I think a lot about how Terrence Tao and the usual 30 (already well-funded) math guys will receive this cash while us early-career math students are left holding the bag.
It's akin somewhat to "donating 100 dollars to the node JS foundation, not the packages that appear when you run npm fund".
> The foundation will manage and award the funding, including through an open call for proposals, to support workshops and initiatives that help researchers evaluate recent AI-assisted results, learn and use new tools, share perspectives and shape collective standards for AI use.
A non-zero amount of it is probably going directly to the AI companies through tokens...
Why not use some of the money to develop open-weight, open-training-pipeline, fully introspectable and hackable LLM-based theorem proving assistants? Make them a commodity in every mathematician's office like other computational tools. Such a project would itself yield research topics.
Isn’t the very pitch ai bros have to their investors: “we’ll replace ppl by tokens.”
If it doesn’t pay for non-permanent staff salary that would be sad for the maths ppl indeed.
OTOH I have a phd in th physics, 15+ y of academic senior researcher experience, now working 60+ h /w on an unpaid internship and using lunch money to pay for tokens.
And I’m by far not most unlucky
Edit: just to put things in perspective, my phd field (string theory) has 15-30M€ annual funding in Europe (per google)
While the contributing AI companies certainly have a lingering conflict of interest, the relevant point is the effort find a constructive way to live with the reality of AI?
Mathematicians are in the same boat as Silicon Valley programmers in the end: AI is doing their job better than them and cheaper. Other professions will join shortly.
The question then becomes, what do humans do? Resigning to die quietly is hardly the most favorable option?
Just because somebody else can do something better than you ever could doesn't make doing it superfluous. There is more to mathematics and software engineering than finding proofs and algorithms.
"Better than them" is just barely in the realm where it's not incredible to discuss, and still quite debatable.
Cheaper than them? That's dramatically unproven and unlikely just on power efficiency alone, even if we accept the suspect assumption the only efficiency anyone should care about is currency marked per line of code or theorem proved.
We're not just going to have to become better existential philosophers, we're going to have to become better examiners of assumptions and claims.
Wasn't it Tao who suggested, fairly early on, that the best way for a researcher to contribute to mathematics may be to drop everything else he or she is working on and study AI instead?
Pretty sure it was Tao but I could be wrong. In any case it now seems more defensible than it did when the idea was first broached.
Why? I thought we already established* that most professional mathematicians are not necessary (in the near future, then maybe "any"), so why would they doom these students with pity grants to basically create unnecessary jobs for them? More practically, wouldn't that money be best served (i.e., raw ROI) by purchasing more tokens on the frontier models?
(*) The existence of this effort itself is a good heuristic.
I'm curious what you as an early-career math student would want the Simon Foundation to do differently from what it says it will do. I hope there is a way for students like to you to get a slice of the pie.
>I think a lot about how Terrence Tao and the usual 30 (already well-funded) math guys will receive this cash while us early-career math students are left holding the bag.
Never understood this sentiment. Theses top researchers could do almost anything else with their skills outside Academia and make far far more money. You don't get rich off grants... They could all presumably walk into Anthropic or OpenAI for near $1M a year in TC.
If you yourself are as cracked as you think you could also do the same...
Getting your foot in the door is always the first step. Sure, you can be as cracked as you want. You can be mediocre as well. None of that matters if you don't have a foundation to start from.
Isn't that basically all of AI for white collar workers?
I haven't escape note that I can do tons of things with AI because I spent the last 10 years building a bunch of side projects and now I can complete those side projects because I know all the magic words.
Gonna need to unionize because the gerontology is just getting stronger.
As much as this looks like a math problem, it's actually an everyone problem. Some hands-on (literally) have more way to go, but otherwise this is a "hop" that the entire society needs to cross. Honestly, I don't think there's going to be be any Math 2.0 as there won't be any other 2.0, at least not in any utilitarian way and the effort to find utility where there's none is misguided at best. The analogy I like to make is that with horses trying to find utility y in the Ford era.
It's also not an OpenAI, Anthropic or any specific name caused problem. This type of progress has always been happening, it's more or less coincidental (like Stigler's law). The problem though is we need to rethink how we operate as a society and too few (IMO) are trying to make this conversation happen.
You cannot use mathematics without understanding it.
It doesn't help you that AI understands it, when you don't. You are the one getting screwed over by others who understand statistics better than you do.
When you're rich enough, you can pay others (or AI) to protect you. But then you're dependent upon them.
So, under a transactional model of social relationships, you are in an arms race over raw intelligence and competency/data. With only one winner, who takes all in the end.
Logically, most people have already lost in that game, so why keep playing that nonsense?
You can't use mathematics without understanding it?
Let's say GPT-23 Astra grinds away for a full month one day and out pops a warp drive. Our best physicists ask it to explain. The resulting stream of text is essentially incomprehensible. But, they build a scale model at its direction to test and sure enough it does the Kessel run in 12 parsecs.
Are you saying we shouldn't hop aboard the USS Enterprise and check out Alpha Centauri because we don't understand the math?
I think what's really happening here is that there's an ivory-tower academic class that feels entitled to make their living at public expense thinking about and writing about their topic of interest, and along comes a new tool that's changing that dynamic up. Meanwhile, in the real world, the value remains with people who can take whatever the tool of the day is and do useful things with it. Which, I think, is why despite all the talk the only professional job losses blamed on AI appear to largely be companies that had a failed strategy of some sort or another and used AI as a boogeyman to do the layoff that they needed to do anyway. To people living in the private sector this isn't seen as a dangerous invader, LLM's are productivity multipliers.
>Let's say GPT-23 Astra grinds away for a full month one day and out pops a warp drive.
In the real world, the frontier labs are still hiring lots of humans for business and software roles (https://openai.com/careers/search/) despite being better positioned than anyone to automate them away with their world-beating models and save a bunch of salaries.
That seems wrong unless you have an unusual definition of "understanding":
* Lots of people use math for calculations without having proven any theorems.
* You can understand a mathematical statement without understanding or even having a proof. There are proofs built on the axiom of choice and conjectured results.
I think you can understand* math in general. I think not understanding something it's a matter of presentation. Also I think the presentation can be improved. A good-quality AI can do both, hence it can get a presentation that you can understand.
Yet this has zero utility (other than your own satisfaction). Once you understand something, you will likely not even do a better job at explaining it to someone else, so the utility is strictly limited to yourself.
So even ignoring ability to understand the problem is the cost/efficiency of understanding (and applying it).
I agree with your other statements, but I feel you're suggesting the non-sense is scoped to just math. It's not it's almost everything that we do (exceptions are social interactions including care taking, etc.)
So in this frame your "nonsense" is (almost) everything that we do. Personally I'd like to keep doing things.
That also means that you will need buy-in from a plurality/majority of that society to make that "hop". This is not going to break politically this election cycle, but it will show up. Barring a 2008 level event, it will likely be the issue with the greatest growth heading into 2028, and that will place the impetus on the "specific name"s to communicate how this isn't just trickle down benefits. Especially when it will be an easy sell to people that the "hop" means real people falling into the gap or getting left behind. They need to figure out a way to make the distribution of benefits more immediate and tangible to everyday folks, because the perception of the distributed costs is a very easy sell in this political environment, regardless of the reality. I can't imagine that getting better over the next two years.
Yeah, the tangibility of benefits really need to be felt, especially for the so called "deplorables" who would like to swing for a politician that can demonstrate that they will get them housing, healthcare, prosperity in their communities. High paying jobs across the educational ladder and in rural areas also wouldn't hurt.
Like my other comment, this might be a public-vs-private sector misconception. I can't help but notice my own employers IT and design departments, which both lean pretty right, openly use Codex to help with about everything. One group is even training their own model at the moment. And our marketing team, which is solid blue? They're the only team in the company allowed to use both Claude and ChatGPT because they claimed, repeatedly and loudly, that both were critical to their jobs because Claude was better at design (they say) and Chat for everything else (again, their claim, not mine).
No one wants a data center in their back yard, but in the private sector I think adoption isn't as political as some make it on Hacker News.
too few are talking about reshaping society because those in power are not letting that happen. the amount of wealth concentrated at the top is staggering and allows them to fortify their position by bribing, buying governments and media.
No, it's not an "everyone" problem yet. Each field is likely on its own timeline. Knowing how well AI is at proving theorems is of only limited use for predicting what will happen and when in other fields.
The yet compressing into now is the definition of singularity. I'd argue that it's "only of limited use" if you don't understand the problem well enough - so yes, it's limited for predicting anything for most people but that doesn't make it an irrelevant aspect at predicting in general.
Why bring up the singularity? It hasn't happened and might not happen the way anyone thinks. For example, the timelines in different fields might not all go vertical at the same time. So, you could get something like an Internet singularity without a corresponding robotics singularity. Also, war is different from civilian applications. The use of drones to bomb data centers doesn't imply that drones will be useful for civilian applications like delivering pizza.
There's no particular reason to believe that solving math theorems generalizes to engineering or robotics without a whole lot of additional work.
I love how "society" is investing billions to develop a tech that makes its own citizens obsolete, but doesn't manage to provide basic healthcare, housing or infrastructure...
That why our ancestors repurposed their pitchforks. History is marked by a drive towards inequality, punctuated by bouts of war and revolution that trigger a reset.
Once the citizens are made obsolete, there is no need for healthcare, housing, or (human) infrastructure. Just electricity, cooling water, and Internet connectivity.
Obsolete citizens don’t need healthcare, housing or infrastructure. They will just die of hunger and exposure and then the rich and powerful can frolic unencumbered in paradise.
Maybe you get conditioned on how the rich usually treats other people, but this view isn't well supported by healthy discussions among the math community wrt recent AI 'disruption'
We're not so far from 'you never had some god given right to be alive, well fed and sheltered. You have a good body, make yourself useful in some industry.'
Math proofs are right in the sweet spot for training LLMs with RLVR. It isn't some general "LLMs are getting insanely smart!". Even most software development itself is miles away from being as well suited to training as math proofs are.
The majority of math research is akin to professional chess. Completely useless and the folks doing it are using their giant brains to play a game that no one outside themselves benefits from.
For what it's worth, most mathematicians are paid to teach, and the amount of research funding going into mathematics is relatively small. Plus, there are rare but important broader advancements due to pure and applied math that are hard to predict in advance (e.g., cryptography, compressed sensing).
Mathematicians also decide what to prove in their research - taste is not a skill we have RLVR'd away (yet, not claiming this is fundamental).
Of course, the field is being fundamentally transformed, it will probably end up looking more like experimental science in the future.
The bulk of the people on this planet do not make their money in advanced math but in mundane jobs that are well within the capabilities of AI as it is today. It will take some time to figure out how to put it all together but all of those jobs are on borrowed time unless there is some kind of regulatory action to stop that from happening.
Perhaps. But as someone who uses AI to automate something that seems in the bucket of things you are talking about - it's harder than it seems, the edge cases are endless, claude code is worse at building real systems than people think and humans are doing a lot more than people realize once you start trying to automate.
All I'm saying is the math advances of late really hasn't changed much outside of math as far as AI is concerned.
> Under a partnership, the Simons Foundation, Anthropic and OpenAI will commit $15 million in combined funding and resources. The foundation will manage and award the funding, including through an open call for proposals, to support workshops and initiatives that help researchers evaluate recent AI-assisted results, learn and use new tools, share perspectives and shape collective standards for AI use.
The foundation was started in 1994, Wikipedia says "one of the largest charitable organizations in the United States with assets of over $5 billion in 2022" - Jim Simons founded the Renaissance Technologies hedge fund.
Simons Foundation also significantly funds arXiv, and also a large number of specific grants across maths and sciences. I don't think there's much agenda here.
The foundation was an early backer of machine learning for science, including funding the development of the Lean proof assistant, which has revolutionized how mathematicians work and made AI-assisted proofs possible. Additionally, the foundation has convened workshops, lectures and collaborations that have brought mathematicians together to explore and discuss AI’s role in the field.
So, basically they created the recent situation in math where a great deals of top mathematicians criticized their methods, even called to boycott their dumped results. And the answer of the AI labs is buying these poor academic souls with 15$ millions? Most of them even as AI tokens? Why do I see a macabre irony here?!
Read "the man who solved the market". It's a remarkable story. He was a remarkable dude, extremely smart, has given a lot of money to promote math and science.
The people here who depict him or whoever runs his funds now as a pure philanthropists are wrong. These tiny investments into academia pay off many times.
So charitable that it launches this initiative with ClosedAI and Misanthropic. There are probably accelerationist and transhumanist nutcases at this foundation.
Can you ever look behind the surface of ... anything at all? Only naive and childlike statements in favor of AI proponents. It is literally like saying: "Prince Andrew and Sarah Ferguson are esteemed members of the magnanimous and generous Royal Family."
This IS me going beyond the surface. The obvious question here is "who is this foundation and are they working with the AI labs". I answered both.
The headline in this piece made it look like maybe a foundation was trying to help mathematician's push back against the unwanted assault on their profession by the AI labs. The section I quoted shows that's not the case.
Also not sure how you interpreted "foundation started by the Renaissance Technology hedge fund billionaire" as a mindless boost.
Respectfully, you didn't answer either. Jim Simons was a brilliant mathematician, has done a lot for math and people involved in math. If you assume they are "pro math and pro math people", the why is simple too.
I assumed Hacker News commenters would find the extra contextual information useful in the same way that I did. I didn't assume they would come to the same conclusions, and I've not come to conclusions myself.
I'm going to defend my comment. I said:
> The obvious question here is "who is this foundation and are they working with the AI labs". I answered both.
You said:
> Respectfully, you didn't answer either.
My first comment started by quoting:
> Under a partnership, the Simons Foundation, Anthropic and OpenAI will commit $15 million in combined funding and resources
That answer the question: are they working with the AI labs?
And then I said:
> The foundation was started in 1994, Wikipedia says "one of the largest charitable organizations in the United States with assets of over $5 billion in 2022" - Jim Simons founded the Renaissance Technologies hedge fund.
I think that's a pretty solid starting answer to "who are they", and it tips people off that Wikipedia can answer in more detail.
It also leaves opportunity for people like yourself to speak to Jim Simons' reputation and fill in more gaps.
> > Under a partnership, the Simons Foundation, Anthropic and OpenAI will commit $15 million in combined funding and resources.
OAI and Ant got blowback for essentially strip mining mathematical discoveries into PR wins for their models, accidentally laying waste to the research field in process. Throwing ~$5M each into PR whitewashing (partially in token credits), seems self-serving.
Kudos to the Simons Foundation for seizing the moment to offer the labs a fig leaf of respectability. Might have been the fastest "Yes" on a grant proposal ever.
Ironically, that has been that way for most people since forever.
Comparing with the situation in programming, where code evaluation (obviously analogous to "understanding") is that bottleneck now, should get people the idea of being in the same boat.
I’d say it’s understanding in general. We currently have zero evidence the AI models can understand mathematical breakthroughs in a productive way. (When they intuit a new technology or theory from a mathematical construct, we’ll be along that way.)
What is that the bottleneck for, though? Certainly, it's tautologically the bottleneck for "humans understanding math"; but what about things like using math to drive discoveries in other fields, or for practical work in CS, or applications elsewhere? I fear that practically those aren't bottlenecked on human understanding.
It is my understand that there isnt a lot of innovation here. Rather the (broad) field of mathematics got mined for solutions that already existed within the corpus.
It implies "We didn't know we already knew how to solve these problems". How is that a good look for mathematics as a field?
Did you read any of the explanations from mathematicians over the last month? What part of them do you disagree with?
For example [1]:
> In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align.
Or [2]:
> Use of AI tools, when done responsibly, can support not just the initial generation of a solution, but all of the valuable followup activities that traditionally flow out of that solution. But at the current time, the opposite is often occurring: problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is "solved", and do not understand the AI output well enough to answer questions on the result, give talks, or otherwise interact with the rest of the field.
> ...
> solutions to open problems are now being harvested at large scale in an unsustainable fashion, leaving entire fields of mathematics much less fertile than when such problems were solved in the traditional "Math 1.0" fashion.
> prompters who have no interest in the broader field itself once their initial target is "solved"
This applies to all fields and pursuits where AI is effective. Yes I think about this with regards to various things I’m working on.
This is just the nature of things, you need to adapt and not throw a tantrum like a child. You need to not behave like Terrance Tao who is essentially like a child in an adult’s body in terms of his behavior and lack of wisdom, and keep in mind he was a child prodigy so this isn’t a knock at all or statement about his intelligence, only his development as a man.
You can mourn, as I have for the field of programming as I knew it which I have loved since I was a child, but you need to move on.
If AI can actually replicate mathematicians, sure. We don’t have evidence it can. We have evidence it can do useful stuff once promoted by human mathematicians. But if all the Terence Taos “move on,” we won’t have those in America anymore.
(The irony of ironies would be the mathematicians prematurely moving on causing American AI progress to stall in the future.)
I completely reject the idea that releasing proofs is bad for the field of mathematics. Yes, it holistically changes the role for mathematicians, and they might not like where the change leaves them, but I do not think it harms the field overall.
Best I can tell the biggest complaints are really just that the future of their career is largely combing through lean and they don’t want to do that. Too bad. Adapt or get off the pot.
Mathematicians need to completely rethink the prestige paradigm. Counting proofs no longer works. That doesn’t mean there’s nowhere for them to go. Now it’s about gleaning human understanding from the lean. Maybe in the future LLMs can do that too and it’ll be all about formulating new conjectures.
>... essentially strip mining mathematical discoveries into PR wins for their models, accidentally laying waste to the research field in process.
Jeeze, that's an almost impressively charged way of saying "private company performing SOTA research on open problems that anyone has been welcomed to approach for over a century" lol
I think it does a disservice to the dialogue to strip away any nuance here and just paint these companies as evil for doing what everyone has been anticipating companies like them doing well before LLMs even existed. It's clearly just trying to fit these events into a specific narrative which does nothing to actually address the inevitability of everything that comes next. Feel free to pressure OpenAI and Anthropic to stop performing math research so that it can just be picked up by whoever catches up and doesn't care about bad PR. I'm sure Musk with Grok will be extra considerate of pure math researchers when he sees an opening to pick up those scraps lol
OpenAI's market cap or valuation estimate went up by about 230 billion dollars within a few weeks after announcing that they solved NS. It can't be known how much of that value change was because of that announcement, but must be at least a good chunk of it.
I’m in the funding markets around this stuff. Nobody took this into account. It’s more for PR with government and potential hires (and maybe some corporate marketing).
Softbank's rally began in Japanese markets on 3 September and American markets on 4 September. OpenAI announced on 8 September. When OpenAI delayed its IPO plans on 13 September, Softbank sank back to its 7 September level [1].
So they want mathematicians to keep prompting and giving feedback to the models for clarifications on their proofs. Then write it all up and publish it in a journal and mention their AI usage. Then suddenly the models end up producing readable and understandable proofs through the "emergence" of the skills because of the scaling laws.
I really can't empathize with treating mathematicians as some sort of AI refugees who need coddling and support. AI is a tool, and competent mathematicians should learn to use it like everyone else. I find it hard to believe that AI doesn't represent a net potential benefit to human understanding of mathematics. Yes it can be misused, but any tool can be misused. Just don't misuse it...
> can't empathize with treating mathematicians as some sort of AI refugees
They may be a vanguard.
> find it hard to believe that AI doesn't represent a net potential benefit to human understanding of mathematics. Yes it can be misused
Have you read Tao’s criticism of AI in mathematics? The concern isn’t mis-use, it’s ecosystem collapse.
A good analogy would be offshoring. If AI causes higher mathematical thought among humans to stop happening for a generation, we could wind up in a state where the field stops progressing because AI is unable to generate new interesting questions or cross-link findings into practical applications.
More directly, the risk is that happens in America but not in a more-thoughtful country.
But it's entirely up to humans whether or not higher mathematical thought ceases due to lazy over reliance on AI.
Just because AI is capable of churning out vomit inducing prose, doesn't mean we need to surrender to a future filled with it. Humans who actually care about what they're doing will use AI when and where it should be used. I trust the intelligence, curiosity and tenacity of mathematicians to learn to work with AI. I don't understand the sky is falling worst case scenario Tao and others seem to be taking as the most likely future.
> it's entirely up to humans to allow higher mathematical thought to stop happening
…yes. That’s why the human mathematicians are having this debate. How to keep the human mathematicians and their founders motivated to keep doing math, potentially more productively with these new tools.
Again I analogize to the situation with developers. There are glass half empty devs who seem to enjoy writing boilerplate and hate AI, and glass half full devs who realize AI when properly used enables an order of magnitude increase in productivity.
If AI saps motivation from some mathematicians, I question where their motivation came from in the first place. Maybe they're just too wedded to the traditional way of doing things and aren't fully appreciating the actual productivity gains AI makes possible.
> glass half full devs who realize AI when properly used enables an order of magnitude increase in productivity
Again, have you read Tao’s recent criticism of AI in mathematics? Nothing you’re saying is disputed.
> If AI saps motivation from some mathematicians, I question where their motivation came from in the first place
Question away. I care about results. If a substantial number of great mathematicians say this is a problem, and a substantial number of students agree, whether they’re unappreciative of their potentially pending unemployment is irrelevant to both that fact and the fact that they’re not going to be producing mathematics. (Again, here. The American mathematical ecosystem collapsing doesn’t mean the same will happen abroad.)
This reprioritization of math would release a tremendous amount of human capital to do other more productive things other than posing yet another abstract puzzle which may or may not have an use in a few hundred years. It's not even clear if the human race can survive until then nor is it justified to spend that resource researching that far ahead instead of just when we need it.
> reprioritization of math would release a tremendous amount of human capital to do other more productive things other than posing yet another abstract puzzle which may or may not have an use in a few hundred years
We don’t know this! We might just have no more American mathematicians because folks who aren’t mathematicians don’t understand that we’re turning mathematical breakthroughs from just a couple decades ago into real, working technology.
> It's not even clear if the human race can survive until then
It’s pretty obviously clear the human race can survive for hundreds more years…
> It's not even clear if the human race can survive until then nor is it justified to spend that resource researching that far ahead instead of just when we need it.
"Climate change is going to kill everyone in 50 years so we'd better work fast if we want to burn all this coal by then"
To merely wish for others not to misuse a powerful tool is a bit naive?
You have to actively design society to accommodate for the dangers it poses.
Of course everybody should "learn to use AI", but the real questions here are wildly different: can everybody use AI? Do the big US companies succeed in capturing the system, effectively shutting out every competitor and how do you imagine to benefit from that? Etc.
one issue is that the tool is wielded both by the user and the provider - each time we augment our skill with its capability, we are improving its capability with our skills.
knowledge workers are building their own gallows and it probably can't be stopped.
yeah its egotistic bs because they built an identity about being attributed in a journal instead of just focusing on the advancement. they collectively rationalize it by saying that the answers aren’t as important, the path to the answers are, despite the answers being what everyone considered them to be using taxpayer and other funding for, and the distributed time used.
they’ve only had a few weeks to deprogram so I’ll let it shake out just a little longer
Is mathematics deprived of the associated knowledge that comes from a human first deriving a proof, how exploring the problem domain including the dead-ends has changed the mathematician's thinking, when a proof is given by AI? It seems that the solving rather than just the solution gave much to mathematics.
Can you explain to me what "navigation" means if AI actually succeeds at automating mathematics? Or is the bet here that the AI companies will fail to deliver?
In some way, yes. The whole situation seems completely grounded in that mathematicians are greedy for status and clout trying to write their name on new discoveries in blood and publish as many papers as possible. And now they are sad because they lost their way to this status.
When you remove this greed and status seeking you might actually end up with a healthy environment.
I don’t think it’s a matter of greed. I’d say it’s about incentives. In every field, people want to progress. I don’t think mathematicians are any different, even though we try to admire and idealize higher principles and the pursuit of knowledge. If you don’t publish papers under your name, you won’t progress in your career or receive enough support to work at the frontier. It’s just a general observation.
I don't think so either, so let's stop the charades and Terrence Tao guest blogs about the field being about some kind of understanding and it actually being about just climbing the career ladder and accumulating status by churning out papers to ensure ones resource accumulation.
It may be true in some cases but as a blanket condemnation of the entire field it makes no sense. Moreover, I can't fathom how you could reach this conclusion if you've actually done any reading on "the whole situation." The reality is precisely the opposite of what you're claiming.
Mathematicians are upset partly because AI companies are "scooping" their work. If you had worked on something for years and this happened, you'd be upset, too. The manner in which this happened with Navier-Stokes was unconscionable. The mathematicians who did the work deserve recognition. OpenAI deliberately stole it from them.
More importantly, the purpose of mathematics isn't to produce proofs. It's to produce mathematics and mathematicians. Working through problems helps people find new mathematics -- and makes people mathematicians. A machine that generates proofs destroys that. It breaks the cycle that makes mathematics fruitful, interesting, and not just self-regenerative but self-propagating.
AI companies aren't just clear-cutting the fields of math; they're sowing them with salt -- and they're doing this precisely because of greed and hunger for status and the title of "first."
Unhinged and honestly nauseating take. Were you hurt by a mathematician at some point? I don't even know where to begin with how negative and backwards this is. I guess I could start by saying that if you replace "mathematicians" in your comment with literally any other profession you could make the same criticism about greed and clout. With the "writing their names in blood" comment, I have no words. I will weep for the world if it turns out that this is how people see math.
Many other professions are somewhat honest about their motivations.
Quants are open about that they just want to make a shitton of money.
The guys I know who work at OpenAI just want an expensive car and a hot wife to fuck.
Mathematicians(and many academics) however have long been hiding behind the guise of furthering human knowledge, understanding things, etc. Then a model does theorem proofs and suddenly there is chaos and the real incentives and motivations are put on display for the world to see.
This is a deeply cynical (not to mention, a touch misogynistic) take on human motivation. This might be true for your small circle of friends but I think it reflects your thinking a lot more than some deep objective truth about people and their careers.
If that is the case and I am wrong, how come there is a crisis in every math department? Why is Terrence Tao publishing copium guest blogs daily about the meaning of mathematics?
And Williams thoughts are kind of idealistic. "Now the credit is shared across the entire field". This "credit" does not give your department grants or further your own career.
Rather it incentivizes you to be the first one to prompt, and to steal ideas from your peers because you can prompt better and have your name on more discoveries.
I never claimed there isn't a crisis. I think the motivation of mathematicians is a mixture of prestige and genuine curiosity and understanding about these abstract problems. I think recent advances are creating a reckoning on how the community-at-large addresses these incentives. It is highly reductive to argue that the only motivation is as crass as you put it.
> The whole situation seems completely grounded in that mathematicians are greedy for status and clout trying to write their name on new discoveries in blood and publish as many papers as possible
You're gonna get downvoted but this is absolutely true. People who've never been in real professional academia don't understand but this is exactly what most very successful academics are like.
> When you remove this greed and status seeking you might actually end up with a healthy environment.
Nah I think you're just gonna have collapse because you've removed all incentive.
Aside from the fact that $15M is couch change for these companies, and aside from the fact that this project is hypocritical and self-serving (as explained by many other posts), the whole idea of naming a supposedly large sum of money in a headline in order to impress is just silly. Whether a project is successful or worthwhile has little to do with how much funding may be lined up, and throwing numbers around is often just a smokescreen for poor planning and execution.
Wonder if they realize these types of things help grow massive resentment against such companies? I'm astounded by how terrible the politics of SV actually is.
how is that different than what's been happening forever? Mathematics has ALWAYS been a "charity". The only thing that changes over time is who gives the money, first it's the church, then it's princes, then government, it's been corporations for a while, this is nothing new.
Except that even the Cosa Nostra is less anti-human than the current tech bros and their foundation fronts.
You really cannot see any difference between the government and corporations supporting something? This "things have always been that way" talking point is getting out of hand.
Genuinely the least they could do for what a pox they are on so many industries, on consumers of electronics, on local municipalities, on the environment...
I mean I can't speak for most people, but if the people I read are any indication, a whole lot of regular people are sick and tired of tech companies announcing their presence in our society and then immediately setting about making daily life worse for everyone but them.
So you'll have to excuse me but I'm not even getting the tiny violin out of the case for this one.
> So what? Who cares what you and a bunch of regular people are tired of?
Anyone in a position of power who doesn't want to end up killed? Like I'm not advocating for violence here, I'm just saying the list of political figures who "didn't care what regular people thought" and the list of political figures who were then subsequently murdered in public acts of political violence are a venn diagram that's practically a circle.
> That doesn't mean you get to take over private companies and start telling them where to spend their money.
I didn't advocate anything like that.
> But I like America, freedom, capitalism.
And I like people being able to live a good life, which Capitalism and lately America itself seem to be opposed to. Do you have an actual counterpoint to make or just more chest-beating?
My point has been reiterated several times, I'm sorry you missed it: you don't get to translate your bad feelings into seizing/directing private companies and how they distribute their compute.
You can say you do, by threat of death for disobedient politicians, but...well, that's bullshit. The people murdering & attempting to murder politicians don't fit the description of "regular people." And you're almost entirely incapable of directing policy with that tactic.
And herein lies the rub: As others have pointed out in another active thread on AI in mathematics: The crisis could be described as one of career, status, and funding vs the general concept of the field. We have now circled back to question of who deserves these tokens!
I belive that the world would be in a much better place if all science was ultimately funded by a global organization such as UN and patents did not exist. If you are a research group that successfully creates something worth replicating then you should be eligable to receive a grant as well as request grants for projects that cost billions of dollars.
There is some success with this kind of strategy already when it comes to space, LHS and ITER come to mind. NASA is somewhat operating on this very same principle although it is a government organization to begin with.
Although the opposite reaction is that you should keep people behind inventions poor to encourage them to create more inventions which ultimately what ends up happening in the real world more often than not. The people who revolutioned the world did get fame and glory, including numerous monetary compensation packages - but compared to the people who sold those inventions they only got a tiny fraction of a fraction, this is especially clear with people who are normal employees and inventions are credited to a company rather than the few people who made it possible.
May be instead of funding military or other countries, they can fund scientist.. And all the tax funded must be in public domain instead of giving it to private companies.
It's akin somewhat to "donating 100 dollars to the node JS foundation, not the packages that appear when you run npm fund".
A non-zero amount of it is probably going directly to the AI companies through tokens...
Much the same way that VC money has been funnelled to Google and Meta through advertising budgets.
If it doesn’t pay for non-permanent staff salary that would be sad for the maths ppl indeed.
OTOH I have a phd in th physics, 15+ y of academic senior researcher experience, now working 60+ h /w on an unpaid internship and using lunch money to pay for tokens.
And I’m by far not most unlucky
Edit: just to put things in perspective, my phd field (string theory) has 15-30M€ annual funding in Europe (per google)
Mathematicians are in the same boat as Silicon Valley programmers in the end: AI is doing their job better than them and cheaper. Other professions will join shortly.
The question then becomes, what do humans do? Resigning to die quietly is hardly the most favorable option?
Just because somebody else can do something better than you ever could doesn't make doing it superfluous. There is more to mathematics and software engineering than finding proofs and algorithms.
Cheaper than them? That's dramatically unproven and unlikely just on power efficiency alone, even if we accept the suspect assumption the only efficiency anyone should care about is currency marked per line of code or theorem proved.
We're not just going to have to become better existential philosophers, we're going to have to become better examiners of assumptions and claims.
Pretty sure it was Tao but I could be wrong. In any case it now seems more defensible than it did when the idea was first broached.
Why? I thought we already established* that most professional mathematicians are not necessary (in the near future, then maybe "any"), so why would they doom these students with pity grants to basically create unnecessary jobs for them? More practically, wouldn't that money be best served (i.e., raw ROI) by purchasing more tokens on the frontier models?
(*) The existence of this effort itself is a good heuristic.
Even if you want to work in research, AI offers a lot of opportunities to do even more research, and less grunt work
Never understood this sentiment. Theses top researchers could do almost anything else with their skills outside Academia and make far far more money. You don't get rich off grants... They could all presumably walk into Anthropic or OpenAI for near $1M a year in TC.
If you yourself are as cracked as you think you could also do the same...
I haven't escape note that I can do tons of things with AI because I spent the last 10 years building a bunch of side projects and now I can complete those side projects because I know all the magic words.
Gonna need to unionize because the gerontology is just getting stronger.
It's also not an OpenAI, Anthropic or any specific name caused problem. This type of progress has always been happening, it's more or less coincidental (like Stigler's law). The problem though is we need to rethink how we operate as a society and too few (IMO) are trying to make this conversation happen.
It doesn't help you that AI understands it, when you don't. You are the one getting screwed over by others who understand statistics better than you do.
When you're rich enough, you can pay others (or AI) to protect you. But then you're dependent upon them.
So, under a transactional model of social relationships, you are in an arms race over raw intelligence and competency/data. With only one winner, who takes all in the end.
Logically, most people have already lost in that game, so why keep playing that nonsense?
Let's say GPT-23 Astra grinds away for a full month one day and out pops a warp drive. Our best physicists ask it to explain. The resulting stream of text is essentially incomprehensible. But, they build a scale model at its direction to test and sure enough it does the Kessel run in 12 parsecs.
Are you saying we shouldn't hop aboard the USS Enterprise and check out Alpha Centauri because we don't understand the math?
I think what's really happening here is that there's an ivory-tower academic class that feels entitled to make their living at public expense thinking about and writing about their topic of interest, and along comes a new tool that's changing that dynamic up. Meanwhile, in the real world, the value remains with people who can take whatever the tool of the day is and do useful things with it. Which, I think, is why despite all the talk the only professional job losses blamed on AI appear to largely be companies that had a failed strategy of some sort or another and used AI as a boogeyman to do the layoff that they needed to do anyway. To people living in the private sector this isn't seen as a dangerous invader, LLM's are productivity multipliers.
In the real world, the frontier labs are still hiring lots of humans for business and software roles (https://openai.com/careers/search/) despite being better positioned than anyone to automate them away with their world-beating models and save a bunch of salaries.
For automated AI shilling ...
* Lots of people use math for calculations without having proven any theorems.
* You can understand a mathematical statement without understanding or even having a proof. There are proofs built on the axiom of choice and conjectured results.
Yet this has zero utility (other than your own satisfaction). Once you understand something, you will likely not even do a better job at explaining it to someone else, so the utility is strictly limited to yourself.
So even ignoring ability to understand the problem is the cost/efficiency of understanding (and applying it).
I agree with your other statements, but I feel you're suggesting the non-sense is scoped to just math. It's not it's almost everything that we do (exceptions are social interactions including care taking, etc.)
So in this frame your "nonsense" is (almost) everything that we do. Personally I'd like to keep doing things.
John von Neumann
No one wants a data center in their back yard, but in the private sector I think adoption isn't as political as some make it on Hacker News.
There's no particular reason to believe that solving math theorems generalizes to engineering or robotics without a whole lot of additional work.
Essentially gifts for the annointed.
Math proofs are right in the sweet spot for training LLMs with RLVR. It isn't some general "LLMs are getting insanely smart!". Even most software development itself is miles away from being as well suited to training as math proofs are.
The majority of math research is akin to professional chess. Completely useless and the folks doing it are using their giant brains to play a game that no one outside themselves benefits from.
Mathematicians also decide what to prove in their research - taste is not a skill we have RLVR'd away (yet, not claiming this is fundamental).
Of course, the field is being fundamentally transformed, it will probably end up looking more like experimental science in the future.
All I'm saying is the math advances of late really hasn't changed much outside of math as far as AI is concerned.
The foundation was started in 1994, Wikipedia says "one of the largest charitable organizations in the United States with assets of over $5 billion in 2022" - Jim Simons founded the Renaissance Technologies hedge fund.
The foundation was an early backer of machine learning for science, including funding the development of the Lean proof assistant, which has revolutionized how mathematicians work and made AI-assisted proofs possible. Additionally, the foundation has convened workshops, lectures and collaborations that have brought mathematicians together to explore and discuss AI’s role in the field.
Second, the whole point of arXiv is open access. It didn't use to be this way. Research being disseminated as widely as possible is a good thing.
https://www.simonsfoundation.org/flatiron/
He has invested in AI for a long time:
https://www.wealthmanagement.com/high-net-worth/family-offic...
The people here who depict him or whoever runs his funds now as a pure philanthropists are wrong. These tiny investments into academia pay off many times.
[1] https://www.simonsfoundation.org/news/from-trust-to-verifica...
[2] https://lean-lang.org/fro/
Quanta magazine is the propaganda arm.
The headline in this piece made it look like maybe a foundation was trying to help mathematician's push back against the unwanted assault on their profession by the AI labs. The section I quoted shows that's not the case.
Also not sure how you interpreted "foundation started by the Renaissance Technology hedge fund billionaire" as a mindless boost.
I'm going to defend my comment. I said:
> The obvious question here is "who is this foundation and are they working with the AI labs". I answered both.
You said:
> Respectfully, you didn't answer either.
My first comment started by quoting:
> Under a partnership, the Simons Foundation, Anthropic and OpenAI will commit $15 million in combined funding and resources
That answer the question: are they working with the AI labs?
And then I said:
> The foundation was started in 1994, Wikipedia says "one of the largest charitable organizations in the United States with assets of over $5 billion in 2022" - Jim Simons founded the Renaissance Technologies hedge fund.
I think that's a pretty solid starting answer to "who are they", and it tips people off that Wikipedia can answer in more detail.
It also leaves opportunity for people like yourself to speak to Jim Simons' reputation and fill in more gaps.
OAI and Ant got blowback for essentially strip mining mathematical discoveries into PR wins for their models, accidentally laying waste to the research field in process. Throwing ~$5M each into PR whitewashing (partially in token credits), seems self-serving.
Kudos to the Simons Foundation for seizing the moment to offer the labs a fig leaf of respectability. Might have been the fastest "Yes" on a grant proposal ever.
It’s like saying the power loom laid waste to the field of textiles.
Ironically, that has been that way for most people since forever.
Comparing with the situation in programming, where code evaluation (obviously analogous to "understanding") is that bottleneck now, should get people the idea of being in the same boat.
It is my understand that there isnt a lot of innovation here. Rather the (broad) field of mathematics got mined for solutions that already existed within the corpus.
It implies "We didn't know we already knew how to solve these problems". How is that a good look for mathematics as a field?
I think we’re still trying to figure this out. Once the proposed proofs are verified and deciphered I think we’ll have a better answer.
For example [1]:
> In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align.
Or [2]:
> Use of AI tools, when done responsibly, can support not just the initial generation of a solution, but all of the valuable followup activities that traditionally flow out of that solution. But at the current time, the opposite is often occurring: problems are being solved autonomously by AI prompters who have no interest in the broader field itself once their initial target is "solved", and do not understand the AI output well enough to answer questions on the result, give talks, or otherwise interact with the rest of the field.
> ...
> solutions to open problems are now being harvested at large scale in an unsustainable fashion, leaving entire fields of mathematics much less fertile than when such problems were solved in the traditional "Math 1.0" fashion.
[1]: https://mathandai.org/
[2]: https://mathstodon.xyz/@tao/117395268130901862
This applies to all fields and pursuits where AI is effective. Yes I think about this with regards to various things I’m working on.
This is just the nature of things, you need to adapt and not throw a tantrum like a child. You need to not behave like Terrance Tao who is essentially like a child in an adult’s body in terms of his behavior and lack of wisdom, and keep in mind he was a child prodigy so this isn’t a knock at all or statement about his intelligence, only his development as a man.
You can mourn, as I have for the field of programming as I knew it which I have loved since I was a child, but you need to move on.
If AI can actually replicate mathematicians, sure. We don’t have evidence it can. We have evidence it can do useful stuff once promoted by human mathematicians. But if all the Terence Taos “move on,” we won’t have those in America anymore.
(The irony of ironies would be the mathematicians prematurely moving on causing American AI progress to stall in the future.)
Best I can tell the biggest complaints are really just that the future of their career is largely combing through lean and they don’t want to do that. Too bad. Adapt or get off the pot.
Mathematicians need to completely rethink the prestige paradigm. Counting proofs no longer works. That doesn’t mean there’s nowhere for them to go. Now it’s about gleaning human understanding from the lean. Maybe in the future LLMs can do that too and it’ll be all about formulating new conjectures.
Jeeze, that's an almost impressively charged way of saying "private company performing SOTA research on open problems that anyone has been welcomed to approach for over a century" lol
I think it does a disservice to the dialogue to strip away any nuance here and just paint these companies as evil for doing what everyone has been anticipating companies like them doing well before LLMs even existed. It's clearly just trying to fit these events into a specific narrative which does nothing to actually address the inevitability of everything that comes next. Feel free to pressure OpenAI and Anthropic to stop performing math research so that it can just be picked up by whoever catches up and doesn't care about bad PR. I'm sure Musk with Grok will be extra considerate of pure math researchers when he sees an opening to pick up those scraps lol
I’m in the funding markets around this stuff. Nobody took this into account. It’s more for PR with government and potential hires (and maybe some corporate marketing).
Softbank's rally began in Japanese markets on 3 September and American markets on 4 September. OpenAI announced on 8 September. When OpenAI delayed its IPO plans on 13 September, Softbank sank back to its 7 September level [1].
[1] https://asia.nikkei.com/business/markets/softbank-group-plun...
On ChatGPT: Settings -> Data controls -> Turn off “Improve model for everyone”
On Claude: Settings -> Privacy -> Turn off “Help improve our AI models”
They can scrape your work after you publish it.
(Yes I know it's not the group directly receiving the founding)
Mathematicians are not dummies?
In a sense, yes. There is no Simons Foundation for laid-off programmers. Taxi drivers and truckers, meanwhile, are really just trying to block change.
> wouldn't that make them the group that needs support the least?
I don't know. From a practical perspective, I am more confident the world will need mathematicians in 50 years than that it will need coders.
They may be a vanguard.
> find it hard to believe that AI doesn't represent a net potential benefit to human understanding of mathematics. Yes it can be misused
Have you read Tao’s criticism of AI in mathematics? The concern isn’t mis-use, it’s ecosystem collapse.
A good analogy would be offshoring. If AI causes higher mathematical thought among humans to stop happening for a generation, we could wind up in a state where the field stops progressing because AI is unable to generate new interesting questions or cross-link findings into practical applications.
More directly, the risk is that happens in America but not in a more-thoughtful country.
Just because AI is capable of churning out vomit inducing prose, doesn't mean we need to surrender to a future filled with it. Humans who actually care about what they're doing will use AI when and where it should be used. I trust the intelligence, curiosity and tenacity of mathematicians to learn to work with AI. I don't understand the sky is falling worst case scenario Tao and others seem to be taking as the most likely future.
…yes. That’s why the human mathematicians are having this debate. How to keep the human mathematicians and their founders motivated to keep doing math, potentially more productively with these new tools.
If AI saps motivation from some mathematicians, I question where their motivation came from in the first place. Maybe they're just too wedded to the traditional way of doing things and aren't fully appreciating the actual productivity gains AI makes possible.
Again, have you read Tao’s recent criticism of AI in mathematics? Nothing you’re saying is disputed.
> If AI saps motivation from some mathematicians, I question where their motivation came from in the first place
Question away. I care about results. If a substantial number of great mathematicians say this is a problem, and a substantial number of students agree, whether they’re unappreciative of their potentially pending unemployment is irrelevant to both that fact and the fact that they’re not going to be producing mathematics. (Again, here. The American mathematical ecosystem collapsing doesn’t mean the same will happen abroad.)
We don’t know this! We might just have no more American mathematicians because folks who aren’t mathematicians don’t understand that we’re turning mathematical breakthroughs from just a couple decades ago into real, working technology.
> It's not even clear if the human race can survive until then
It’s pretty obviously clear the human race can survive for hundreds more years…
"Climate change is going to kill everyone in 50 years so we'd better work fast if we want to burn all this coal by then"
Not in the same extinction-class event way. In large part because hiring developers is still profitable.
Also, not remotely as well organized or proactive as mathematicians anpparently are. So maybe less vanguard than the cannon fodder at the front.
You have to actively design society to accommodate for the dangers it poses.
Of course everybody should "learn to use AI", but the real questions here are wildly different: can everybody use AI? Do the big US companies succeed in capturing the system, effectively shutting out every competitor and how do you imagine to benefit from that? Etc.
knowledge workers are building their own gallows and it probably can't be stopped.
they’ve only had a few weeks to deprogram so I’ll let it shake out just a little longer
The whole discourse of past few weeks has been mathematicians claiming the opposite.
When you remove this greed and status seeking you might actually end up with a healthy environment.
I don’t necessarily disagree but it seems like the AI companies are just as status seeking and infinitely greedier.
It may be true in some cases but as a blanket condemnation of the entire field it makes no sense. Moreover, I can't fathom how you could reach this conclusion if you've actually done any reading on "the whole situation." The reality is precisely the opposite of what you're claiming.
Mathematicians are upset partly because AI companies are "scooping" their work. If you had worked on something for years and this happened, you'd be upset, too. The manner in which this happened with Navier-Stokes was unconscionable. The mathematicians who did the work deserve recognition. OpenAI deliberately stole it from them.
More importantly, the purpose of mathematics isn't to produce proofs. It's to produce mathematics and mathematicians. Working through problems helps people find new mathematics -- and makes people mathematicians. A machine that generates proofs destroys that. It breaks the cycle that makes mathematics fruitful, interesting, and not just self-regenerative but self-propagating.
AI companies aren't just clear-cutting the fields of math; they're sowing them with salt -- and they're doing this precisely because of greed and hunger for status and the title of "first."
Perhaps to some maths is about progress, like other sciences, rather than self-portrayal
Quants are open about that they just want to make a shitton of money.
The guys I know who work at OpenAI just want an expensive car and a hot wife to fuck.
Mathematicians(and many academics) however have long been hiding behind the guise of furthering human knowledge, understanding things, etc. Then a model does theorem proofs and suddenly there is chaos and the real incentives and motivations are put on display for the world to see.
See professor Williams' thoughts on a recent conjecture that openai proved: https://people.csail.mit.edu/virgi/thoughts.txt
And Williams thoughts are kind of idealistic. "Now the credit is shared across the entire field". This "credit" does not give your department grants or further your own career.
Rather it incentivizes you to be the first one to prompt, and to steal ideas from your peers because you can prompt better and have your name on more discoveries.
You're gonna get downvoted but this is absolutely true. People who've never been in real professional academia don't understand but this is exactly what most very successful academics are like.
> When you remove this greed and status seeking you might actually end up with a healthy environment.
Nah I think you're just gonna have collapse because you've removed all incentive.
Seems that space is really about that
You really cannot see any difference between the government and corporations supporting something? This "things have always been that way" talking point is getting out of hand.
So you'll have to excuse me but I'm not even getting the tiny violin out of the case for this one.
That doesn't mean you get to take over private companies and start telling them where to spend their money.
This isn't about sympathy for one, or even all of these companies. I hate more than one of them myself, and wish for their demise.
But I like America, freedom, capitalism.
Anyone in a position of power who doesn't want to end up killed? Like I'm not advocating for violence here, I'm just saying the list of political figures who "didn't care what regular people thought" and the list of political figures who were then subsequently murdered in public acts of political violence are a venn diagram that's practically a circle.
> That doesn't mean you get to take over private companies and start telling them where to spend their money.
I didn't advocate anything like that.
> But I like America, freedom, capitalism.
And I like people being able to live a good life, which Capitalism and lately America itself seem to be opposed to. Do you have an actual counterpoint to make or just more chest-beating?
You can say you do, by threat of death for disobedient politicians, but...well, that's bullshit. The people murdering & attempting to murder politicians don't fit the description of "regular people." And you're almost entirely incapable of directing policy with that tactic.
https://ai.google/gemini-for-science/
We will only give the free tokens to the top X% of scientists, which is now a much smaller pool and you are unlikely to be considered LLMs or not.
1. exceptionally high IQ
2. Enough resources to bootstrap yourself
Those are who survives in the new economy with any modicum of quality of life.
There is some success with this kind of strategy already when it comes to space, LHS and ITER come to mind. NASA is somewhat operating on this very same principle although it is a government organization to begin with.
Although the opposite reaction is that you should keep people behind inventions poor to encourage them to create more inventions which ultimately what ends up happening in the real world more often than not. The people who revolutioned the world did get fame and glory, including numerous monetary compensation packages - but compared to the people who sold those inventions they only got a tiny fraction of a fraction, this is especially clear with people who are normal employees and inventions are credited to a company rather than the few people who made it possible.
How shameless can you be?