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Ten advances in mathematics and theoretical computer science

openai.com

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Re: Ten advances in mathematics and theoretical computer science

#21

Post by DroneBetter »

danielrmay wrote: post #4

I'm enjoying learning about these hard problems, but this line about credit made me chuckle: > We helped prepare the manuscripts and formalize the proofs in Lean, and we take responsibility for their correctness Offering to take responsibility for the correctness of a proof written in Lean feels like volunteering to be the fall guy in case someone finds a flaw in basic arithmetic, no?

well, a bug in the Lean kernel was discovered last week by way of an LLM tricking itself and its handler into believing it had found a non-constructive proof of the existence of a nontrivial Collatz cycle, see https://infosec.exchange/@0xabad1dea/117002106099986943 and https://lipn.info/@mevenlennonbertrand/116997917683191056

Re: Ten advances in mathematics and theoretical computer science

#23

Post by 0x5FC3 »

traes wrote: post #16
0x5FC3 wrote: post #9

How much do you all think it would cost to "buy" these advances from PhDs, practicing scientists?

This isn't really a productive way to think about these things, IMO. It's quite possible it would take hundreds of years for any specific group of PhDs to solve them. Or one individual PhD could have the correct flash of insight and solve it in a month. There's absolutely no way to predict this, besides trying to gauge the apparent simplicity of the proof or counterexample (which is likely to be misleading). Until so…

I understand and I am not trying to deny the impressiveness or the velocity of AI in general. But at some point we have to ask how much do we trust the labs at face value without much transparency of how they got to the results when there is trillions of dollars on the line.

Re: Ten advances in mathematics and theoretical computer science

#25

Post by cure_42 »

NitpickLawyer wrote: post #15
zkmon wrote: post #11

> claiming human authorship for a proof generated entirely by an AI system would misrepresent both the system’s contribution and the nature of genuine human intellectual work. AI has no self-awareness. It's a tool. When you assemble a furniture using a screw driver, the torque force interacts with the molecular forces inside the metal and miraculously it transfers the force to the screw though a clever geometry desig…

A better analogy would be a manufactured object, say 3d printed for simplicity. The 3d printer is given an input, and an object manifests itself after some time. We say that the creator of the object is the person turning on the machine, sending the data, and collecting the object. Not the machine itself.

I'd say the creator is the one who created the 3d model, not the one who pushed the print button.

Re: Ten advances in mathematics and theoretical computer science

#26

Post by ratmice »

traes wrote: post #10
piker wrote: post #2

I don’t feel the existential dread of mathematicians is correct. It seems to me in fact these results are bringing math mainstream. I now personally look forward to the interpretations and discussions of the significance of such results by human mathematicians. Now I understand that it’s mostly the super stars benefitting from the increased attention. Folks who are less established don’t share in that glory. But on t…

Every time someone makes a comparison to chess I die inside. Chess is a spectator sport primarily funded by a few eccentric billionaires. Players artificially constrain themselves in timed environments knowing that they will never be able to produce better moves than a smartphone because a select few people find it interesting. Only ~30 top professionals actually make enough money to have a full career playing chess,…

Another noteworthy difference is that Stockfish is also gpl.

Re: Ten advances in mathematics and theoretical computer science

#27

Post by traes »

einpoklum wrote: post #14
aabhay wrote: post #6

My main gripe here is the lack of transparency around the total experiment and construction. I doubt that they simply pointed their model at these ten specific problems alone and gave the model one shot; therefore the $2000 number could be completely misleading, similar to P-value hacking by not disclosing the total experimental setup. I want to know: 1. How many total problems were given to the model, and what perce…

Also, have there been examples of researchers not affiliated with OpenAI (or another LLM creator), who have done something similar? Another question I have is whether or not OpenAI 'simply' hired capable combinatorics researchers to work on problems, and they have, and the use of the model is incidental / secondary to their work.

> Also, have there been examples of researchers not affiliated with OpenAI (or another LLM creator), who have done something similar?

A couple small ones that I've seen (example here [0]), but not anything of the magnitude that OpenAI and Anthropic have put out. Likely just related to token limits.

> Another question I have is whether or not OpenAI 'simply' hired capable combinatorics researchers to work on problems, and they have, and the use of the model is incidental / secondary to their work.

I think their output has reached a level that precludes this possibility, but I of course don't have any hard proof.

[0]: https://www.reddit.com/r/math/comments/1uxj3cy/after_openais...

Re: Ten advances in mathematics and theoretical computer science

#28

Post by jacki »

traes wrote: post #16
0x5FC3 wrote: post #9

How much do you all think it would cost to "buy" these advances from PhDs, practicing scientists?

This isn't really a productive way to think about these things, IMO. It's quite possible it would take hundreds of years for any specific group of PhDs to solve them. Or one individual PhD could have the correct flash of insight and solve it in a month. There's absolutely no way to predict this, besides trying to gauge the apparent simplicity of the proof or counterexample (which is likely to be misleading). Until so…

[flagged]

Re: Ten advances in mathematics and theoretical computer science

#29

Post by baq »

danielrmay wrote: post #12
emil-lp wrote: post #7

Earlier quoted context omitted.

No, the correctness isn't for the "inside the Lean proofs", but for the translation of "human language math" and its formal Lean variant.

I see. It still feels like a bit of an oddly solemn way of saying "this is the part we admit responsibility for"

It’s more than you get from free software - you get no proofs, no warranties and any responsibility of its authors are their pure good will. Reminder lean proofs are software!
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