Thomas Bloom

@prz_chojecki How are you measuring 'no progress'? Is it that each model is coming up with the same initial arguments but no further? Or are you feeding in the previous model's output and asking if it can get any further?

I have one Erdos problem I test all new models on. Funny that GPT 5.2 made some initial arguments, 5.4 cleaned them a bit and there's no progress past that with 5.5, 5.6 or Fable 5. Models are getting better of course.

@compute25 @natsothanaphan Thanks, I'll read that paper. I agree that people should be more widely aware that the "chain of thought", despite the name, is not necessarily what the model actually "thought".

@thomasfbloom @natsothanaphan It may be interesting as a plausible reconstruction of how a mathematician could have reached the proof. My objection is only to treating it as evidence of how the model actually reached it , also there is substantial research behind my claim , do check out the paper too

A very nice proof! A thread with a couple of comments:

@compute25 @natsothanaphan Whether or not it reflects what happens in reality though, it still reads like a plausible explanation of how, say, a human might have thought to discover the same proof. Which still makes for interesting reading.

@compute25 @natsothanaphan Fair enough. I was referring to why mathematicians would be interested in the chain of thought - to understand how the proof came to its final form. If the chain of thought does not actually reflect that, I agree that's a problem.

@compute25 @natsothanaphan Wrong how? In that the chain of thought does not reflect that?

@thomasfbloom @natsothanaphan and the second use case is the wrong one infact lol

@compute25 @natsothanaphan The former is not needed - the final writeup is all that is needed to understand/verify the proof (or it is not a complete writeup!) The chain of thought is useful for the latter.

@natsothanaphan @thomasfbloom There is a major difference between: “This trace helps a mathematician reconstruct or verify a proof.” and: “This trace tells us how the model internally discovered the proof.” also please don't cite anthropic's ridiculous papers

@Martin778192374 These are the important questions now, and I discuss AI results with those in mind. Very different context from a human proof.

@Martin778192374 "Is AI replacing human mathematicians?" Or "is AI doing a different kind of research?" Or "is AI capable of producing proofs that require fundamentally new ideas?"

@Martin778192374 No, this is not what I said - this proof is a new proof to an old, well known, problem in graph theory. An impressive achievement for anyone, whether human or AI.

@thomasfbloom You have basically just defined that what an AI does as being easy, not really new, within reach or whatever, no matter what it is. It by definition couldn't the AI is good. Enjoy the crowd-pleaser success even with these rather disappointing takes.

@alexwei_ But I don't have time to doodle right now, so someone will probably beat me to it.

@alexwei_ It would be even nicer if one could just write down directly what a suitable t-map is, rather than proving it exists indirectly via considering the dual. I guess this can be done, and with it one would have an even shorter 'magical' proof.

@compute25 @natsothanaphan Why is it fraud?

@natsothanaphan @thomasfbloom well that's wrong and to put it simply a pretty fraud pov

@littmath Agreed! I'm also encouraged by the fact that they have very good human mathematicians in house, who (based on the unit distances, I assume also with double cycle) take a careful look at proofs now before making a public announcement.

I’m kind of a fan of OpenAI’s decision to devote some resources to math. Obviously there’s a PR aspect but I much prefer a pdf signed “OpenAI” to the new trend of signing one’s name to short arxiv preprints to which one didn’t contribute anything meaningful.

@kvallier I have not seen (but they may exist) attempts to use linear algebra over F_2 in this way to make the most of this Fano flow, despite how natural it is in hindsight.

@kvallier I wouldn't say "very near misses" (at least from what I've seen in the literature, but hopefully experts can soon comment better on the context). I meant more that this key step (of constructing a double cycle cover from a Fano flow) has a lot in common with existing papers.

@QRDL Aha, thanks!

@thomasfbloom Retrieval Augmented Generation... the searching of relevant papers and putting it into the prompt (5.6 Sol has a 1M token limit)

@QRDL What does RAG stand for?

@thomasfbloom Perhaps, but I think for RAG it would have cited. My guess it failed to cite because it implicitly knew it from deep neural network knowledge.

@jam_Omni @thomasahle Then I'm afraid I don't know what this means, so I am unqualified to read or comment on it. I would be interested in a proof of the combinatorial bound, but you say you do not provide this.

My method doesn't attempt deriving the classical combinatorial bound. It instead formalizes a constraint-governance route, It is an endpoint-transfer argument: the constraint formalism fixes the admissible carrier and certificate regime, then rules out the standing of every same-scope residual endpoint alternative, forcing the bounded-motif endpoint branch.