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

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

#201

Post by rzerowan »

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…

More of a 'its the journey' rather than the destination type of thing.Since the insights , quirks, tricks and procedures gained along the way allows insights intoother at that moment unknown problem/domains in the future.

As far as researchers sharing their data/notes with the AI hyperscalars looks like that would be coming to an end wihth a mor guild-like structure going forward to prevent their progress being fron-run by the AI labs.

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

#202

Post by cozzyd »

vessenes wrote: post #3

That’s not untrue. But it’s also a misstatement of mathematical history. Many leading mathematicians historically have been highly competitive — Gauss comes to mind. Woe betide the lesser intellect that sent Gauss some ideas. The Newton Leibniz controversy was very serious business at the time in the UK and the continent. It was considered at the least a sin to reveal that sqrt(2) was irrational to those outside Pyth…

   It was considered at the least a sin to reveal that sqrt(2) was irrational to those outside Pythagoras circle
perhaps a 2 sin 45?

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

#203

Post by nozzlegear »

apetresc wrote: post #189
sashank_1509 wrote: post #180

Earlier quoted context omitted.

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

That’s a skill issue.

Will somebody please let Professor Tao know that he's simply experiencing a skill issue?

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

#204

Post by augment_me »

_alternator_ wrote: post #55
olalonde wrote: post #49

Can't mathematicians still gain novel insights by reverse-engineering AI-generated proofs? Just like chess players learn new concepts by studying what engines play.

Yes, and they will. But what's happening here is that the system that cultivates mathematics (and mathematicians) is recieving likely the biggest shock of its history. How do you reward merit and identify talen when people can't absorb the number of proofs being generated, much less understand them? Perleman's proof of the Poincare conjecture took several years for the mathematical community to digest; the proof of N…

Well maybe its time to pivot from mathematics, and science as whole from personal attribution to being about progress of the field? Maybe your contribution to humanity as a mathematician is to find the right meaningful question to ask, and not to stamp your name on some fact?

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

#205

Post by [deleted] »

matherial wrote: post #108
olalonde wrote: post #49

Can't mathematicians still gain novel insights by reverse-engineering AI-generated proofs? Just like chess players learn new concepts by studying what engines play.

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…

[deleted]

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

#206

Post by pixl97 »

evenhash wrote: post #197
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.

> An AI-generated solution always provides ... proof that there is a solution This is only true in the most trivial sense. A solution is a solution, sure... but how do you know it's a solution, and not an incoherent jumble of words? A human has to review and vouch for it. Just because the AI gives you an arxiv-worthy PDF, or a Lean proof which compiles, doesn't mean it proves what the AI says it does. The AI could gi…

I might be wrong, but making an assumption that you could learn to read the mathematical output of the AI long before you could write a solution yourself. But hey, what do I know, I'm not a mathemagition.

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

#207

Post by pixl97 »

derektank wrote: post #102
torben-friis wrote: post #65

Earlier quoted context omitted.

Humanity is very biased for the culmination of work, considering everything that comes before and after busywork for the lower masses. Replicating a paper is just as valuable scientifically as publishing it, but how many careers advance through replication? If we move the goal from "find the solution" to "clear up the LLMs work" that doesn't bode well neither for the attractiveness of the problem nor for the career o…

>Replicating a paper is just as valuable scientifically as publishing it, but how many careers advance through replication? I don’t think this is true, especially for novel or unexpected results. I suppose it depends on what you mean by scientifically, and there is a debate in the philosophy of science about what the value of research even is, but a successful replication does not result in substantial updates to one…

Hello.

You have created a fraud machine. Why? With no answer checking then why not make up the most fraudulent crap you can get away with?

Examples: A huge portion of recent non-reproducable science papers.

---

Your thinking, along with everybody that's doing this rat race is causing the pumping out of papers with questionable data, but very little to ensure we are actually making correct science.

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

#208

Post by bityard »

senshan wrote: post #165

From "Jokester" by Isaac Asimov 1956: "Early in the history of Multivac, it had become apparent that there was one big bottleneck: the questioning procedure. Multivac could answer the problems of humanity, all the problems, if -- if it were asked meaningful questions. But as knowledge accumulated at an ever-faster rate, it became ever more difficult to locate those meaningful questions." [0] https://web.archive.org/w…

I don't see why that should be a problem, as we already know the answer is 42 in any case.

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

#209

Post by bronson »

pixl97 wrote: post #206
evenhash wrote: post #197

Earlier quoted context omitted.

> An AI-generated solution always provides ... proof that there is a solution This is only true in the most trivial sense. A solution is a solution, sure... but how do you know it's a solution, and not an incoherent jumble of words? A human has to review and vouch for it. Just because the AI gives you an arxiv-worthy PDF, or a Lean proof which compiles, doesn't mean it proves what the AI says it does. The AI could gi…

I might be wrong, but making an assumption that you could learn to read the mathematical output of the AI long before you could write a solution yourself. But hey, what do I know, I'm not a mathemagition.

What does "mathematical output of the AI" even mean? A proof? Intermediate tokens?

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

#210

Post by pixl97 »

bee_rider wrote: post #142
nilkn wrote: post #89

Earlier quoted context omitted.

It's easy to come up with new open problems. It's hard to come up with new open problems that seem to teach us something fundamentally new about the world. Our current batch of problems went through a complex selection process over decades (or centuries) based not purely on difficulty but also on perceived insightfulness. I studied math, but I am not a mathematician, so I think I have a slightly different perspective…

I haven’t been following the AI proof stuff very closely, but the impression I got was that these models are producing massive Lean programs that prove the statement one way or another, but are quite difficult to fully understand. Actually, I have to admit I don’t really know what math is. With physics we suspect there’s a universe, and when we study physics we’re improving our description of the behavior of that uni…

I think part of mathematics is taking things that don't fit in our head and giving them human abstractions so they can.

Take infinity. Infinity can't fit in your head, hell, it can't fit anywhere, but you can abstract away the endlessness and look at infinities of different sizes, et al.

Now, is there a single formula for something actually represented in this world that would take most of a humans life just to read it, no idea.

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