"I'm on a war footing": Terry Tao and the crisis in math
nytimes.comIn a world with better economic system, such progress in Artificial Intelligence and automation would have been viewed more positively, I mean who doesnt want to work less and have AI make rapid discoveries in scientific field. Instead we are filled with anxiety and dread of what will happen to our jobs and how we will survive.
That's a big part of it, but I don't think it paints the whole picture. We are also losing the bits of work that were actually enjoyable. The challenge, thinking and creativity gave us something we enjoyed. Now we're like border collies in a world with no more sheep and now even the ball comes back by itself.
Another one that comes to mind is Marge Simpson in the Hank Scorpio episode where all labor in the house was automated and she turns to drinking out of boredom.
I think there should be a political movement that retries socialism with AI. Basically nationalize everything and then automate everything. I think people could get behind that. Basically fully automated luxury communism.
Chile in the 1970s, anyone?
That was a scam or at least overblown in scope, the "control room" you see in pictures was basically a movie prop, and their idea was basically to connect that room to every factory/port/mine with teletypes, it's similar in spirit to what a modern stock should do.
I think there should be a political movement that retries capitalism with AI. Basically liberate everything and then automate everything. I think people could get behind that.
>nationalize everything
The government does not have an incentive to run anything efficiently as they cannot go bankrupt. Imagine if AI was run like the DMV.
Putting monopoly control of it in the hands of government also makes it extremely likely that whoever is in power will use it to manipulate public opinion + elections as well as encoding their political values into it.
What do you think a Trump-controlled AI would say if I asked about the war in Iran? We’ve already seen examples of companies encoding their beliefs into the system (see Gemini saying nuclear war is preferable to misgendering Caitlyn Jenner), imagine how much worse it would be if politicians were given control instead.
You think people can get behind that? Like if Trump's US suddenly decided everything is state property and Elon Musk will be helping people automate everything, people will be like yeah that sounds good.
AI isn't making math discoveries. It's generating a metric shitload of syllogism slop, whuch may or may not correspond to reality. We will probably never know, because really who has time for this bullshit?
It's a little funny how quickly the conversation goes from "AI will never be able to {my-field}" before turning into "We cannot have AI ruining {my-field} with its obviously superior abilities"
If OpenAI had never made a push to get good at maths, we might still have a sizeable group of peopne stuck at that first line. I say that because I still hear in discussions the naive rebuttal "But we'll still need _someone_ to {one-step-up-in-hierarchy}" . Although you have to be curious now how long that sentiment can last.
The good news for those doing abstract maths might be that, now that OpenAI have proven that their AI can do the job in principle, there's probably not much left in it for them to keep going. Mathematicians should know better than anyone the lack of a direct profit motive in doing the work that they do.
(Edited for clarity)
Hacker news is not really a good place to talk about nuances involving academia. I don't expect VC minded hackers comprehend how someone can devote years of their lives working minimum wage trying to answer questions which earn them a fancy title on a piece of paper, for that matter.
A lot of us here are VC minded hackers *because* we spent years of our lives working minimum wage jobs in academia and then eventually realized we preferred to build!
Or preferred to eat. I love teaching, and I'm good at it. If it were more valued by society then I'd do more of it. As it stands, I'm in adtech, and I teach a little piano and math on the weekends.
I am one of those. I'll also say I never felt the kind of emotion in software building that I did when working on PhD problems.
Or maybe to earn proper money?
> A lot of us here are VC minded hackers because we spent years of our lives working minimum wage jobs in academia and then eventually realized we preferred to build!
This is a disingenuous framing. I've "built" more in academia than in some jobs I had, and some VC-backed startups are renowned not for building but for their lack of ethics.
"Building" is not the discriminating factor.
I spent years programming for myself, for free. I did this because I loved it, not because I was interested in the VC game.
But you did something else for a paycheck in the meantime, right? They're talking about what mathematicians do for their meager paycheck.
> But you did something else for a paycheck in the meantime, right? They're talking about what mathematicians do for their meager paycheck.
Grigiri Perelman, who was awarded the Fields Medal, notoriously refused the prise because he stated no other recognition was needed.
Or hone their craft to best express their art and share their human experience
A large fraction of people are open source contributors, hobby game devs, and various other types of people who fall under "devote years of your life with no formal remuneration"
> If OpenAI had never made a push to get good at maths
By snooping on work math researchers were doing on their platform and then overtaking them when sufficiently close to completion? isn't that what happened i'm not sure
I have to confess to being wrong in exactly that way in the past. On the other hand it is probably always good to behave as if the next step up in the hierarchy is still available. There's no point letting these things spoil your day twice.
Now I'm forced to think about it much more carefully. I don't believe that current LLMs can find every possible proof on their own from now on. I also agree that the PR returns have fully diminished. Given how hard it's been in recent years to fund e.g. a poorly paid postdoc, I doubt there's a ton of money lying around for getting the best models to work on mathematics problems. I think there's a chance we're heading into a really good era. I was able to make so much progress back when Google search was a useful research tool...
so far it's been programming and math, the two fields most people would naturally assume computers would be good at :P
not saying it's not possible ai will continue to expand to more fields, but i don't think it's a coincidence that both math and programming are easily automatically verifiable. in fact for programming their effectiveness drops substantially once you remove any sort of testing or verification loop, and i imagine it doubly-so with math. try getting an agent to build something without any tests or verification, you'll see it go back to near-2024 levels. half of the work i do with agents is setting up a harness that can take and analyse screenshots, send direct input to the application, and compare results. this is something that should come standard with every harness.
if we can build automatic verification for more fields is a different and perhaps more relevant question.
> so far it's been programming and math, the two fields most people would naturally assume computers would be good at :P
If that is true, then only because "most people" have no understanding of what differentiates programming and math from "computation". Computers (as the term suggests) have always been extremely good at the latter, and useless at the former. It's only 2–3 years ago that computers, by way of LLMs, have started being good at the former.
> obviously superior abilities
if you think that's the takeaway, you're not listening to any of the people affected by AI
I am myself one of them. This is just me doomposting as lightheartedly as I can muster.
I guess you didn't read the article? The end of it quotes Tao about how much more there is to discover in mathematics, and he expects humans using AI to get there.
My point was not that AI from now on should be done away with in mathematics research. I was rather commenting on the likelihood of AI companies continuing the "strip mining", as Tao put it, of his field.
What if we meet extraterrestrial life? Would we ban them from showing us all the math they already solved and/or invented?
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.
The rug being pulled is the expectation of a reasonably high-trust ethical environment. The question to be asked is: What will graduate study look like in an utterly zero trust ethical environment?
If there is still such a thing as graduate study. If there is still such a thing as study. Tell me what to say to someone about to enter college about why it isn't a waste of their time.
> He described it at 'strip mining'
Strip mining what, platonic reality? Mathematicians don't have a monopoly on mathematical truth. It doesn't exist for their benefit.
It is usually not the monopolist who is protesting against strip mining, it is usually the monopolist doing the strip mining and the environmentalist protesting it. Which is to say, I don’t think mathematicians are claiming a monopoly on mathematics, but I think AI might.
Strip mining interesting conjectures. AI can answer interesting(pedagogically valuable, carrying important implications, etc.) mathematical questions in formally correct gibberish far faster than mathematicians can generate them. Until AI can replace the conjectures it resolves on its own, it's consuming a finite resource.
Will AI be unable to produce new conjectures?
The papers created by AI on math, right now, are torturous reads. Figuring out what is actually going on in them, is the work of months or even years.
I’ve seen multiple conference submissions that read like English, but take hours of effort to disentangle and figure out what they mean.
There is a limited number of known interesting problems that are worthwhile to engage in. New ones are found and understood, but it is a slow process and it is dependent on understanding and verification, not generation of content.
Saying AI will create new ones, strengthens the strip mining analogy. The idea that AI will find other problems parallels the idea that firms can cut down a forest and plant them elsewhere.
The conversation on HN is driven by non mathematicians, to whom math is a subject, like “nature”. It’s not their core business. The original post by Tao is a better source of information on what he means.
Does creativity need sentience?
No. Genetic diversity and natural selection have created many intricate, beautiful, and useful structures. Unless someone is willing to argue that Darwinian selection is sentient, it's clear that theres at least one non sentient process that is creative.
It doesn’t exist for OpenAI’s benefit either. The point of the “strip mining” analogy is that they are churning through the mathematical landscape in a way that optimizes for the number of problems solved rather than the amount of understanding of those problems.
Well they've been doing that to devs for a couple of years now and yet mathematicians seem to be much more vocal whingers (might be selection bias in the articles I'm reading though).
AI is coming for all of us knowledge workers, nobody is immune.
Um…us devs have been whinging with the best of them thank you very much.
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.
> 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?
would someone who runs faster 100m also somehow drive better?
This tool belongs to somebody (capitalist!) else and in a new world better tools will always win, not individuals anymore. And it feels like to go from being Rembrandt to CVS employee who takes passport pictures - result much better quality and cheaper but no skill and glory.
Interestingly, the dynamics strongly resembles the industrial revolution when from highly skilled manufactures society moved to factories with power machines. And it all came down who owns means of production. Now AI is a new means of production for all white collars jobs and if the industrial revolution taught is the way to go, nothing good will come out of it.
Nothing good for skilled labor you mean, especially in the short to medium term - just like in the industrial revolution. If the new technology is any good, it will produce desired things (let's say medical breakthroughs?) faster.
I don't particularly like AI, but if AI replaces developers and other knowledge workers, not everyone is worse off, and I don't mean just capital owners.
That’s like thinking that computers will belong to “capitalists.” It’s already clear that AI is going to be a commodity you’ll be able to rent for barely more than the price of electricity.
No matter how cheap it is, people will never be able to come anywhere close to affording what giant corporations can.
I'm somewhere in the middle on that. People used to think that computers would be owned only by large corporations, then home computers appeared and improved. It's getting tight now that logic scaling is mostly exhausted, at least with current operating principles. Even so, new specialized hardware and model improvements may help (for inference). Training seems to be the biggest problem, it seems hard to democratize.
And that's why Alta Vista still reigns supreme in search.
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.
That's just a tool you rent and cannot own or make/improve/repair yourself.
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.
Until AI agents are embedded in glasses and everyone gets comfortable with sending their conversations to AI, the smartest person in the room is still going to be the smartest person in the room because they say smart shit. Or until the dumb guy types into their phone and says smart shit. Given the pushback to Meta's glasses, I think that'll be a differentiator for a bit longer still. Even before LLMs, you could check Wikipedia and different rooms treat the people that do that in different ways. And then there's the "Don't be a meat proxy" movement.
Not all rooms are real face to face. Smartest person also needs time to think and lookup information. Worst smartest person can think on one hypothesis at a time.
I don’t think that is correct. For consistently good results, you need to set the right goals and be able to judge the quality of your outcomes. Even if you don’t do the hard work in between some thinking is required for non trivial work.
No. It's just people who built an identity on the power that their intelligence afforded them. We view that power and the intelligence itself as the same thing, but they're actually separate.
100%. We are moving to a time where do-ers will matter more than talkers.
A wild thing to say about Terry Tao.
Ironic, given that all the alleged do-ing will be done by talking with an LLM.
lol
The only thing that will matter is capital, which will translate directly into all the talking and doing needed to make more money.
If your takeaway from all of this is that some other group of people has the special-est skill that can never be replicated by a computer, I fear you’re missing the point.
Builders, please! Do-ers is not the preferred nomenclature, dude.
Come now. You are using an LLM to perform as much of the work as possible/affordable. You're a User.
this isn't a guy who built the railroads here
According to whom?
You think OpenAI is run by a bunch of idiots? Being the smartest person in the room is becoming exponentially more valuable.
Well, it's certainly headed by one.
Asshole and idiot are different categories.
Yes. If the early 21st century was the revenge of the nerds, this will be the undoing of that.
I made that comment a few days ago.[1] It saddens me. It may not be wrong.
What? This is like a drive by shooting or something. Several PhD students almost certainly lost months of work, and others considering a PhD will have more doubts. Those problems aren't necessarily important because of the solutions, but because mathematicians can make unique contributions to mathematics in the process of solving them. LLM proofs haven't created any new mathematics techniques.
Everyone who built an identity on earning a living doing useful work for other people is going to have to come to grips with that no longer being part of their identity.
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.
I'm in this boat too and I find it a bit strange that this hasn't been more emphasized by mathematicians themselves.
So far, a lot of the hullabaloo has been around solving legacy problems, but more interesting and more important for actually progressing mathematics is the generation of new insight and new problems. Someone had to pose all those problems OAI is solving in the first place, in some cases, ages ago.
The collective letter response to navier strokes, sort of touched on this, but still didn't really emphasize the epistemic value of problem generation explicitly. I find it sort of strange that this has been so underemphasized.
I think their expectation is that “problems” as we’ve understood them just won’t be nearly as important to mathematical research going forwards. The field will look more like e.g. economics, where progress sounds more like “developed our understanding of the microeconomic foundations of macro” than “breakthrough on the Coase transaction cost problem in five dimensions”.
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've never heard a particular reason why the Millennium Problems were of special interest. They had resisted solution despite significant effort, but I don't know if Riemann or Navier and Stokes had ever singled those out as especially high priorities. They started as ordinary problems and became known for their durability.
So I'm not sure if it's something we should expect from a machine, just because we don't expect it from mathematics either. Maybe the machines will interrupt that process because we've changed how we go about looking, but perhaps not because old problems are solved.
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).
It isn’t a benchmark though. Not yet. They rely on mathematicians to check the proofs including all lemmas. And on other mathematicians checking the reviews. Without being on the OpenAI payroll of course. Now they have flooded the zone, overwhelming the review capacity of the whole field by at least one order of magnitude. It is the move of 15-year-olds holding tools they shouldn’t have access to.
LEAN.
Better approach: "holy sh*t, I can solve way harder math problems now". I bet openai would have loved to have Terry on their team leading the 'solve math' department.
It's telling that isn't his response.
War against who? You don't need to make enemies out of things where you can avoid.
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.
Or is it possible they have entire teams dedicated to this effort? Building an internal “math platform”.
“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)
Jimmy Carr in 2008:
> Of course you get a lot of right-wing people saying "oh these Poles; they come over here taking our jobs". I think if a guy from Poland arrives and he doesn’t speak the language, he doesn’t have any money and he doesn’t know anyone, and he takes your job on the first day – you’re shit, fuck off."
https://www.youtube.com/watch?v=t2ICmOYP8gs
Somehow I think "taking our jobs" concerns are going to be a lot more palatable.
'Ey 'ook 'e' 'obs!
Hurr durr durrr!
the rallying cry 10 years ago was "learn to code" ironically.
the live video interview on numberphile comes without the New York Times' narrative filter
Highly recommend.
I dont know what the future will hold, but in the past each time technology took over a profession, it ended up opening more doors than it closed. However the transition has always been rough.
I have faith that when AI settles, it too will open more doors than it has closed.
I must be missing something.
1. If it costs $6-22 million to produce a paper that the brightest minds in maths can't understand and use, this trend will stop soon enough on its own.
2. Why are these minds complaining that there are no authors to discuss the paper with? There are OpenAI researchers to talk to. If they refuse, because they themselves don't understand, then don't bother with it? You're responsible for your time. Write a response on what's unclear, and move on. What's the point of whining about others writing things you don't understand? See point 1.
3. If LLMs can be used to solve problems, that leaves more time for mathematicians to come up with follow-ups. That seems a great way to speed up the field, no? Just be sure you understand the solution before expecting anyone else to spend time on reading it.
Anyone without a big C in their job title will be on war footing soon enough.
Cobblers
So Carpenters are okay but plumbers and electricians are not.
Carnival Barkers
CEO? Circus clowns?
Is there an echo in here?
It is easy. We heard many angry programmers going ballistic about (un)maintainability of slop. That's the same, but very much more complex: imagine a large proof that maybe looks correct but it was written by a mentally unstable person that just committed suicide. What is its value?
"looks correct" vs "verified correct by a formal verification language"
Can you help me understand the difference in your analogy?
I imagine this is what farriers felt when the automobile came out.
> 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.
> 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.
> 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.
"Burns down the societal structures for gaining mathematical knowledge"
"Not our problem lmao, our IPO valuation went up"
The Asshole’s Lament
And thus, the Tech Bro has reached the final stage in its developmental lifecycle.
Is it useful to us all? I read thru the results list and despite years of college and graduate math classes only understood the statement of like five or ten. Prof Tao and his colleagues are able to spot the thing in their work that make faster imaging possible; are you?
Look at programmers, we took it in strides
talk for yourself
> 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.
It’s not pessimistic at all. Look at the advances in math thanks to hundreds years of pursuit to prove Fermat’s Last Theorem before Andrew Wiles finally did it in the 90s. You will not get that with LLM. That’s what mathematicians are mourning over.
I’ve been on the other side of that, getting badgered for details by people who don’t have the conceptual frameworks to understand what I’m doing, and my experience is that it doesn’t really work. Sometimes, when they have a concrete goal in mind, they can communicate it to me and I can produce a demo showing that the software I’m working on achieves their goal. More often, they ask questions that don’t fully make sense, and can’t understand either my answers or my guidance towards the questions they should be asking.
If I were a Claude instance, rather than a software developer fielding these questions as a small component of my job, could I take a step back and instruct them from first principles until they do understand? Maybe. But maybe there’s just too big of a gap to be crossed in one step.
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 genie only knows the details that other people already formulated, because it doesn't actually think for itself, it just regurgitates human thought. That's what everyone seems to be forgetting.
Remove the human theorizing and the LLM won't be able to fill in that gap. All it can do is remix. It cannot formulate and, equally importantly socialize new mathematical theory. Without social acceptance and promulgation theory is meaningless. I might have a private "sort of graph theory but not" studying a slew of new mathematical objects called quizzgams, but if I cannot actually articulate this theory to anyone and get an active participatory body of people around it, it's pointless. Any "theory" an LLM can create de novo is such a theory. Because, again, it doesn't actually produce novel thought, just novel byte sequences. A thought is more than just its encoding, it is processual and social, which all the nerds and vc bros seem to not understand.
This reminds me of the X Minus One episode "A logic named Joe".
> 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.
In which case why are we funding mathematicians?
Why? Philosophical position: https://wiki.roshangeorge.dev/w/Observation_Dharma
>The lab agreed to sponsor a workshop at the institute for what Dr. Tao said was $60,000 to $70,000
That's a lot less than i expected. The value he gave back to them should be at least 2 magnitudes higher.
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.
> 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?
This is a general point rather than an argument supporting the GP comment, but it can be shockingly hard to know what the correct response to particular situations is, or predict how a system will respond. For example, one system I know had difficulty differentiating people laying on the road from unmapped speedbumps (particularly at night), but was very good at recognizing them standing up. Someone spent a lot of time testing with dummies until perception improved. Another had no idea how to handle people in fursuits and halloween costumes, because it was incorrectly applying animal behavioral models to pedestrians.
That's why the latest self-driving systems include reasoning models that draw from the massive amount of knowledge embedded in LLMs. Language evolved to communicate things that are not here and now after all.
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.
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.)
>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.
It feels like it's happening every Thursday and nobody cares. They just give people credit watch coupons or what's it called, and move on with their business. Worst case, a few pennies in fines.
Well 99.99% is you have a major data breach every decade or so, but there are lots of companies, so on aggregate across all of them it's every Thursday.
But if CVS leaks your purchases on a weekly basis, it's probably going to affect people's willingness to shop there. (Or at least to use non-cash.)
>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.
Consider that the average person interacts with motor vehicles much more often than they would with a potential cure for cancer
It's a well known problem in AI. It's called Moravec's paradox.
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.
>roles that ai cannot replace
Which role is that, and why you think so ?
alot of investment related roles, those require reading human emotions and pleasing people, a pretty face and pleasant demeanor with emotional intelligence helps more than raw iq.
On one hand, i think investment is no longer fair game. Take a look at what the rich doing in US, blatant inside trading without any consequence.
On other hand, in a completely fair market, i think AI can make profit. A lot of traders just stay at home and monitor news.
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.
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.
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.
Blue collar is embodied, white collar is abstracted.
> 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.
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.
One way to think about this is that the parts of our brain that are responsible for spatial reasoning and the basic automatic stuff we do day to day to just navigate the worlds are evolutionarily the most sophisticated and oldest. Evolution has so taken over this job that most of the time it's automatic and we don't even think about it, which makes it feel easy even though it's wildly complicated when you actually sit down and try to analyze and intellectualize basic stuff like navigating a 3D space in which almost anything can happen.
Intellectual pursuits are, by comparison, relatively new. Part of the reason they might seem so impressive to us is simply because we can't rely as much on eons of biological evolution, so even though what we are doing most of the time is really simple it seems "smart and sophisticated" compared to the far more complex mental operations that we are lucky are just automatic.
Think about it, you have an entire complicated as hell biological interior system that your brain manages continuously without so much as a conscious thought.
This is also why this hubris around the idea that LLMs rival human intelligence is quite laughable. If anything one of the major reasons they are so "great" is because they don't have to deal with a host of issues themselves (their computation is not responsible for keeping their bodies alive and hearts beating 24/7, data center ops takes care of that, unlike our computational system which, in addition to solving all these intellectual problems, also needs to regulate the body continuously)
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.
> Everything below L4 is _incredibly stressful_ and unpleasant to drive, because you have to be constantly aware and alert without having anything to do.
Hasn't been my experience for the past year or so, give it a try sometime. Incredibly relaxing and frees up my mind to focus on potential hazards further than just one car length in front of me. Sometimes (don't hate me) frees up my hands/eyes to handle other things that need some temporary attention. Traffic jams, getting cut off by impatient drivers, being stuck behind slow drivers, none of it bothers me. I'm chilling out and talking to my kids and enjoying the scenery.
In that case, autopilot is the correct term.
Pilots still are required to be able to take over immediately for an autopilot system and are responsible and accountable for all those items you list and more.
Calling it autopilot is precisely what it is, calling it self driving would be false marketing.
That is an absolute _hogwash_ of an explanation, and it comes up every single time this discussion is had.
We are talking about cars, not planes. Driven by regular people, not pilots.
It's a term chosen specifically to evoke a certain connotation among the majority of people, and you know it.
With this line of reasoning I can sell any car as a plane without wings. It flies, but only off a cliff, and doesn't land, but I only said it flies, not that it lands.
Most people expect other things from something marketed as flying, but specialists know that this is exactly how most things fly. And lawyers know to read the fine print.
/s and argumentum ad absurdum, sorry for eristic tricks.
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.
I don't know if this will happen in math, but in other fields where computers have outstripped humans (chess and poker, for instance), there's been a loss of creativity, but there have also been other forms of creativity that take its place. There was a period of reeling where we had to figure out what it meant to just be able to know answers to the question that made the game fun, but there's also a moment of realization: just because a computer says something doesn't mean we can't make it our own. Using poker solvers to find creative non-equilibrium strategies can still be fun: the ingenuity comes from using the tools to think out side the box. Or, finding a nicer set of abstractions that explains why a strategy does a certain thing, and then starting to notice it showing up other places.
For math, just because we know a thing is "TRUE" doesn't mean the investigation is done. The folks that love math are driven by solving puzzles, and the puzzle is still there, only changed: instead of being "is this true?", the puzzle is now "why is this true?" Building theories, finding nicer proofs, etc: there is still plenty of room for creativity.
But in the meantime, it really is tragic that so many young minds have had their work stripped away from them.
Chess and poker as spectator sports have a high incentive to see humans compete fairly, and I think that's the reason why there are such strong anti-cheating measures (at least in chess; in poker, too, I suppose).
And the economy puts no such large incentives on much of the remainder of economically valuable work being purely human, quite the opposite actually. And instead of regulating the AI industry (which produces the "cheating tools"), they get trillions of investment. So this seems to be going in the opposite direction where it is actively worked against humans staying economically relevant.
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?
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?
Sure you can make Claude produce documentation & code that is readable. You need to steer it and show it how you want it to write. When it gets it wrong, find counter examples so it can learn the style you want. Otherwise it's going to write what it thinks is best. What is best for LLM comprehension and efficiency is not necessarily best for the human.
> 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 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.
I keep waiting to hear that some LLM has produced a fully rigorous quantum field theory
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.
"just". I think you should "justify" your use of "just".
Because it comes across as "ooh, you're just going through the five stages of grief, dummy! Look I've taught you psychology 101. Now that you know about grief, you might as well skip to the next cycle already. Support me on Patreon. Like, comment, subscribe"
Pointing out that someone is "just" grieving is not helpful.
I'm seeing this a lot in the past months of AI-for-math discussions. Had to get this off my chest.
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.
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 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".
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.
>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?
Wouldn't throwing that money into GPU be better because AI is smarter and faster ? So they would reach their goal even faster ?
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
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.
The reason we fell first is because we embraced the copilots. We used them heavily, this gave them more and more training data on top of the code they slurped up from our using their assistants. Soon the assistant became the agent who killed the human.
They also had a rich starting point from open source code (which we somehow gave up without realising it). All of this won't happen as efficiently for these other fields, but it will happen, much in the way you've described. We (swes) turned out to be a rather dumb group of people, which is hilarious since we think we're clever.
The only moat we have is the human to human element, we need to talk to other humans in the business. Customers, etc. But once they're replaced by machines or automation, then machine to machine communication will be the preferred mode of communication and work and the legacy humans will be increasingly cut out of the loop. Human in the loop is a death sentence we just don't realise it.
>Tao has stated plainly that he thought LLMs would go the route of assistants, like co-pilots.
As one of the smartest people in the world, he is so naive to believe that those capitalists will stop at that.
> 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?
Fine. I will self-servingly dismiss his concerns. They don't concern the important people here: me, myself, and I.
To bend a phrase, if you have to ask...
I think it's a bit of an unfair characterization, see this post for the nuances in how the math community approached the development:
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.
Show me the mathematicians ecstatic about OpenAIs recent results.
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.
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).
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.
Pure Mathematics is closer to philosophy or art than it is to empirical science.
In Pure maths, people are not generally solving problems because of some pressing practical need, it's purely out of intellectual interest, and if we're lucky there's some immediate practical application. More often, the knowledge sits in pure form for a while and years down the road some new invention, or practical consideration, or other field finds a useful application.
Just like literature and visual art, it serves an important epistemic and social function even in spite of its immediate lack of raw practicality.
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.
> 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.
I wish Terry the best.
I would usually have been part of the downvoting brigade for this comment.
But to be honest the reaction from the ivory tower here is seemingly quite telling to a layman watching from afar.
It looks far more like this was some extremely gatekept community where you were only allowed to work on sanctioned things if so deemed worthy. Better not step one someone’s toes lest you get exiled! How much progress was lost due to newcomers never working on a problem due to told not to?
It’s starting to make those old timey Usenet kooks look a whole lot less crazy to me. They seemingly were right about this part.
Mathematics was funded and supported by a whole bunch of janitors and blue collar workers busting their asses to let entire departments of thinking men and women work on hard problems for the betterment of society. If it was just a super special friends club the whole time that was gatekeeping what amounts to a hobby, it’s going to me much harder to justify such a social contract.
Honestly not even sure what to think at this point. Extremely disappointing to me the more I read from these people.
Wow really? I didn't know all pure mathematicians were elitists
You are right, we should get rid of their profession