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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

#21

Post by henryfjordan »

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…

The story of the cubic equations is another great example: https://en.wikipedia.org/wiki/Cubic_equation

Dudes straight up used to hoard solutions to equations and use them in math battles.

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

#22

Post by epestr »

usrnm wrote: post #6
enraged_camel wrote: post #4

Earlier quoted context omitted.

[flagged]

Do you have a real argument to make rather than just appealing to authority?

And the other an appeal to tradition. There was only one Gauss to scoop and focusing on him misses the larger math culture which Terry might be aware of, where most trust others to not scoop.

And if any mathematician's AI usage on a problem leads to scooping, the volume of agents involved gives them a huge advantage which could prompt mathematicians to not use LLMs.

Though you can say Terry's claim is a slippery slope.

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

#23

Post by GolfPopper »

ozgung wrote: post #18

No matter what happened this must be a wake up call for all of us. We’re basically sharing everything we have with these companies/AI systems. This is wildly different than a human wiretapping our private messages. Because it is systematic and automated in an astronomical scale. There is no real privacy in this new world. Law? I think “National Security” is a good enough excuse to screen anything constantly, includin…

>We’re basically sharing everything we have with these companies/AI systems.

My sense of the word 'share' is that it traditionally involves agency by all parties involved. There are a lot of words in English for describing taking things without permission and profiting thereby - words like piracy, banditry, and larceny.

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

#24

Post by cattenwallen »

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…

I think you're misunderstanding the point of math problems. Mathematics is as much a process as it is a result. This is why even from early on, relatively rudimentary mathematics questions you are graded by your capacity to correctly achieve the desired process to the answer than getting the answer correct. The risk here is that AI generated proofs removes the process part of mathematics, where actually interesting concepts live (because then you can apply novel concepts to other unsolved problems and then thereby unlock new concepts that way...) Sure you can kind of try to reverse-engineer it but you lose the entire intuition and "we tried applying it in X, Y, Z ways and it didn't work" intuition, because even the non-working process can teach you about how not to apply the working process to novel problem spaces.

Basically: Tasting a delicious soup doesn't tell you how to layer the flavors, but if you want to be a good chef, you better be learning flavors more than you learn dishes!

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

#25

Post by magicalhippo »

enraged_camel wrote: post #11
usrnm wrote: post #6

Earlier quoted context omitted.

Do you have a real argument to make rather than just appealing to authority?

So let me get this straight: you're saying that Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history? And me pointing this out is merely an appeal to authority? Get outta here.

Knowing the math that was developed through history, and knowing how that math was developed and the circumstances around it are two fundamentally different things.

Clearly Tao knows the former, but apriori that does not imply he knows the latter.

Not saying he doesn't, just saying one does not imply the other.

Even if you go back and read the original papers, you'll miss all that which happened beyond the page.

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

#26

Post by lo_zamoyski »

enraged_camel wrote: post #11
usrnm wrote: post #6

Earlier quoted context omitted.

Do you have a real argument to make rather than just appealing to authority?

So let me get this straight: you're saying that Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history? And me pointing this out is merely an appeal to authority? Get outta here.

> Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history?

If Tao has a knowledge of the topic (which he does), then it isn't by virtue of being a mathematician per se, but by virtue of an interest in the history of mathematics (which he has). Knowledge of math is enormously helpful here, but it does not imply historical knowledge.

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

#27

Post by derangedHorse »

techas wrote: post #20
Jtariiiii wrote: post #10

Earlier quoted context omitted.

Also Andrew Wiles working in secret for 7 years out of fear of someone scooping him.

I've always found the story of A. Wiles sad and frustrating. He worked in secret for 7 years. He submitted a (incorrect) proof at year 4 or so. Reviewers found a problem, but he decided kept all secret for many years after. He didn't even proof the last theorem of Fermat directly, he proved some conjeture that someone else before him, proved that it implied Fermat last theorem... I found this behavior against healthy…

While I can sympathize with this perspective, I don’t think it’s right to call it driven by “ego.” Sometimes one just wants to go at a problem without being second guessed on approaches or led astray with suggestions by others.

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

#28

Post by johnsmith1840 »

I mean, hasn't it always been this way? If something valuable is within reach and you disclose it, someone else might reach for it?

Just because the length of the arm is longer with an AI org doesn't mean it's somehow fundamentally a different system.

The future is that if you don't use AI your work is a lot easer to reach against someone else who has it.

That dude hand writing code with punchcards can be lapped by a 20yo with python, what's different?

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

#29

Post by The_Blade »

techas wrote: post #20
Jtariiiii wrote: post #10

Earlier quoted context omitted.

Also Andrew Wiles working in secret for 7 years out of fear of someone scooping him.

I've always found the story of A. Wiles sad and frustrating. He worked in secret for 7 years. He submitted a (incorrect) proof at year 4 or so. Reviewers found a problem, but he decided kept all secret for many years after. He didn't even proof the last theorem of Fermat directly, he proved some conjeture that someone else before him, proved that it implied Fermat last theorem... I found this behavior against healthy…

> He didn't even proof the last theorem of Fermat directly, he proved some conjeture that someone else before him, proved that it implied Fermat last theorem...

I think that was Ken Ribet?

Grigori Perelman and the Poincaré Conjecture is more interesting. IIRC he turned down Millennium and was decidedly not all about the Fields Medal - mostly because Richard Hamilton didn't get credit? Anyway, I am grateful I had the opportunity to learn about Poincaré in college taking a few classes from a professor who was a key contributor to the conjecture and got a Fulbright for it when I was there

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

#30

Post by sobrey »

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…

Not a mathematician.

The issue I see with a handed-over proof is tunnel-vision: you explore only the understanding of the proof.

Without a proof, your exploration branches out much further, in directions that could seem fruitless, but may uncover new understandings that are now "hidden" because the handed-over proof drastically lowered the incentives to find them.

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