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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

#32

Post by raincole »

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…

Sorry, OpenAI's take is correct here. If you're not convinced, here is how they prompted LLM: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98... [0]

A slightly smarter highschooler could write these. I could write these. It's clear as day that the LLM, not the human, did the heavy lift. It'd be ridiculous to give full credit to whoever wrote the prompt.

[0]: Not one of the proofs in the linked article, but from OpenAI too.

Re: Ten advances in mathematics and theoretical computer science

#34

Post by NitpickLawyer »

cure_42 wrote: post #25
NitpickLawyer wrote: post #15

Earlier quoted context omitted.

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.

(let's assume that)My 3dprinter is special. It has a bunch of values + an algorithm (i.e. a neural network) that takes input as tokens and outputs a printed object.

Re: Ten advances in mathematics and theoretical computer science

#35

Post by traes »

DroneBetter wrote: post #21
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

That seems to have been more of a sensationalized joke. Even your link has a disclaimer in it now. Read this chat from the researcher who did this:

https://leanprover.zulipchat.com/#narrow/channel/270676-lean...

Re: Ten advances in mathematics and theoretical computer science

#36

Post by simianwords »

0x5FC3 wrote: post #23
traes wrote: post #16

Earlier quoted context omitted.

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.

The level of conspiracy theory is nuts

Re: Ten advances in mathematics and theoretical computer science

#39

Post by traes »

avaer wrote: post #37

What happens when OpenAI et al stop being open about these things, and just pack it into the training?

Not much point to pure math being kept secret, in all honesty. There isn't really industrial value, its only purpose (to them) is showing off their model's capabilities. More realistically they'll just stop paying for it.

Edit: Oh, are you suggesting they just use it to privately improve their models? I imagine a few more correct proofs would have a very marginal benefit, if any. Also, they'll probably just get extracted, meaning it still gets out but OpenAI doesn't get to fancily announce it themselves.

Re: Ten advances in mathematics and theoretical computer science

#40

Post by simianwords »

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…

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