Tao: Open math problems being non-renewably mined by AI • Hacker News Board

Re: Tao: Open math problems being non-renewably mined by AI

#181

Post by SpicyLemonZest » Wed, Sep 09, 2026, 2:11 AM UTC

johnsmith1840 wrote: post #126

SpicyLemonZest wrote: post #116

Earlier quoted context omitted.

> Not sure what the point of this argument is. Do we have mathematics for the sake of mathematicians good mental health and career or to solve and discover novel problems? Why should we care if mathematicians can understand proofs if they are correct? Most modern mathematical problems are sufficiently abstract that their proofs or disproofs have no direct application. There's no problem you can fix or invention you c…

So...why can't an AI do the exact same thing? Make AI so it understands math better for future math to understand more math. Unless your argument is that mathematicians are effectively useless? I am assuming that's not your point though.

Perhaps an AI could! Today they do not, because the people driving them understand constructing the proof rather than understanding the proof to be "the problem".

(I suppose it's possible that in some distant AI future there might be no value in people understanding theoretical math, but I'm pretty skeptical of that; to me it seems like the same error as thinking nobody needs to understand multiplication because you can ask the computer to solve any multiplication problem.)

Re: Tao: Open math problems being non-renewably mined by AI

#182

Post by orangecat » Wed, Sep 09, 2026, 2:12 AM UTC

_alternator_ wrote: post #169

paxys wrote: post #166

Earlier quoted context omitted.

What theft? LLM output has never been copyrightable.

I'll give you the benefit of the doubt. GP was referring to the use of copyrighted material to train LLMs.

Which is not "theft" according to current legal precedent, and also common sense.

Re: Tao: Open math problems being non-renewably mined by AI

#183

Post by btilly » Wed, Sep 09, 2026, 2:13 AM UTC

gradus_ad wrote: post #16

>"While it may be technically infeasible to completely prohibit the use of automated tools to perform indiscriminate solution extraction, I believe that we can still designate many classes of problems as being desirous of a careful analysis that not only solves the problem, but identifies insights from the solution process, and learn more about the difficulty landscape for nearby problems, and for which raw solutions…

Perhaps reading https://www.math.toronto.edu/mccann/199/thurston.pdf will help.

The point of mathematics is not to prove results. It is to build conceptual thinking about mathematics. Important problems are important because in order to solve them we have to build concepts tying different things together.

We're not searching for answers. We're searching for insights. Trying to understand the problem causes us to draw the connections and find those insights.

AI gives us answers. But it doesn't help us build those insights. AI has a complete mastery of existing human insights. But doesn't build new ones from its own experience. In a real way, it does not find the opportunity to really learn.

So it tackles problems and either solves them or not. If solved, we now have an answer. If not, it's too hard for humans.

Re: Tao: Open math problems being non-renewably mined by AI

#184

Post by jfrbfbreudh » Wed, Sep 09, 2026, 2:14 AM UTC

pvillano wrote: post #179

The way to tame a profit-maximizer is to make the most profitable choice the one that creates the most societal good. I would like to see the Clay Institute give zero recognition for formalizations without human-readable proofs. That would incentivize OpenAI to scram or create something that's actually useful.

It would be trivially easy to convert Lean into English, so I’m not sure what the human-readable criteria gets you. There are also human written proofs that are considered not human-readable by most of the mathematics community (ABC conjecture).

Re: Tao: Open math problems being non-renewably mined by AI

#185

Post by Ar-Curunir » Wed, Sep 09, 2026, 2:14 AM UTC

dvt wrote: post #52

I'm with @nilesh on this one, and not exactly sure how merely the existence of a solution precludes the advancement of human knowledge. If a problem is "solved" (say, symbolically verified) without any insights gained, it doesn't seem very interesting to the profession. Navier-Stokes is a bit different (because there's a prize attached, so "scooping" matters), but almost all interesting problems don't have any prizes…

Current career structure of mathematicians works partially by looking at whether they have solved novel and interesting problems, or at least done theory-building that can help solve such problems. Many mathematicians are also motivated by being the world's first to solve such problems

Removing this measure suddenly means that academic mathematic norms need to adapt rapidly, and, even more importantly, intrinsic motivation for many mathematicians needs to change rapidly. That is understandably a sea change for the current mathematics community.

Re: Tao: Open math problems being non-renewably mined by AI

#186

Post by matherial » Wed, Sep 09, 2026, 2:14 AM UTC

traes wrote: post #161

matherial wrote: post #108

Earlier quoted context omitted.

Pure math is practiced mostly for the intellectual thrills and recognition among a very small group of peers. There's little else to it. You don't become rich, you don't become a celebrity. You teach students, write papers, and probably know most other people who work in the same subfield as you. Tao is a sort of a celebrity of the quarter on HN, but I promise you that outside this forum, almost no one has ever heard…

> Now, Tao is a sort of a celebrity of the quarter on HN, but I promise you that outside this forum, almost no one has ever heard of him. This is an absurd thing to say. Hacker news is not the only place that knows about the most famous mathematician in the world. Glancing at Google Trends he seems to be roughly as famous as Linus Torvalds. Not exactly a household name but by no means obscure.

I'm going to charitably assume that you forgot to include quotes around the names in your query, because that's absolutely not what Google Trends shows.

Stop 100 people on the street in NYC or Berlin or Tokyo and I bet none of them will be able to name any living mathematician. A few of them might know Linus, though.

Re: Tao: Open math problems being non-renewably mined by AI

#187

Post by Ar-Curunir » Wed, Sep 09, 2026, 2:16 AM UTC

jfengel wrote: post #75

I didn't realize that open math problems were a finite resource. I recall a story about some famous mathematician (Gauss?) dismissing interest in Fermat's Last Theorem claiming that he could crank out problems of equivalent interest. Clearly Tao knows a hell of a lot more than I do about this, but I'm surprised that math that close to completion.

You can indeed generate many nonsensical problems. Generating ones which require interesting and non-trivial mathematics is much more difficult.

Re: Tao: Open math problems being non-renewably mined by AI

#188

Post by abdullahkhalids » Wed, Sep 09, 2026, 2:17 AM UTC

gpm wrote: post #71

vouaobrasil wrote: post #48

Earlier quoted context omitted.

Actually there will because if you've actually ever spent time doing math, you only really get to that level of truly understanding and appreciating the stories if you've actually done the hard work yourself, which in turn will be economically infeasible due to AI. The analogy is interesting but incomplete and misleading.

I've actually spent time doing math and literally everyone I know who knows math learnt it by reproving things that people proved before them. I don't see why AI proving things makes this form of learning any more economically infeasible than the field of mathematics already is - and since it was apparently economically feasible before AI I expect it to stay that way.

There are two stages to learning research level math. First you learn to reprove other people work. This is relatively easy because the language, notion and prior explanations have already been optimized to help prove the next thing, and you know a solution exists. Then in your PhD you try to solve problems you don't really know a solution exists, and if it does, how long and complicated it is, what techniques will be used, etc.

You need to solve the second to get a PhD. For good reason. The second is way harder than the first. And now AI is making second way obsolete. It's not the end of the world, but it is the end of how things have been done for centuries.

Re: Tao: Open math problems being non-renewably mined by AI

#189

Post by apetresc » Wed, Sep 09, 2026, 2:18 AM UTC

sashank_1509 wrote: post #180

dbmikus wrote: post #158

Earlier quoted context omitted.

An AI-generated solution always provides two pieces of info: 1. proof that there is a solution 2. a solution that you can work backwards from to build understanding Maybe the solution is pretty inscrutable, but it's almost always better than nothing. So, both of these pieces of info would be at least marginally useful for advancing human knowledge.

It demotivates mathematicians. That’s a pretty large negative!

That’s a skill issue.

Re: Tao: Open math problems being non-renewably mined by AI

#190

Post by morpheos137 » Wed, Sep 09, 2026, 2:20 AM UTC

nafey wrote: post #76

dvt wrote: post #64

Earlier quoted context omitted.

> Mathematicians will be less likely to work on a problem if there is a solution Yes, that is Tao's premise, I'm just not sure I buy it. Suppose an oracle existed which could answer any question truthfully. Let's ignore the mechanics of this for now, but it could say things like "the Riemann hypothesis is False" or whatever and we would take it as gospel. Does this mean that we wouldn't have mathematicians or physici…

I think his point is that AI is not creating new problems. It may solve "the Riemann hypothesis" but may completely fail to posit a "Mythos hypothesis" which is vital to advance the field. In fact, achieving the former may make the latter even harder because it will disincentivize production of human mathematics which has till now been the only source of "interesting" problems. FWIW this is my understanding of his ar…

The sphere of human comprehensible mathematics is finite. Once everything is solve it is not necessary to advance the field. The recurring error her is to say ai is not the product of human effort but another agent. Ai is human. Ai may well be speeding up human comprehension of math to its limits in which case there is no further need to advance the field and mathematicians might need to get a job. Why is this a bad thing?