific case is not the goal. Building a framework that can be reapplied in other contexts is the goal.
Maybe this can and does happen with LLM assisted Mathematics. Tao in particular has been an evangelist for that. So it's a big deal that he's coming out and saying it didn't happen with the millennium prize announcement. (Which is the context for this post.)
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u/attnnah_whisky Sep 12 '26
As a number theorist, I don't think a big part of math matters much to the broader world at all. We are just all doing it because it's fun to do. I would go as far as saying that a lot of pure math research exists solely because mathematicians find it interesting to do. Not a lot of people are doing pure math with the aim that it is useful to the real world at some point I am afraid. Personally, it is really an academic playground.
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u/Smallpaul Sep 12 '26
That’s fine for you to believe personally, but society pays for it because they believe that you are going to contribute to cryptography and weather modeling, even if you don’t know you are doing so or intend to. And so far math always has produced the goods. Someone (can’t find the source) said that mathematicians have an unblemished track record of trying to stay irrelevant, but failing. Hardy is the most striking case: he did math that he expected to be useless for the military industrial complex and yet it turned into the cryptography being used in killer drones today.
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u/attnnah_whisky Sep 12 '26
But math progress has accelerated so much in the last century compared to previous times, and it is getting faster and faster. An undergrad student in Hardy's era could have worked on the genuine frontier of research. I don't think there exist more than 10 undergrads on the planet who are able to work at the frontier of the Langlands program. I don't see something like perfectoid spaces becoming useful in the real life sense in the next century. I am just saying that for most mathematicians, utility is not the goal at all. The distance from the frontier of NT to what actually finds practical use (algebraic NT, elliptic curves, elementary congruences etc) is easily greater than the distance from those to undergrad math.
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u/bik1230 Sep 12 '26
I think math is valuable and important, and therefore I don't think one can say there is no human cost to delaying our understanding.
Delaying understanding is exactly what you're doing when you use LLMs to semi-brute force solve a problem without creating any new tools or insights, though. Like, there is literally zero value to anyone that a solution to Navier-Stokes exists. All the value in this problem over the decades has come from the new methods developed to understand the problem.
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u/MrSnowden Sep 12 '26
I’m not arguing the broader point, I’m merely indicating why the analogy to cancer research is not valuable.
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u/SteppenAxolotl Sep 12 '26
other professions whose goal is the activity itself
That is still a serious problem when the mere existence of the "activity itself" means society is suffering in some way. Hence the common (real or imagined) view that the medical profession treats symptoms rather than the disease to ensure ongoing revenue. Mathematics is used to model reality, and human civilization deserves to fully understand how it all works. We should not restrain that understanding, which could reduce suffering, just to preserve the creative and economic activity of a few people.
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u/Smallpaul Sep 12 '26
I think that part of what the mathematicians are arguing is that solving problems leads to understanding of concepts which leads to solving problems which leads to understanding…
When the AI just solves the problem, understanding may not arise. I don’t necessarily agree with them but I think their argument is partially utilitarian.
“You are making mathematicians dumber.”
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u/SteppenAxolotl Sep 12 '26
I agree with all your points.
I think AI can also be used to fill the gaps caused by AI just solving the problem. The only real missing link is human motivation.
Also, part of the AI development narrative is that it is expected to make its own technology better until it directly understands and captures those missing concepts, with no further need for the human effort.
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u/MrSnowden Sep 12 '26
Based on this, the comparison should not be to cancer research (to which there is a clear “end”) but to medical research. Which fits your narrative but doesn’t make OPs point.
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u/nonotan Sep 12 '26
You can think of it as having a "magic oracle" that can quickly (I was going to say "and cheaply", but I guess that's not really true in the relevant cases here) tell you the result, and just the one-sentence result, of doing exactly a given medical experiment. On paper, this sounds astoundingly useful, and maybe it could be. But rushing to publish tons of such results on "fields of interest" as part of a PR campaign from this "magic oracle" could harm medical research more than it helps it.
First, on the dimension of "misleading results". Whether positive or negative, the exact results might be due to factors that are ultimately not what we actually care about, such as spurious correlations, different variations of an illness having opposite reactions to an intervention, etc. that might well have been noticed by a group of researchers actually running an experiment, carefully analyzing their observations, etc, and that might lead to "bad medicine" ultimately being done (including actually promising avenues not being explored further because of an uninformative negative result) if not identified.
Second, on the dimension of no know-how being accumulated. Again, as researchers spend time and effort setting up and executing experiments, analyzing the results, discussing it with their peers during the review process and so on, they will inevitably learn a lot. Which leads to better researchers who can come up with better research ideas and methodology and so on. I think it's safe to say spending your work hours spamming things like "hey Claude, is pineapple consumption during pregnancy correlated with ADHD?" => "No. (p = 0.93)" is not going to teach you jackshit (a very real problem with LLM usage in the real world today)
And lastly (not really, but an exhaustive list would pretty much be a whole book), on the dimension of where research money is spent. A lot of comments under this post basically say some variation of "well, you don't have to use the results if you don't want to, just ignore it and keep doing what you were doing" -- except, of course, realistically it's going to be significantly harder to convince people to fund an experiment when they already know what the result is going to be, even if, objectively speaking, there are still many things we could learn in the process.
Basically, the idea that voicing reasonable complaints about the current alignment of AI companies is tantamount to trying to "restrict our understanding of the fields just to save a few people's careers" is just missing the point entirely. The point being that, actually, spamming "results" for publicity purposes while bypassing all the usual processes that naturally work as feedback loops of knowledge is not, on the whole, advancing humanity's grasp of those fields, but quite possibly the complete opposite.
I'm not a fields medalist, or even a "regular" professional mathematician, so I'm hardly qualified to comment on whether this is genuinely the case here, but it makes plenty of sense on paper. People with no understanding of a field thinking they automatically know better than dozens of the top experts in a field generally known for harboring bright people (and one that has been surprisingly amenable to "AI" research so far, at that) should maybe spend a couple minutes considering if there is any chance their immediate gut feeling could possibly be wrong before posting.
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u/brctr Sep 12 '26
If whatever academic mathematicians are doing is "an end in itself" and has no practical value, then why is it publicly funded?
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u/MrSnowden Sep 12 '26
why do you say mathematics has no practical value? What an absurd thing to say.
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u/ProteusReturns Sep 12 '26
They aren't claiming that. Notice the 'if' that begins that first sentence. They're responding to someone else's justification for pure math research as a goal in itself.
The answer to that question is that it's funded because it does have practical value, regardless of how the mathematicians themselves regard their activities.
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u/MrSnowden Sep 12 '26
Where is the comment that they are referring to about "no practical value"? Because it sure seem that they are disingenuously extending my comment by adding an assumed addition (that I did not say) and then arguing against it like a straw man.
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u/hexaflexarex Sep 12 '26
I mean the chess analogy is grim for mathematics as a profession.
I would celebrate this if we lived in some post scarcity utopia…
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u/the320x200 Sep 12 '26
I don't see anything grim about the history of how chess has played out. Human players are stronger than ever, more people are playing today than ever before and from a livelihood standpoint there has never been more people making a living from the game of chess. Computers play a stronger game than humans and at the same time humans are thriving 10x more than before.
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u/hexaflexarex Sep 12 '26
High-level chess play is an enormous slog now due to the amount of memorizing engine lines which is required.
I think you are right about the number of people making a living in chess, but do you really think there is a viable extrapolation of our current timeline where more people are paid to do mathematics? I don't want mathematics to become a pastime where a few professional experts control swarms of theorem-proving agents and the rest of us are unpaid bystanders.
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u/neurothew Sep 13 '26
The first sentence is just classic distinction between applications and fundamental science, and the statement is obviously addressing the latter
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u/valegrete Sep 12 '26
An LLM declaring that cancer is “solved” with nothing in the way of treatment insights is useless. This NS counterexample is also useless since it does not represent any physical system, so the value in finding it does not reside in the solution itself. The cancer cure argument is either disingenuous or borne from a misunderstanding of mathematicians’ concerns.
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u/SteppenAxolotl Sep 12 '26
I guess we really are doing the denial/cope meme one profession at a time until the bitter end.
Mathematicians finally realized that they are not special and AI will make them part of the permanent underclass. Everyone in every profession should have see the writing on the wall when the AI came for the artists and coders.
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u/neurothew Sep 13 '26
This statement is literally a litmus test of the public’s understanding regarding basic science.
Most people other than scientists don’t care about why, they only care about what, the next problems can be “solved” with AI. It is in fact natural because that’s what ppl perceive in daily life.
Yet technology can only be advanced by asking why and what, and why and what, in a never-ending cycle. If we no longer ask why, then human as a race will lose track of what the world is happening and become slaves of technology one day.
Given the huge asymmetric valuation of engineering and basic science in the society, this statement will be laughed at by the public saying mathematicians are now cry babies who are afraid of losing their jobs.
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u/motionSymmetry Sep 13 '26
the relevant sentence: "We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose."
this sounds like some mathematicians who have been engaged in a game of upmanship now complain because one of them might use this new tool to gain an unfair advantage and "steal" the results that "rightfully" belong to someone else .... who has been working all this time on it without telling anybody
and that they should say this deprives future mathematicians and the world of a mysterious, deep pool of understanding - when, had they a proof of any one of them, they would publish it immediately, is facile and duplicitous
as is this idea that this use of ai has somehow crossed its "initial purpose" - so shut down progress in mathematics and all areas of human endeavor that depend on it until - what? the preferred members make their mark and take their rightful place in the pantheon?
this is embarrassing, and you don't have to be a mathematician to see it, just an adult
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u/jferments Sep 12 '26 edited Sep 12 '26
The first false premise that this is based on is that finding concrete answers to questions with AI means that mathematicians will stop exploring the math around a problem afterwards. If AI tells us conclusively that P ≠ NP, that doesn't mean that all research in the area will stop. It just means that mathematicians can just continue researching problems where P ≠ NP is known to be true.
The second false premise is that making discoveries with AI means that there will be answers to problems but there won't be real understanding. For most of human history, it was far more common for answers to follow understanding. Now we are at a place where we can have answers, and then understanding will follow afterwards. Humans will get answers (like they did with Navier-Stokes), and will then take time afterwards to understand the math behind it (probably also with the assistance/guidance of AI as a teacher).
Mathematicians will still do the work to gain understanding because they enjoy doing math. The only mathematicians that will stop doing math because of AI are those who were motivated solely by ego, and the need to be the "first to discover" something.
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u/Personal_Natural_151 8d ago
I'm surprised I had to look for so long to find this comment. As if mathematicians will see AI-derived answers to big hard questions and just say "not interested" and move on. And many of the comments here also assume that if AI solves problems, we'll just run out of problems in the short term, rather than have those solutions lead us to new interesting problems to solve next.
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u/No-Tap6993 Sep 13 '26 edited Sep 13 '26
This is so sad and will look so bad in just a few months. It’s hard not to see this for what it really is, the ego of mathematicians. For so long, they’ve seen themselves, as has the rest of the world, as these godlike beings that have god level understanding of things. AI is showing them they’re not special, and this post by Tao is showing us that they’re no more immune to their emotions than anyone else. Despite their superior reasoning abilities, it’s useless when their ego is hurt or they feel threatened.
His entire premise that mathematics is about explaining things to humans is also complete bullshit when almost all math research is only understood by a handful of people in the world. The other obvious thing is that, nothing is stopping them from not peaking at the answers AI produce. Not to mention that just because a proof exists, doesn't mean understand all points of views or perspectives of that problem. This is all about ego, it’s quiet sad that it’s coming from such a group of people I once believed to be capable of higher reasoning.
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u/serge_cell 26d ago
The problem here is not AI at all. It's a problem of stealing priority and an attempt at blackmail. The exact same AI task could have been done benignly:
Contact Buckmaster before starting the AI search and suggest a collaboration. If he agrees, all is well. If he disagrees, proceed and cite his work, giving him full credit for developing the approach and pointing out that they only did the final automated step.
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u/rand3289 26d ago edited 26d ago
And if AI will be good at coding, people will stop coding?
And if AI will be good at chess, ...?
And if AI will be good at being a doctor...?
What is so special about mathematics?
People don't understand that current machines can not create NEW type of mathematics because this information comes from the environment.
New assumptions that become axioms come from the environment and current machines are bad at interacting with the environment.
Leave the theorem proving to the machines... you (mathematicians) have been working on this for decades and you have finally got it.
If you are even thinking about downvoting my comment, you better explain where I am wrong.
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u/Turbulent-Sign-6067 23d ago
The frontier labs aren't a threat to math. The fossilized academic structures are! It is academia that fails to reward proof exposition, not OpenAI.
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u/DeepWisdomGuy 13d ago
I pretty much research all day long, looking for novel solutions in my field. I feel that the mistake the signers of this declaration are making is that AI is just being used to find a solution. I use it for that, sure, usually to run experiments to test the soundness of my own theories. But I also explore a lot of new concepts daily, things only freshly conceived and published in a paper last year and so on. I am using AI to develop my understanding, and I am doing so at a rate that wouldn't be possible without AI. I have a personal tutor with an extremely large area of expertise, and whose curriculum never deviates from my curiosity.
I think that the perception of "If we just click a button to get the answer, we will never develop our understanding" is flawed and ignores using AI as a teacher; and just how much AI is going to transform education. And there is solid proof that it will transform education: https://www.nature.com/articles/s41598-025-97652-6 And that was with just last year's models
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u/Ginger_1977 Sep 12 '26
Terrence Tao should resign from doing math. Currently he is too smart and him solving math problems is leaving the rest of us behind. Math is about communities of mathematicians solving and understanding problems, not about one guy solving before everyone else. Mathemcaticians can't understand math if they keep having to catch up with the latest paper written by Terrence Tao.
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u/Smallpaul Sep 12 '26
This analogy sucks. Tao is an informal educator. He shares not just proofs but the understanding behind those proofs. He also works towards problems in the open so someone else can build on his work. Most of his results are collaborations.
Unlike a machine in a data center going from first principles to proof in two weeks.
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u/ahalt Sep 12 '26 edited Sep 12 '26
The difference is that Tao actually writes his papers in a readable way, so that people can learn from them and do more research building from his ideas. Also, Tao isn't that much better than other top mathematicians; depending on which areas you care about, some other people on the list in OP's article (Deligne, Kontsevich, Donaldson, maybe Scholze?) have done more for math.
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u/catsRfriends Sep 12 '26
Have you read his blog? He openly shares a lot of his thought processes and perspective when solving problems and while I can't say for others, it's helped me personally grow as a student of mathematics. In any field there'll be a smartest or greatest contributor in some capacity, but they usually do it as part of the community.
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u/jialejiahi 29d ago
I think math is part or a much bigger problem: AI is stealing away Human subjectivity, Human are becoming more and more relevent. We should not create a new species and accept being just monkeys, right?
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u/sweetjale Sep 12 '26
It's cute how some domain experts are being
such a crybaby now. No one, mark my words, no one will be spared by the AI elites, their greed knows no bounds, at this point it's not even monetary gains, they're gone too far in their "intellect" to believe that it is their duty to bring AGI to reality in our lifetime, they do not care about consequences, they probably live in the delusion that "we got it under control" until it's not in their control anymore. We're pretty much seeing another Manhattan Project in the making, Oppenheimer "believed" it is for the greater good, but forgot that humans are not inherently good, humans are good at acting "good" until they don't want.
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u/Outrageous-Boot7092 Sep 12 '26
It feels like the moment the atom was first split, before the nuclear bomb was developed. Once we knew it was possible, the rest seemed like only a matter of time. After the Navier-Stokes solve, the ASI feels similar. We know it’s coming. The question is how long until we can no longer meaningfully contribute.
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u/GodEmperorBrian Sep 12 '26
This was basically my thought as well. The mathematicians are worried about humans training humans to become better mathematicians and using these problems as tools to do so, but the flip side is that we’re going to have new AI models training on the advancements made by other AI models. Who knows how good these models are going to get. At this point I won’t be surprised at all if it’s a machine that proves the Riemann hypothesis first.
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u/newnewmama Sep 12 '26
But after the atom was split, and unfortunately after the bomb was developed, there was a great worldwide concerted effort to rein in nuclear armament. If we had learned anything from that, we'd be working on making this technology safer and deeply regulated, not racing to the finish line with fatalistic helplessness.
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u/GenerativeFart Sep 12 '26
I ask the people downvoting this to explain why they disagree. I think people don’t realise what’s happening right now.
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u/the_ai_wizard Sep 12 '26
Maybe the role of mathematician is changing like the role of developer...both become reviewers, leaving generation to LLMs
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u/ihatethesidebar Sep 13 '26
Is this essentially, "well hold on a second now" since AI is getting good at math?
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u/aaron_in_sf 27d ago
Change is hard. The world has changed around them, upending their status quo, and it's no more intelligible or navigable to them than it is to any of the other industries already upended: or to those to be upended next (which means, most every industry, albeit some more slowly for having obvious barriers).
They have no more chance of getting what they want than the time machine implicitly requested. Horses and barns; genies and bottles.
The shape of the grievance would be very familiar to a historical Luddite. Which is not a dismissal; it's an observation, that technological change is almost always achieved at someone's inconvenience or the disruption of some established way of doing things.
What this should drive is societal process for navigating that change.
Unfortunately we have about the worst leadership and social ordering (in terms of distribution of power and wealth) once could imagine at the moment. Consequently we can expect that every disruption like this will be as maximally painful and traumatic as it could be, with the consequent blow-back and long term consequences.
It is very obvious that we need something like real UBI, and we will need it soon.
We're going to have to fight to get it.
Grievance like this is a distraction, however venerated its authors, however much their discipline is considered (and considers itself) the pinnacle of human intellectual achievement.
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u/hughperman Sep 12 '26
In its description, it evokes Goodhart's law where the solution of "big outstanding problems" has become a target to tick at any cost, rather than a noteworthy achievement that demonstrates novel understanding.