This includes a proof of Barnette's Conjecture, which is one of the graph theory conjectures that I tried attacking with SOTA models a few months ago. I like it because it is easy to understand with a basic knowledge of graph theory. I spent quite a bit of time on it and failed. Their proof looks approachable at first glance.

https://github.com/openai/math/blob/main/preprints/Paired-st...

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jboggan 31 minutes ago | parent | next [-]

I've been messing with that problem since 2002. I'm curious if you were trying the dual spanning tree direction (which is what the purported proof is using) or working with cycle construction on the original graph. I was working heavily with edge-Kempe swaps but couldn't quite get there.

I am now very interested in the explicit calculation of Hamiltonian cycles in the non-bipartite case, and/or the calculation of their absence. If P=NP I think that's going to be a great route of attack.

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an0malous 3 hours ago | parent | prev | next [-]

Any idea what made OpenAI successful where you weren’t?

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kulahan 3 hours ago | parent | next [-]

Trillions of dollars might be a bit of an advantage.

	▲	an hour ago \| parent [-]
		[deleted]

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seanmcau 3 hours ago | parent | prev | next [-]

Probably the model OAI used that is strictly better than whichever SOTA - 3 months model OP used?

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sebzim4500 3 hours ago | parent | prev | next [-]

Presumably it's mainly the better model, I don't see much evidence of a particularly advanced harness based on the reasoning traces that they provided.

	▲	an0malous 2 hours ago \| parent [-]
		That’s what I was wondering. Thanks.

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whamlastxmas 3 hours ago | parent | prev | next [-]

Their internal model is allegedly like 4x as capable as the publicly available ones

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ForHackernews 3 hours ago | parent | prev | next [-]

They ingested all of his sessions with their SOTA models from a few months ago. ;)

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ndriscoll 2 hours ago | parent | next [-]

Crazy how all these problems were simultaneously on the precipice of being solved before ScoopenAI (I came up with that) stole their work. The rate that mathematicians have suddenly made progress is only bested by the rate that OAI has ramped up their theft haha it's nuts. Good thing it'll never get better at explaining ideas though (since they're all stolen) so there'll still be that.

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digitaltrees 3 hours ago | parent | prev [-]

The fact that this is plausible should be deeply disturbing and disqualifying for openAI. The fact that they may prevail and win is a travesty of our failed system.

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zeroonetwothree 3 hours ago | parent | next [-]

What does "win" mean? There is no prize for this, and having someone discover a proof benefits us all.

	▲	vuurmot 3 hours ago \| parent \| next [-]
		The prize is a tenure for the researcher, and in OpenAI's case, a higher valuation when they IPO? In this case, the tenure is gone, and OpenAI has increased their valuation
	▲	breezybottom 3 hours ago \| parent \| prev [-]
		Sure there is. A job, tenure, professional respect, Fields medal.

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fnordpiglet 3 hours ago | parent | prev [-]

Disqualifying for what? If you develop a proof you aren’t competing for something, you’re expanding the frontier of knowledge. It’s a binary state of the world, either it’s proven or not. Prevail and win what exactly?

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zzzeek 2 hours ago | parent | prev [-]

I'm going to guess the ability to hold a million individual details in an attention space at once, compared to the typical human capacity for about six or seven

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TeeWEE 2 hours ago | parent | prev [-]

Did you validate the proof? Who did?