Comment by prideout
1 day ago
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...
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.
Any idea what made OpenAI successful where you weren’t?
Trillions of dollars might be a bit of an advantage.
Trillions?
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Probably the model OAI used that is strictly better than whichever SOTA - 3 months model OP used?
Nah.
The model is probably comically big and inefficient but big enough
Finally, size really does matter!
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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.
That’s what I was wondering. Thanks.
They ingested all of his sessions with their SOTA models from a few months ago. ;)
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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Their internal model is allegedly like 4x as capable as the publicly available ones
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
Did you validate the proof? Who did?