The social fabric that produces math got ripped up by marketing guys who didn't even bother to check their work.
He described it at 'strip mining', 'rude', and said that many grad students, who are given problems like these as a part of their training, had the rug pulled out from under them (because its customary to let people know you are working on something to prevent this kind of thing).
And your whole analysis is that Tao is worried about his 'identity', status, and 'being a differentiator'.
This is projection on your part. People have values that bear no resemblance to yours and it would behoove you to learn to recognize that.
How does that make any sense? Why do you assume that someone more intelligent would not be able to wield any AI tooling better than an average or below average human? Just curious if you're thinking short term or long term on this.
I mean, clearly "tooling" is not a perfect analogy for AI. As others have pointed out, if you pay money and get back a full website, app, game etc. it feels a lot closer to a service.
It's like asking why an expert pizza maker is not in a better position to succeed now that he has an excellent pizza delivery number he can call to have one available to his specification in an instant.
Has OpenAI shared any new interesting _problems_? I.e. do more than strip-mine mathematics, as said in the article, but said: "Here is a question I cannot answer, it's interesting for this and that reason, I believe it's true for this and that reason, it's beyond me though, have at it." Has that happened yet?
Considering that this is where the mathematician excels over machine wouldn’t that only offer a new view from such a mathematician that “OpenAI has rapaciously stolen from mathematics that last dignity: of choosing worthy problems”? Perhaps with sufficient effort the community of mathematicians may yet forestall such an effort.
I find it weird to blame OpenAI for using math as a benchmark. If they hadn't done so, then in three months, say, after releasing Bel, someone else would have used math as a benchmark for it (like mathematicians already do since Fable 5 and 5.6 Sol). The result would have been the same (hundreds of open problems solved quickly).
One aspect that currently frustrates me is that even paying for the highest plans and spending multiple quotas across all flagship models, I still haven’t been able to reproduce any of the amazing feats Anthropic and OpenAI gush about.
I suspect their internal harness, models, and thinking budget far outstrip anything us peasants have access to (never mind the compute).
So saying that they achieve all these headline results with 3 hours of GPT Pro is disingenuous. If that were so, hundreds of math phd students would’ve already recognized it.
I’m coming to the realization that my monthly subscription is only helping subsidize their real internal AGI, and my interactions are a small amount of human feedback and creativity which they can strip mine should they choose to.
Same as code, the llm can generate vast amounts and it seems to work, but no one understands the documentation Claude Code, or other LLMs, produce. Essentially, garbage because, to make use of it you need to be able to understand it, usually at a cost (unquantified), and if only LLMs do then what is the point?
It turns out it doesn't matter, because outside of a few narrow bands like Claude Code, no one cares what documentation an LLM writes for your project, because no one is ever going to go looking for someone else's project or library to solve their problem anymore.
So either an LLM decides to pull in your project as a library for reasons, in which the LLM can understand the documentation, or else no one besides the creator is using it anyway. So it doesn't matter.
Why would anyone use someone else's AI-coded project if they can get their own version that better fits their own needs in less time?
I find it interesting that, several years ago when discussing AI, folks used to focus on how automation would first come for blue collar work. Things like driving being automated and truck drivers replaced. And then eventually on the horizon we would see things like this.
But we still have no self driving cars. Seems like the automation came by in the opposite direction. Perhaps driving will actually be the final thing automated.
While I agree with your statement overall, as someone who drives everyday in LA alongside Waymos without anyone inside of them I must disagree with this aspect of it.
A better formulation would be: we don't know if we have self-driving cars.
Because if it became fashionable for pedestrians to wear large green dresses with red balls, and everybody would wear that, we have no idea what the AI would do.
We still have no general self driving cars. What we have is a bunch of geofenced tests. While we are closer than ever, we are still seemingly a long way away from truck drivers being obsolete was foretold over 10 years ago now.
The inconvenient truth is the “desk jobs” involving a human operating a computer are far easier to automate than piloting a physical vehicle through a complex environment… A desk job is doesn’t require lidar and cameras…
It was too easy to assume that an AI would never approach human intelligence and hence would only be used for “boring” jobs like driving.
I’ve long disliked the hype around AI but now see that human intelligence is perhaps slightly overrated, at least in terms of the loftier positions seemingly requiring such.
Claude Opus puts to shame any highly caffeinated “10x” software developer. Not saying it’s perfect, but damn good. It can knock out difficult code analysis/reverse engineering more than 20-40x faster than I can. There was even a time long before AI when people thought the same of me…
Hell, at this point, I’d rather deal with Claude than a low-cost offshore team that puts up crappy implementations with endless go-backs and rewrites. I say this from actual experience, not xenophobia. There likely are some high performing offshore teams, I just wasn’t lucky to have the chance of working with one. Have had a couple of local colleagues that were worse… Claude’s probably much cheaper too.
Unfortunately, the “knowledge worker” jobs historically tended to be higher paid.
On one hand, AI is a major asset to experienced professionals with access.
On the other hand, it robs junior engineers hard-fought experience - much like watching a movie instead of reading the book.
And longer term, I think the entire economic structure of society is going to change. Doctors, lawyers, software developers, engineers — none of these are safe from AI reducing the need for headcount.
human intelligence was always overrated, at least in terms of it's actual value to society. phds are often unemployed or "overqualified" for the roles they apply for, roles that pay the most are often roles which are less deskbound and more client-facing, roles that ai cannot replace.
An LLM automating web developers with 99% success rate saves the company millions of dollars and allows them to launch products and features faster.
A truck or a car that has a 99% success rate would be the top threat to society and quickly rise to the leading cause of death under 30 if widely deployed.
“99% success” is too vague to be especially meaningful in such different use cases.
99% successful web development where the 1% missing is security that and the company leaks its entire repository of user data every few months is not good.
99% successful car driving where 99% of 5-year periods have zero accidents per car is an order of magnitude safer than the average driver. (And gut feeling, I suspect approaching the tail-end of the safest drivers on the road.)
An LLM automating web developers basically puts the company out of business. Why would customers pay a developer when they can just build it themselves?
There are a lot of things that people are capable of doing themselves that they pay other people to do for them.
I agree that LLMs have and will continue to increase the number of activities that people can DIY. But I believe many people will still choose to pay for others to do things on their behalf.
Human level embodiment took 10,000x longer to evolve than human level abstract and symbolic information processing, and is also probably 10,000x harder to replicate in an alternative form.
Driving is heavily regulated, and there are a million interest groups lining up to sue to stop self-driving. Imagine all the people who make their money from car crashes, for example.
Yeah, as always in AI hard things are easy and easy things are hard. How many times have I heard condescending comments from programmers that radiologists are just about to be replaced by AI. And well, AI turned out to get kind of okayish at programming much faster than being acceptable at being radiologist.
Developers are guilty of making reasonable projections based on contemporary industry trends, and they're getting slapped by unexpected revolution in computer science.
Self driving in a winter storm? Self driving in torrential rain? Self driving when mud covers a sensor it needs? Self driving if it hits someone? Pretty sure Tesla would say you were driving it then.
Exactly. Everything below L4 is _incredibly stressful_ and unpleasant to drive, because you have to be constantly aware and alert without having anything to do.
In the case of Tesla, daring to call such a system "Autopilot" is a breathtaking level of irresponsibility. You are responsible for the vehicle you are driving, practically, morally and legally, even if a companies' marketing and the system itself does its very best to divest you from that simple and obvious truth.
Something I'm noticing a lot is that automation finds easy footholds in unregulated industries because there's no basis to push back on it. And there's a lot more tolerance for poor quality work in unregulated industries too.
Broadly speaking, this is proof that there will be no jobs coming after AI.
All past inventions have put some of the most miserable humans out of a job. Farming by hand is hard, so is copying books and don't even get me started on the dullness of making clothes by hand.
Driving all day isn't all that far off, though still much better than the above and definitely better than riding horses all day.
Telegraph operators? Hell no. Dude sitting in an elevator all day? No thanks.
It's always been from the other end. This time around, there's gonna be some 10-20 years of robot manufacturing, then a universal lifetime of robots fighting misaligned robots until enough paperclips have been manufactured.
Or you know, we block out the sun and live in caves or whatever you fancy.
Is Terence Tao just another AI booster nowadays, by the sheer amount of PR generating posts? Reading HN one might think that there is only a single mathematician in the world left.
I remember just last year he said the LLM were like incompetent assistants, but not completely useless. The tech advances are mind boggling just looking back at that.
I do believe after the initial shock mathematicians will be able to use their math knowledge to solve practical problems, instead of lets solve this conjecture, prove this age old math riddle, how the pattern is possible. They may have some uses in fringe areas, but it doesn't seem all that useful. These guys are obvious quite brilliant, so when they combine it with other fields which they can branch to due to LLM's, they can still stay relevant. Ask your software engineer how that went.
Math isn't useless. One of its defining features is its "unreasonable effectiveness" in formulating scientific ideas. It's hard to say exactly why it's so useful, but it is, even if mathematicians aren't trying to make it useful.
It's not at all clear whether the kind of math created by LLMs will retain the usefulness of the old math. LLMs are good at rigor but bad at intuition. It's not even really clear if the rigor was ever all that important. Theoretical physics is full of people using math in ways that don't meet the bar of rigor that mathematicians set for themselves, but they have enough physical intuition for what they're doing, so it doesn't matter. It's an open question whether post-LLM math will continue to supply scientists with the kinds of ideas that they need from it.
Mathematicians might just be experiencing the first phases of the cycle of acceptance - resistance and anger, next is depression then eventually embracing it. Software developers as a whole are a bit further along the cycle.
IMO the most useful thing a mathematician can do is not solve “practical problems” but to come up with conjectures and riddles that look around several dark corners of math at once. The proving of a conjecture is a bit of a sport done to impress people with your cleverness; but the clever person was the one who made the conjecture to begin with.
Given the trajectory of LLMs to date I see them helping construct proofs for conjectures but not devising new conjectures of any material substance any time soon. The challenge is, as Tao has said elsewhere, part of being able to formulate a conjecture is by exploring the landscape around it by doing proof research. Seeking answers finds useful questions. The fear is the tools will take away the exploration of the landscape. But that’s silly IMO. It takes a special type of lazy to let a tool take away your understanding that’s important for what you’re goal is, and a special type of passion to learn with a powerful tool. The passionate will adapt and progress will accelerate, not slow down.
For instance Tao has posted some of his interrogations of proofs with AI assisted reasoning and it didn’t seem to diminish his ability to establish insight rapidly, but to shut down avenues rapidly and to pivot and expand his understanding rapidly. The insight was all his own, as was the path of inquiry. The understanding of the output was his as well. He carries it into tomorrow and uses it to formulate new more interesting conjectures the next day. The AI ceased to “exist” as soon as the inference turn was over.
The hand wringing is pointless and lame. John Henry moves aren’t necessary or useful, and when I see a tunnel boring project now I see tons of people well employed there, just the holes are bigger and better, and they’re engineers instead of strong backed hammer slingers.
> Much as one cannot unhear a movie spoiler or a crossword clue, one cannot explore a problem as profitably and richly once one is aware of an existing solution
Certainly, it’s like being made aware of cheat codes to video games: One doesn’t enjoy the game as much after but surely knowing something is true means you can find many other things that come from the pathway to it now that you know it’s true. Lots of science and tech is like this where someone shows something is doable and then people find better ways to do it but until that person showed it was doable there was no progress.
> I am horrified by the many person-years” of research, particularly by young mathematicians, “being casually disrupted or destroyed,” he wrote.
That’s what technology does. And he might be upset but we’re the ones paying for it and frankly, I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Most notable is the fact that the released facts are like “treated waste”. But if the question was worth answering and the value is only in a good answer and not simply a correct answer, then the value has simply not been realized.
But that feels strange then that the value is in the good answer, not just a right answer and yet one finds oneself unable to go get the good answer because a correct answer exists.
The fact that any answers are made public at all is useful to us all. That’s free knowledge. Would it have been better if OpenAI had discovered this very achievable fact and not said anything? Surely the papers, post discovery would have spoken of the “hoarding” of such “essential human knowledge”.
> The fact that any answers are made public at all is useful to us all. That’s free knowledge.
When mathematicians discover new results, they automatically become experts during the process, and then go around giving talks to explain their results, methods, and intuitions to other mathematicians. After years or sometimes decades of refinement and a healthy dose of serendipity, some of the mental frameworks percolate to other fields.
No one from OpenAI is willing to give a talk on any of their 300+ results because their machines have decoupled formal proofs from actual knowledge.
Right so this goes to the other alternative; there's still useful work for mathematicians after all in dissecting, distilling, and generalizing these results. But according to some we now inhabit an excluded middle where the AI produces useless results but also makes these problems useless for mathematicians to study further.
> I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
But the value in seeking mathematical answers was never in the answers themselves. It was in the things one discovers along the way, the questions asked, the tools developed. The artisanal fashion is the part that benefits non-mathematicians.
These AI proofs only serve as an I-told-you-so. They're not creating surrounding theory which can later turn out to have useful applications elsewhere.
> That’s what technology does. And he might be upset but we’re the ones paying for it and frankly, I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Would you prefer if graph theory didn't exist but we could answer if you can pass all bridges in Königsberg, without going through same bridge twice?
Or if we could answer any question without knowing why? What about answering Hilbert without theory of Godel's Incompletness theorem? Or knowing Nth digit of Pi without calculus.
Because that's essentially what you're asking for. If you gave humans a Djinn that
could answer perfectly any question, it would kill most of our endeavors. Because it's not a problem that was unsolved for years "It's just the thing Djinn already answered so why bother?" Even if one is extremely curious, and devote a chunk of their life answering it, others would not see value in that curiosity. Because a Djinn can answer it in a few minutes.
Imagine you are Euler and magical Djinn's exist (that possess all mathematical knowledge written up to that point exist and function identical to LLMs). You ask it to tell you answer to the bridge riddle and it says that's not possible and even gives some plausibly sounding examples even. Then it throws a 11 pages of gibberish proofs at you, which are all true but very convoluted.
And what if you start digging into it? Won't other people say - "Hey Euler go back to ploughing the fields? We can have Djinn's answer all the math questions but this field isn't going to plough itself."
Today's, the Djinni-Euler's equivalent of someone looking at LLM's Navier Stokes equation proof.
Perhaps they would discover new Liquid Set theory that would turn Liquid dynamics from a field fraught with problems into a beautiful mathematically simple meadow.
> And what if you start digging into it? Won't other people say - "Hey Euler go back to ploughing the fields? We can have Djinn's answer all the math questions but this field isn't going to plough itself."
Seems like an overly pessimistic take to me.
If you have a magical Djinn happy to answer questions, why wouldn't you badger it a bit for the details? I can't imagine Euler of all people just wanted the answer.
> I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Given that this is pure mathematics we're talking about, for the most part: Why?
Perhaps you are a mathematician and so these questions are relevant to you, but for most of us, these questions and their answers will not make any tangible difference in our lives or society.
Maths has made a very real and tangible difference to society. The easy, obvious, answer is online banking, which wouldn't work without crypto, which is pure maths. There are many more.
It used to be that Pure Maths got to affect the real world via Physics (and that odd thing where last decade's interesting mathematical exploration turned out to be the solution to this decade's Physics discovery). But t'internet consumes Pure Maths pretty much raw.
Terrence Tao was very supportive of AI and formalizing math with lean when it looked like it was giving ‘generalists’ like him an edge over mathematicians too deep into one particular niche field.
But now that it’s letting everyone, including mathematicians who are perhaps too specialized, explore ideas and patterns from related math fields, he’s suddenly ‘on a war footing’.
I don't think it is self-serving. Tao has stated plainly that he thought LLMs would go the route of assistants, like co-pilots. But what he feels now is that they are actually being engineered to be replacements. His claim is that the way OpenAI dropped these math results isn't "assisting" anyone, so we should all read between the lines.
Consider any man at his job, fighting the good fight. Your boss says "I've hired this man to assist you" and you are happy to finally have some help with your difficult task. Then one morning you come into work and see that the coming day’s work was done overnight by this other fellow. And the realization sinks in, he isn't there to help you, he is there to replace you.
In this view his reaction seems totally expected. I expect many professionals, e.g. doctors, lawyers, accountants, etc. will make this realization sooner or later. The companies are saying these tools will assist professionals, but in reality they are aiming to replace them.
> The companies are saying these tools will assist professionals, but in reality they are aiming to replace them.
If anyone doubts this, consider that Anthropic considers its TAM to exceed $30 trillion which is nearly the entire GDP of the US and 25% of the world GDP.
Only makes sense if they believe they will massively replace labor. Which, to their credit, they used to admit openly and publicly and only stopped because some crisis PR people told them "hey maybe you shouldn't say the quiet part out loud while the hoi polloi still have the power to stop this from happening".
I’m not making a claim one way or the other about the intent of these companies, but if your product made labor 3x more productive, you could still easily justify a TAM of the entirety of US GDP, without resulting in anyone losing their jobs. Obviously, here in reality, AI does act as a near 1:1 replacement for people in some roles, so we should expect some job losses. But I don’t think there’s any reason we should expect the entire US labor force to be automated away any time soon, even taking these assessments at face value
Do their own hiring practices reflect that ambition? They sure seem to be recruiting a lot of humans for typical roles in business, legal, and engineering. If they want to flex the power of their models to automate human jobs, why not lead by example?
> They sure seem to be recruiting a lot of humans for typical roles in business, legal, and engineering.
They have practically infinite investor money to throw at salaries (lost in the noise of how much they are spending on compute) so why not use it for now to reach their goal as fast as possible?
My thesis isn't that they have already achieved the ability to replace massive amounts of the labor pool, just that that has to be their goal given their stated TAM.
> If they want to flex the power of their models to automate human jobs, why not lead by example?
They don't want to flex this. They realized (after a false start) that it is better for them to avoid talking about this in public.
That doesn't mean their goals changed, they just realized that flexing before the goal is achieved could endanger the goal being achieved through political backlash.
You do realise Anthropic's management, after throwing its tantrums, gets a seeing to and has to do what its investors want? Which is pump up the valuation.
You might be mistaking my comment as a value judgement rather than an attempt to charitably explain the latest media communications from Tao. I detect in his position that some trust he granted the AI companies has been violated.
You are, of course, right that doctors, lawyers and accountants have more control over the environment they work in compared to mathematicians. But it doesn't change the underlying argument Tao is making. Your observation that those professions will react differently is likely to be true and only time will tell how effective their response will be.
But AI "assistants" is a marketing approach being made to all professionals at this time. Tao is implying this is a Trojan-horse strategy. If you let the assistants in without reasonable protections, you may lose control over the environment you are trying to protect.
you may not be aware of it but society largely runs on the results of maths, clueless indeed. and regulated or not, if there are financial savings to be made anyone can be shoved under the bus.
One might say, in the end, what's wrong with being self-serving? Are we _all_ meant to be self-sacrificing? Are we all meant to be the eggs that get cracked to build this wonderful future ommlette?
> basically both sides now dislike that he flip flopped
No, the dumb thing is the idea that there are "sides".
> basically both sides now dislike that he flip flopped
Literally the only people with this opinion of Tao are internet forum warriors who have no expertise in the field and who's opinion of Tao don't matter in the slightest.
> who's opinion of Tao don't matter in the slightest.
Similarly, Tao being ‘on the warpath’ does not matter in the slightest when it comes to formalizing math and finding proofs to important unsolved problems with AI.
“I’m on a war footing,” he said while grabbing coffee during a two-day math workshop at the University of California, Los Angeles, that was rife with talk about the existential crisis that artificial intelligence has created in his field.
I've never perceived him as 100% supportive. He has rather been open-minded about a new technology and exploring what it can do. Now it turns out it can destroy his field, so he's naturally against it (at least against the destruction, not necessarily against the technology)
I think ‘destroy his field’ is ‘destroy his method of being famous in the field’.
Terrence Tao is famous because of solving problems better that most mathematicians because he has an uncanny ability to look across different math fields. AI gets everyone this ability for 20 to 200$ per month, eventually free.
Most mathematicians are happy to see interesting problems in their field being solved, and are looking to build on these to find more interesting problems.
The point is to make the field progress by discovering new things!
Who gets credit for what and how credibility is assigned is going to be muddy for a while but that’s the case whenever a bunch of new science happens in close sequence. History is full of math/science discoveries having debated and dubious provenance.
I can't see how the field can even exist - not to say progress - if any problem can be solved before a human can understand it. Looks like mathematics without mathematicians, "progressing" in the same way as paperclip optimizer progresses in its productivity.
It provides deep insights into logic, computation, provides tools for us to understand the universe, establishes mind blowing relationships between seemingly unrelated things.
For example “how much information can a black hole contain?”
To whom? If there are no humans in the field, there is no one to get the insight. Maybe you are right, and there is just a new type of a mathematician being born, but as an outsider I just can't see what they could look like, what will be left for humans to contribute
> Realistically, math will be done by well funded teams of people instead of cult of personality mathematicians.
Most math is already being done by meagrely funded mathematicians. The entire US federal budget for mathematics is like $100M. One college football coach can already make 10 percent of that. No mathematician is making bank.
Is the implication of all this that mathematics research should get a cash injection to pay for high-powered computational tools?
> Is the implication of all this that mathematics research should get a cash injection to pay for high-powered computational tools?
Math will, sure. Mathematicians, doubtful. After all, most high end physics research with billions in funding is now done by postdocs making a lower middle class salary.
Realistically, math will be done by well funded teams of people instead of cult of personality mathematicians.
Also, insights from scientific discoveries are for everyone. You do not have to understand the complex multi dimensional algebraic geometry of general relativity to appreciate that gravity bends time as well as space. You don't need to understand fifty years of linear programming research to use a modern solver.
So as every high schooler. That doesn’t mean much for actual results similar to what OpenAI “generated”, and doesn’t quite explain the “war footing”, does it?
We’ve yet to see the democratizing fantasies in math field to materialize.
For me it just shows that modern math is not that important and mostly ego driven. If it was important, mathematicians would cherish the progress. I can't imagine bio researchers get mad that AI cured cancer.
It was devastating to learn in my late 20s that 99.9999% of what the average person does is based on personal ego and not a communal vision of the future.
There are plenty people in every discipline that prioritize their ego over measurable progress towards a stated goal - even less so a community focused goal.
The TLDR seems perhaps tongue-in-cheek, but it's a worthy thought: the situation where our best experts find new science to be inscrutable is close at hand, if not here now.
Humans have been guilty of burying things we don't understand for millenia. Will we continue to do so "because AI"?
> They “used math for what they needed, which was to evaluate their models,”
OAI first paper on the prize was a pretty shitty thing to do. But the rest of this looks like they are just mining the corpus and taking a brute force approach to do it.
Im going to say this again, the "pure math" academic types need to get a grip. Plenty of your peers got PHD's and happily made a fortune in finance, while screwing the world (See 2008 housing bubble) and none of you said a peep about that.
> Im going to say this again, the "pure math" academic types need to get a grip. Plenty of your peers got PHD's and happily made a fortune in finance, while screwing the world (See 2008 housing bubble) and none of you said a peep about that.
Everyone who built an identity on being the most intelligent in the room is going to have to come to grips with that no longer being a differentiator.
The social fabric that produces math got ripped up by marketing guys who didn't even bother to check their work.
He described it at 'strip mining', 'rude', and said that many grad students, who are given problems like these as a part of their training, had the rug pulled out from under them (because its customary to let people know you are working on something to prevent this kind of thing).
And your whole analysis is that Tao is worried about his 'identity', status, and 'being a differentiator'.
This is projection on your part. People have values that bear no resemblance to yours and it would behoove you to learn to recognize that.
How does that make any sense? Why do you assume that someone more intelligent would not be able to wield any AI tooling better than an average or below average human? Just curious if you're thinking short term or long term on this.
I mean, clearly "tooling" is not a perfect analogy for AI. As others have pointed out, if you pay money and get back a full website, app, game etc. it feels a lot closer to a service.
It's like asking why an expert pizza maker is not in a better position to succeed now that he has an excellent pizza delivery number he can call to have one available to his specification in an instant.
100%. We are moving to a time where do-ers will matter more than talkers.
A wild thing to say about Terry Tao.
Builders, please! Do-ers is not the preferred nomenclature, dude.
According to whom?
this isn't a guy who built the railroads here
intelligence in its purest form was never a bottleneck for humans.
Has OpenAI shared any new interesting _problems_? I.e. do more than strip-mine mathematics, as said in the article, but said: "Here is a question I cannot answer, it's interesting for this and that reason, I believe it's true for this and that reason, it's beyond me though, have at it." Has that happened yet?
+1 Good to know I’m not the only one!
This will be interesting to watch: Where will AI creating and solving problems in a loop lead to.
It'd be interesting if AI is great at solving problems but struggles to pose them.
This leads to the comment I've seen many mathematicians make that humans should refocus on understanding not just proofs and mechanics.
AFAIK it has not happened.
Considering that this is where the mathematician excels over machine wouldn’t that only offer a new view from such a mathematician that “OpenAI has rapaciously stolen from mathematics that last dignity: of choosing worthy problems”? Perhaps with sufficient effort the community of mathematicians may yet forestall such an effort.
> wouldn’t that only offer a new view from such a mathematician
Don't invent things to get mad about, please.
They steal from the commons! They add to the commons!
I find it weird to blame OpenAI for using math as a benchmark. If they hadn't done so, then in three months, say, after releasing Bel, someone else would have used math as a benchmark for it (like mathematicians already do since Fable 5 and 5.6 Sol). The result would have been the same (hundreds of open problems solved quickly).
[dead]
One aspect that currently frustrates me is that even paying for the highest plans and spending multiple quotas across all flagship models, I still haven’t been able to reproduce any of the amazing feats Anthropic and OpenAI gush about.
I suspect their internal harness, models, and thinking budget far outstrip anything us peasants have access to (never mind the compute). So saying that they achieve all these headline results with 3 hours of GPT Pro is disingenuous. If that were so, hundreds of math phd students would’ve already recognized it.
I’m coming to the realization that my monthly subscription is only helping subsidize their real internal AGI, and my interactions are a small amount of human feedback and creativity which they can strip mine should they choose to.
“They took’er jobs!”
Funny when it’s someone else eh?
Just learn a new trade Terry.
(I am kidding if it wasn't obvious)
https://archive.li/0LTWn
the live video interview on numberphile comes without the New York Times' narrative filter
Highly recommend.
Link: https://youtu.be/bAnwMdfcMVw
Same as code, the llm can generate vast amounts and it seems to work, but no one understands the documentation Claude Code, or other LLMs, produce. Essentially, garbage because, to make use of it you need to be able to understand it, usually at a cost (unquantified), and if only LLMs do then what is the point?
> if only LLMs do then what is the point?
It turns out it doesn't matter, because outside of a few narrow bands like Claude Code, no one cares what documentation an LLM writes for your project, because no one is ever going to go looking for someone else's project or library to solve their problem anymore.
So either an LLM decides to pull in your project as a library for reasons, in which the LLM can understand the documentation, or else no one besides the creator is using it anyway. So it doesn't matter.
Why would anyone use someone else's AI-coded project if they can get their own version that better fits their own needs in less time?
Anyone without a big C in their job title will be on war footing soon enough.
Cobblers
CEO? Circus clowns?
Is there an echo in here?
Carnival Barkers
I find it interesting that, several years ago when discussing AI, folks used to focus on how automation would first come for blue collar work. Things like driving being automated and truck drivers replaced. And then eventually on the horizon we would see things like this.
But we still have no self driving cars. Seems like the automation came by in the opposite direction. Perhaps driving will actually be the final thing automated.
Blue collar is embodied, white collar is abstracted.
> But we still have no self driving cars
While I agree with your statement overall, as someone who drives everyday in LA alongside Waymos without anyone inside of them I must disagree with this aspect of it.
A better formulation would be: we don't know if we have self-driving cars.
Because if it became fashionable for pedestrians to wear large green dresses with red balls, and everybody would wear that, we have no idea what the AI would do.
It would work fine. seriously what are you on about?
We still have no general self driving cars. What we have is a bunch of geofenced tests. While we are closer than ever, we are still seemingly a long way away from truck drivers being obsolete was foretold over 10 years ago now.
“General” would mean winter driving and I’m not aware of any large-scale tests of things like icy conditions on hills.
Edit: nevermind. https://www.cbc.ca/news/business/waymo-toronto-winter-self-d...
Waymo has been winter driving in Tahoe since 2016 or so. Hard to find icier conditions with bigger hills.
TIL, thanks. That’s heartening to hear as I live in one of those places, or I used to?? The last winter was scary mild.
The inconvenient truth is the “desk jobs” involving a human operating a computer are far easier to automate than piloting a physical vehicle through a complex environment… A desk job is doesn’t require lidar and cameras…
It was too easy to assume that an AI would never approach human intelligence and hence would only be used for “boring” jobs like driving.
I’ve long disliked the hype around AI but now see that human intelligence is perhaps slightly overrated, at least in terms of the loftier positions seemingly requiring such.
Claude Opus puts to shame any highly caffeinated “10x” software developer. Not saying it’s perfect, but damn good. It can knock out difficult code analysis/reverse engineering more than 20-40x faster than I can. There was even a time long before AI when people thought the same of me…
Hell, at this point, I’d rather deal with Claude than a low-cost offshore team that puts up crappy implementations with endless go-backs and rewrites. I say this from actual experience, not xenophobia. There likely are some high performing offshore teams, I just wasn’t lucky to have the chance of working with one. Have had a couple of local colleagues that were worse… Claude’s probably much cheaper too.
Unfortunately, the “knowledge worker” jobs historically tended to be higher paid.
On one hand, AI is a major asset to experienced professionals with access.
On the other hand, it robs junior engineers hard-fought experience - much like watching a movie instead of reading the book.
And longer term, I think the entire economic structure of society is going to change. Doctors, lawyers, software developers, engineers — none of these are safe from AI reducing the need for headcount.
human intelligence was always overrated, at least in terms of it's actual value to society. phds are often unemployed or "overqualified" for the roles they apply for, roles that pay the most are often roles which are less deskbound and more client-facing, roles that ai cannot replace.
An LLM automating web developers with 99% success rate saves the company millions of dollars and allows them to launch products and features faster.
A truck or a car that has a 99% success rate would be the top threat to society and quickly rise to the leading cause of death under 30 if widely deployed.
“99% success” is too vague to be especially meaningful in such different use cases.
99% successful web development where the 1% missing is security that and the company leaks its entire repository of user data every few months is not good.
99% successful car driving where 99% of 5-year periods have zero accidents per car is an order of magnitude safer than the average driver. (And gut feeling, I suspect approaching the tail-end of the safest drivers on the road.)
>quickly rise to the leading cause of death under 30 if widely deployed.
Wait, aren't human-driven cars already the leading cause of death under 30?
An LLM automating web developers basically puts the company out of business. Why would customers pay a developer when they can just build it themselves?
There are a lot of things that people are capable of doing themselves that they pay other people to do for them.
I agree that LLMs have and will continue to increase the number of activities that people can DIY. But I believe many people will still choose to pay for others to do things on their behalf.
Examples?
the point was that 99% rate of success is good enough when failure means nothing, not so much when it means dead people.
So, a treatment that cures cancer 99% of the time but kills the patient 1% of the time is unacceptable?
You have to look at the benefit of something when balancing against a cost.
Human level embodiment took 10,000x longer to evolve than human level abstract and symbolic information processing, and is also probably 10,000x harder to replicate in an alternative form.
Driving is heavily regulated, and there are a million interest groups lining up to sue to stop self-driving. Imagine all the people who make their money from car crashes, for example.
It seems fairer to say that the Waymo fleet has >4,000 driverless cars [1]. There is still a long way to go, but it's rising.
[1] https://pages.skybrian.com/2026/waymo-robotaxi-fleet/
> But we still have no self driving cars.
Do you live under a rock?
0 self driving cars in my country
There are no elephants in my country, they must not exist.
Uh, they aren’t trustworthy and they aren’t fully autonomous. So no, we indeed do not.
By that standard we don't have human drivers either.
The physical world is still more difficult and messy than discrete logic (theorems, software).
Yeah, as always in AI hard things are easy and easy things are hard. How many times have I heard condescending comments from programmers that radiologists are just about to be replaced by AI. And well, AI turned out to get kind of okayish at programming much faster than being acceptable at being radiologist.
> folks used to focus on how automation would first come for blue collar work
Developers are guilty of hubris and they are getting slapped back to reality.
Developers are guilty of making reasonable projections based on contemporary industry trends, and they're getting slapped by unexpected revolution in computer science.
I have a self driving Tesla, as do many others.
Self driving in a winter storm? Self driving in torrential rain? Self driving when mud covers a sensor it needs? Self driving if it hits someone? Pretty sure Tesla would say you were driving it then.
(Supervised)
Yeah, I'm supervising, and I don't think I've had to take over any time this year.
In 2025 it was occasionally driving weird. Today it's a much better driver than me.
> I don't think I've had to take over any time this year.
That just makes you less prepared when you do have to take over. That's the danger of almost-perfect self driving.
Exactly. Everything below L4 is _incredibly stressful_ and unpleasant to drive, because you have to be constantly aware and alert without having anything to do.
In the case of Tesla, daring to call such a system "Autopilot" is a breathtaking level of irresponsibility. You are responsible for the vehicle you are driving, practically, morally and legally, even if a companies' marketing and the system itself does its very best to divest you from that simple and obvious truth.
Driving is actually regulated.
Something I'm noticing a lot is that automation finds easy footholds in unregulated industries because there's no basis to push back on it. And there's a lot more tolerance for poor quality work in unregulated industries too.
Broadly speaking, this is proof that there will be no jobs coming after AI.
All past inventions have put some of the most miserable humans out of a job. Farming by hand is hard, so is copying books and don't even get me started on the dullness of making clothes by hand.
Driving all day isn't all that far off, though still much better than the above and definitely better than riding horses all day.
Telegraph operators? Hell no. Dude sitting in an elevator all day? No thanks.
It's always been from the other end. This time around, there's gonna be some 10-20 years of robot manufacturing, then a universal lifetime of robots fighting misaligned robots until enough paperclips have been manufactured.
Or you know, we block out the sun and live in caves or whatever you fancy.
Is Terence Tao just another AI booster nowadays, by the sheer amount of PR generating posts? Reading HN one might think that there is only a single mathematician in the world left.
Case in point: https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...
> Is Terence Tao just another AI booster nowadays
The information in the article suggests that he regrets his prior hyping of AI.
He'll eventually get to the acceptance stage for the loss of what was.
I remember just last year he said the LLM were like incompetent assistants, but not completely useless. The tech advances are mind boggling just looking back at that.
I know he says he’s ant talk a human about the proof, but why can’t he talk to ChatGPT?
Is the cost prohibitive , or a proprietary model?
I do believe after the initial shock mathematicians will be able to use their math knowledge to solve practical problems, instead of lets solve this conjecture, prove this age old math riddle, how the pattern is possible. They may have some uses in fringe areas, but it doesn't seem all that useful. These guys are obvious quite brilliant, so when they combine it with other fields which they can branch to due to LLM's, they can still stay relevant. Ask your software engineer how that went.
Math isn't useless. One of its defining features is its "unreasonable effectiveness" in formulating scientific ideas. It's hard to say exactly why it's so useful, but it is, even if mathematicians aren't trying to make it useful.
It's not at all clear whether the kind of math created by LLMs will retain the usefulness of the old math. LLMs are good at rigor but bad at intuition. It's not even really clear if the rigor was ever all that important. Theoretical physics is full of people using math in ways that don't meet the bar of rigor that mathematicians set for themselves, but they have enough physical intuition for what they're doing, so it doesn't matter. It's an open question whether post-LLM math will continue to supply scientists with the kinds of ideas that they need from it.
Mathematicians might just be experiencing the first phases of the cycle of acceptance - resistance and anger, next is depression then eventually embracing it. Software developers as a whole are a bit further along the cycle.
IMO the most useful thing a mathematician can do is not solve “practical problems” but to come up with conjectures and riddles that look around several dark corners of math at once. The proving of a conjecture is a bit of a sport done to impress people with your cleverness; but the clever person was the one who made the conjecture to begin with.
Given the trajectory of LLMs to date I see them helping construct proofs for conjectures but not devising new conjectures of any material substance any time soon. The challenge is, as Tao has said elsewhere, part of being able to formulate a conjecture is by exploring the landscape around it by doing proof research. Seeking answers finds useful questions. The fear is the tools will take away the exploration of the landscape. But that’s silly IMO. It takes a special type of lazy to let a tool take away your understanding that’s important for what you’re goal is, and a special type of passion to learn with a powerful tool. The passionate will adapt and progress will accelerate, not slow down.
For instance Tao has posted some of his interrogations of proofs with AI assisted reasoning and it didn’t seem to diminish his ability to establish insight rapidly, but to shut down avenues rapidly and to pivot and expand his understanding rapidly. The insight was all his own, as was the path of inquiry. The understanding of the output was his as well. He carries it into tomorrow and uses it to formulate new more interesting conjectures the next day. The AI ceased to “exist” as soon as the inference turn was over.
The hand wringing is pointless and lame. John Henry moves aren’t necessary or useful, and when I see a tunnel boring project now I see tons of people well employed there, just the holes are bigger and better, and they’re engineers instead of strong backed hammer slingers.
> Much as one cannot unhear a movie spoiler or a crossword clue, one cannot explore a problem as profitably and richly once one is aware of an existing solution
Certainly, it’s like being made aware of cheat codes to video games: One doesn’t enjoy the game as much after but surely knowing something is true means you can find many other things that come from the pathway to it now that you know it’s true. Lots of science and tech is like this where someone shows something is doable and then people find better ways to do it but until that person showed it was doable there was no progress.
> I am horrified by the many person-years” of research, particularly by young mathematicians, “being casually disrupted or destroyed,” he wrote.
That’s what technology does. And he might be upset but we’re the ones paying for it and frankly, I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Most notable is the fact that the released facts are like “treated waste”. But if the question was worth answering and the value is only in a good answer and not simply a correct answer, then the value has simply not been realized.
But that feels strange then that the value is in the good answer, not just a right answer and yet one finds oneself unable to go get the good answer because a correct answer exists.
The fact that any answers are made public at all is useful to us all. That’s free knowledge. Would it have been better if OpenAI had discovered this very achievable fact and not said anything? Surely the papers, post discovery would have spoken of the “hoarding” of such “essential human knowledge”.
Overall, I find the thing unconvincing wholly.
> The fact that any answers are made public at all is useful to us all. That’s free knowledge.
When mathematicians discover new results, they automatically become experts during the process, and then go around giving talks to explain their results, methods, and intuitions to other mathematicians. After years or sometimes decades of refinement and a healthy dose of serendipity, some of the mental frameworks percolate to other fields.
No one from OpenAI is willing to give a talk on any of their 300+ results because their machines have decoupled formal proofs from actual knowledge.
Right so this goes to the other alternative; there's still useful work for mathematicians after all in dissecting, distilling, and generalizing these results. But according to some we now inhabit an excluded middle where the AI produces useless results but also makes these problems useless for mathematicians to study further.
Yes there's still useful work only mathematicians can do, what is the incentive system that encourages them to do it? Currently, none.
This is not OpenAI's problem.
It's their problem if we make it their problem.
edit: lest this be misconstrued, it can become their problem if it is wildly unpopular and undesireable behavior is regulated away.
I advocate for this path.
And thus, the Tech Bro has reached the final stage in its developmental lifecycle.
> I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
But the value in seeking mathematical answers was never in the answers themselves. It was in the things one discovers along the way, the questions asked, the tools developed. The artisanal fashion is the part that benefits non-mathematicians.
These AI proofs only serve as an I-told-you-so. They're not creating surrounding theory which can later turn out to have useful applications elsewhere.
Look at programmers, we took it in strides
> That’s what technology does. And he might be upset but we’re the ones paying for it and frankly, I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Would you prefer if graph theory didn't exist but we could answer if you can pass all bridges in Königsberg, without going through same bridge twice?
Or if we could answer any question without knowing why? What about answering Hilbert without theory of Godel's Incompletness theorem? Or knowing Nth digit of Pi without calculus.
Because that's essentially what you're asking for. If you gave humans a Djinn that could answer perfectly any question, it would kill most of our endeavors. Because it's not a problem that was unsolved for years "It's just the thing Djinn already answered so why bother?" Even if one is extremely curious, and devote a chunk of their life answering it, others would not see value in that curiosity. Because a Djinn can answer it in a few minutes.
Where's that from?
Now math isn't my wheelhouse, but every LLM I've seen provides far more than just the final answer and is quite willing to answer questions.
It's from this: https://www.youtube.com/shorts/afLSVRFzsFc
Imagine you are Euler and magical Djinn's exist (that possess all mathematical knowledge written up to that point exist and function identical to LLMs). You ask it to tell you answer to the bridge riddle and it says that's not possible and even gives some plausibly sounding examples even. Then it throws a 11 pages of gibberish proofs at you, which are all true but very convoluted.
And what if you start digging into it? Won't other people say - "Hey Euler go back to ploughing the fields? We can have Djinn's answer all the math questions but this field isn't going to plough itself."
Today's, the Djinni-Euler's equivalent of someone looking at LLM's Navier Stokes equation proof.
Perhaps they would discover new Liquid Set theory that would turn Liquid dynamics from a field fraught with problems into a beautiful mathematically simple meadow.
> And what if you start digging into it? Won't other people say - "Hey Euler go back to ploughing the fields? We can have Djinn's answer all the math questions but this field isn't going to plough itself."
Seems like an overly pessimistic take to me.
If you have a magical Djinn happy to answer questions, why wouldn't you badger it a bit for the details? I can't imagine Euler of all people just wanted the answer.
Well you could, but would it produce its own unique theory just to simplify for people? Probably not. It definitely didn't do it for Navier Stokes.
This reminds me of the X Minus One episode "A logic named Joe".
https://www.youtube.com/watch?v=HQuH5nI-pHQ
> I’m happier to have more questions answered than for fewer answered but in an artisanal fashion.
Given that this is pure mathematics we're talking about, for the most part: Why?
Perhaps you are a mathematician and so these questions are relevant to you, but for most of us, these questions and their answers will not make any tangible difference in our lives or society.
Maths has made a very real and tangible difference to society. The easy, obvious, answer is online banking, which wouldn't work without crypto, which is pure maths. There are many more.
It used to be that Pure Maths got to affect the real world via Physics (and that odd thing where last decade's interesting mathematical exploration turned out to be the solution to this decade's Physics discovery). But t'internet consumes Pure Maths pretty much raw.
Why? Philosophical position: https://wiki.roshangeorge.dev/w/Observation_Dharma
In which case why are we funding mathematicians?
I find this entirely self serving.
Terrence Tao was very supportive of AI and formalizing math with lean when it looked like it was giving ‘generalists’ like him an edge over mathematicians too deep into one particular niche field.
But now that it’s letting everyone, including mathematicians who are perhaps too specialized, explore ideas and patterns from related math fields, he’s suddenly ‘on a war footing’.
I don't think it is self-serving. Tao has stated plainly that he thought LLMs would go the route of assistants, like co-pilots. But what he feels now is that they are actually being engineered to be replacements. His claim is that the way OpenAI dropped these math results isn't "assisting" anyone, so we should all read between the lines.
Consider any man at his job, fighting the good fight. Your boss says "I've hired this man to assist you" and you are happy to finally have some help with your difficult task. Then one morning you come into work and see that the coming day’s work was done overnight by this other fellow. And the realization sinks in, he isn't there to help you, he is there to replace you.
In this view his reaction seems totally expected. I expect many professionals, e.g. doctors, lawyers, accountants, etc. will make this realization sooner or later. The companies are saying these tools will assist professionals, but in reality they are aiming to replace them.
> The companies are saying these tools will assist professionals, but in reality they are aiming to replace them.
If anyone doubts this, consider that Anthropic considers its TAM to exceed $30 trillion which is nearly the entire GDP of the US and 25% of the world GDP.
Only makes sense if they believe they will massively replace labor. Which, to their credit, they used to admit openly and publicly and only stopped because some crisis PR people told them "hey maybe you shouldn't say the quiet part out loud while the hoi polloi still have the power to stop this from happening".
I’m not making a claim one way or the other about the intent of these companies, but if your product made labor 3x more productive, you could still easily justify a TAM of the entirety of US GDP, without resulting in anyone losing their jobs. Obviously, here in reality, AI does act as a near 1:1 replacement for people in some roles, so we should expect some job losses. But I don’t think there’s any reason we should expect the entire US labor force to be automated away any time soon, even taking these assessments at face value
Do their own hiring practices reflect that ambition? They sure seem to be recruiting a lot of humans for typical roles in business, legal, and engineering. If they want to flex the power of their models to automate human jobs, why not lead by example?
https://www.anthropic.com/careers/jobs
> They sure seem to be recruiting a lot of humans for typical roles in business, legal, and engineering.
They have practically infinite investor money to throw at salaries (lost in the noise of how much they are spending on compute) so why not use it for now to reach their goal as fast as possible?
My thesis isn't that they have already achieved the ability to replace massive amounts of the labor pool, just that that has to be their goal given their stated TAM.
> If they want to flex the power of their models to automate human jobs, why not lead by example?
They don't want to flex this. They realized (after a false start) that it is better for them to avoid talking about this in public.
That doesn't mean their goals changed, they just realized that flexing before the goal is achieved could endanger the goal being achieved through political backlash.
You do realise Anthropic's management, after throwing its tantrums, gets a seeing to and has to do what its investors want? Which is pump up the valuation.
You're not this naive are you?
Amazing, truly.
> But what he feels now is that they are actually being engineered to be replacements
lol. lmao even.
I guess there is a first time for everything.
"doctors, lawyers, accountants, "
Regulated fields - another clueless poster lol.
I know many of you really hate whats happening but don't try and project it on other professions where the environment is different.
Society largely never cared about maths.
You might be mistaking my comment as a value judgement rather than an attempt to charitably explain the latest media communications from Tao. I detect in his position that some trust he granted the AI companies has been violated.
You are, of course, right that doctors, lawyers and accountants have more control over the environment they work in compared to mathematicians. But it doesn't change the underlying argument Tao is making. Your observation that those professions will react differently is likely to be true and only time will tell how effective their response will be.
But AI "assistants" is a marketing approach being made to all professionals at this time. Tao is implying this is a Trojan-horse strategy. If you let the assistants in without reasonable protections, you may lose control over the environment you are trying to protect.
> Regulated fields - another clueless poster lol
Out of sheer, idle curiosity: were you actually laughing when you typed that out?
you may not be aware of it but society largely runs on the results of maths, clueless indeed. and regulated or not, if there are financial savings to be made anyone can be shoved under the bus.
One might say, in the end, what's wrong with being self-serving? Are we _all_ meant to be self-sacrificing? Are we all meant to be the eggs that get cracked to build this wonderful future ommlette?
To bend a phrase, if you have to ask...
Fine. I will self-servingly dismiss his concerns. They don't concern the important people here: me, myself, and I.
I think it's a bit of an unfair characterization, see this post for the nuances in how the math community approached the development:
https://news.ycombinator.com/item?id=50128468
entirely fair.
basically both sides now dislike that he flip flopped
its either you are anti-AI all the way or flexible and adaptive without making strong opinions that can be put on record.
most people are in the latter and its growing. math is solved.
> basically both sides now dislike that he flip flopped
No, the dumb thing is the idea that there are "sides".
> basically both sides now dislike that he flip flopped
Literally the only people with this opinion of Tao are internet forum warriors who have no expertise in the field and who's opinion of Tao don't matter in the slightest.
> who's opinion of Tao don't matter in the slightest.
Similarly, Tao being ‘on the warpath’ does not matter in the slightest when it comes to formalizing math and finding proofs to important unsolved problems with AI.
> Similarly, Tao being ‘on the warpath’
Do you think that this is a quote from the article you just read?
I swear half the comments here are just from people reading dunks on r/singularity and x and getting real mad at strawmen.
“I’m on a war footing,” he said while grabbing coffee during a two-day math workshop at the University of California, Los Angeles, that was rife with talk about the existential crisis that artificial intelligence has created in his field.
> “I’m on a war footing,” he said
So not remotely the same thing.
I've never perceived him as 100% supportive. He has rather been open-minded about a new technology and exploring what it can do. Now it turns out it can destroy his field, so he's naturally against it (at least against the destruction, not necessarily against the technology)
I think ‘destroy his field’ is ‘destroy his method of being famous in the field’.
Terrence Tao is famous because of solving problems better that most mathematicians because he has an uncanny ability to look across different math fields. AI gets everyone this ability for 20 to 200$ per month, eventually free.
Most mathematicians are happy to see interesting problems in their field being solved, and are looking to build on these to find more interesting problems.
Hm... I'm not a mathematician, but why would these new more interesting problems not be solvable in the same way by the same - or newer - models?
They will be, that’s the point.
The point is to make the field progress by discovering new things!
Who gets credit for what and how credibility is assigned is going to be muddy for a while but that’s the case whenever a bunch of new science happens in close sequence. History is full of math/science discoveries having debated and dubious provenance.
I can't see how the field can even exist - not to say progress - if any problem can be solved before a human can understand it. Looks like mathematics without mathematicians, "progressing" in the same way as paperclip optimizer progresses in its productivity.
Math doesn’t exist to make mathematicians famous.
It provides deep insights into logic, computation, provides tools for us to understand the universe, establishes mind blowing relationships between seemingly unrelated things.
For example “how much information can a black hole contain?”
> provides deep insights
To whom? If there are no humans in the field, there is no one to get the insight. Maybe you are right, and there is just a new type of a mathematician being born, but as an outsider I just can't see what they could look like, what will be left for humans to contribute
> Realistically, math will be done by well funded teams of people instead of cult of personality mathematicians.
Most math is already being done by meagrely funded mathematicians. The entire US federal budget for mathematics is like $100M. One college football coach can already make 10 percent of that. No mathematician is making bank.
Is the implication of all this that mathematics research should get a cash injection to pay for high-powered computational tools?
> Is the implication of all this that mathematics research should get a cash injection to pay for high-powered computational tools?
Math will, sure. Mathematicians, doubtful. After all, most high end physics research with billions in funding is now done by postdocs making a lower middle class salary.
There is a huge jump from
AI solves math problems to
> If there are no humans in the field
Realistically, math will be done by well funded teams of people instead of cult of personality mathematicians.
Also, insights from scientific discoveries are for everyone. You do not have to understand the complex multi dimensional algebraic geometry of general relativity to appreciate that gravity bends time as well as space. You don't need to understand fifty years of linear programming research to use a modern solver.
> But now that it’s letting everyone
Eh... That “everyone” is a multi billion (trillion?) $ company paying top mathematicians specifically hired for generating math proofs.
No, pretty much every math PhD student and researcher is now using the AI+lean combo.
So as every high schooler. That doesn’t mean much for actual results similar to what OpenAI “generated”, and doesn’t quite explain the “war footing”, does it?
We’ve yet to see the democratizing fantasies in math field to materialize.
Which makes complaints by mathematicians about it absurd. They should just stop flapping their lips; there is no putting the genie back in the bottle.
For me it just shows that modern math is not that important and mostly ego driven. If it was important, mathematicians would cherish the progress. I can't imagine bio researchers get mad that AI cured cancer.
Maybe partially.
I think this sort of progress, compounded over the next N years will serve to cleanly split useful math from the ego driven math you speak of.
Certainly there are enormously impactful pure math results yet to be found, but we have no idea really which directions to pursue.
I wonder if this is going to look like the chemistry-alchemy split in the rear view mirror.
It was devastating to learn in my late 20s that 99.9999% of what the average person does is based on personal ego and not a communal vision of the future.
There are plenty people in every discipline that prioritize their ego over measurable progress towards a stated goal - even less so a community focused goal.
Its just the modern day version of the stuff they told in the religion hey-days.
Humans aren't that original. We just reinvent stuff we used to do to suit the present day, with our own twist.
TLDR: "I didn't understand this proof and there is no one to explain it to me"
The TLDR seems perhaps tongue-in-cheek, but it's a worthy thought: the situation where our best experts find new science to be inscrutable is close at hand, if not here now.
Humans have been guilty of burying things we don't understand for millenia. Will we continue to do so "because AI"?
Inscrutable through lack of effort communicating (OpenAI) is different from inscrutable because it’s high level hard to understand (Grothendieck).
> They “used math for what they needed, which was to evaluate their models,”
OAI first paper on the prize was a pretty shitty thing to do. But the rest of this looks like they are just mining the corpus and taking a brute force approach to do it.
Im going to say this again, the "pure math" academic types need to get a grip. Plenty of your peers got PHD's and happily made a fortune in finance, while screwing the world (See 2008 housing bubble) and none of you said a peep about that.
Plenty of welders made weaponry that killed babies and none of the famous DIY Youtubers spoke out against that either.
> Im going to say this again, the "pure math" academic types need to get a grip. Plenty of your peers got PHD's and happily made a fortune in finance, while screwing the world (See 2008 housing bubble) and none of you said a peep about that.
They call it the most populist post of all time.