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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

#301

Earlier quoted context omitted.

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.

Download a book and you are a thief

Download 1 million books and you are OpenAI

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

#302
post #277

Earlier quoted context omitted.

You miss the point. Humans don't mind competing with others. I love competition, but I don't want to compete with you and your machine. I love to play chess, I don't care if you are grand master, whoop my ass. But not if you are going to pair up with stockfish. I don't even care if you are a newbie that started playing yesterday with an ELO rating of 900. If I wanted to play the damn computer I'll do it myself. Likew…

Could you tell the difference between a grandmaster and stockfish if playing them online? If not, why would you care which one you are playing against?

Of course you can. Stockfish plays very different compared to a human, and it never ever blunders or makes mistakes.

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

#303
post #293

Earlier quoted context omitted.

It is theft under common sense.

Only in the sense that you reading a book from the library also constitutes theft of knowledge. Does it?

If I stole someone's private research notes and republished them loosely in my own words, they'd correctly be pissed

This was unpublished research that was stolen, and constitutes plagiarism and academic fraud by even the strictest definition

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

#304
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 math is compressible structure. That's why we care about something like the Riemann hypothesis but, to use Tao's example, we really couldn't care less about computing the 10^10^10th digit of pi. The first compresses a vast amount of information about the primes, while the second decompresses information that we've already compressed (a few lines of code can define every digit of pi).

Most patterns that exist are incompressible. Math is basically a search for those compressions that do exist. An example I personally really like is the amplituhedron: a geometric structure that humans have just barely been capable of recognizing compresses information about scattering amplitudes and Feynman diagrams. That one happens to be within our reach, but it's right at the edge, and we can only imagine what glorious, wondrous compressions exist in abundance beyond the edge. Math accessible only to superintelligence would exist entirely beyond that edge, compressing patterns whose existence we cannot even detect using objects and constructions that we cannot grasp.

As an aside, I also think this is why AI is quickly becoming superhuman at math: intelligence is essentially a form of pattern compression.

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

#305

Earlier quoted context omitted.

Mathematics isn't art. It doesn't gain its value in human affairs from being interesting to study. I fail to see why we should cater to that.

What is it, if not an art?

Truth.

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

#306

Earlier quoted context omitted.

Funny, the stuff that was stolen is still there. A strange kind of theft. Copyright maximalism is a bad look on a site called "Hacker News." Perhaps other sites beckon.

> Copyright maximalism is a bad look on a site called "Hacker News." Perhaps other sites beckon. Frankly it's more of an insult to the "hacker" name to be apologising for big companies profiting off of frontrunning existing work for PR purposes, if the claims about piggybacking on human-directed efforts/prompting are true. Being pro-copyright in order to protect the work of an individual from being reconstituted into…

"Corporate machine," yadda, yadda, whatever, go sell it on Reddit. The model running on the box in my basement is almost as good as the one we're talking about here, and may in fact be just as good by this time next year... and it couldn't have existed under your proposed regime.

Yes, OpenAI is likely to be found to have acted like a slimeball in this instance, or at least the employee in question may have. But you can't fix that without making laws that will make everything else worse... and only here in the US.

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

#307

Earlier quoted context omitted.

My computer contains the prime factorization of probably several dozen (if not more) large integers, and I refuse to share them with anyone! (Because they are my private RSA keys)

Why are you still using RSA?

Where else are you going to keep your large primes?

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

#308

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…

> 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 give you the same PDF/Lean code and says it proves the opposite, how would anyone know the difference?

> You can't advance human understanding unless you produce things that humans can understand.

And you can't advance human understating unless you maintain that understanding.

I can see a version of the junior software engineer problem here: AI wrecks the problems that could train and motivate the next generation mathematicians, so students abandon the field because there's no place for them. The senior mathematicians who can review/vouch/prompt for AI output like Tao retire and die. Then there's no more math that anyone can understand and no more open problems for it to solve.

And that's probably happening already. I've read articles about AI performing the journeyman work that mathematicians cut their teeth on, rendering years of work obsolete, and derailing the careers that work was meant to start.

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

#309

There's nothing that AI won't be able to mine and accomplish (aside from being literally human), it's only a matter of hardware and scale at this point. Generalized problem solving is a factor of search efficiency over the problem space. The actual software part is all figured out, the only open questions are how to do things efficiently and what the trade-offs are from a hardware perspective, but if hardware paradig…

> it's only a matter of hardware and scale at this point.

The AI companies have already bought up the world’s entire supply of hardware. There won’t be any more.

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

#310
post #51
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…

The mathematical community was very competitive in its early years, but in the last 70 to 100 years, it has been generally less competitive and very collegial. The community was in a good place, and progress has been very good. In a few cases when competitiveness was ramped up, it lead to bad behaviour and destructive fights. Few would like to return to those competitive years.

Maybe it’s a dynamic equilibrium? We will become competitive for a while, then run out of questions, which in turn rewards pockets of collaboration?
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