As threatened, OpenAI dropped a shitload of math papers. 722 to be precise: github.com/openai/math/blob/ma… None solve Millennium Prize Problems or other ultra-famous conjectures. Paper number 312 proves a version of the Homotopy Hypothesis, one of my favorite math problems. I guess I was the first to call it the homotopy hypothesis. It says homotopy types are "the same" as "infinity-groupoids". Depending on how you make the quoted phrases precise, this hypothesis comes in many versions: some easy, some hard. None of the OpenAI papers will affect my work.
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OpenAI have dropped a list of maths problems their latest AI has proved. It is properly bonkers. github.com/openai/math/blob/ma…
A contrary take on these dumps of math results: *if* these models are going to be built and released anyway, then it's better that the results come out like this than that a bunch of random users get the proofs out of the model and all try to claim credit and priority. The challenges for the field of mathematics (and far beyond) are fundamentally due to the rapid improvement of the models, not due to OpenAI's approach to releasing the results. github.com/openai/math/blob/ma…
OpenAI: "A counterexample to Hadwiger's conjecture" We disprove Hadwiger's conjecture by constructing arbitrarily large graphs whose chromatic number exceeds their Hadwiger number. The examples have independence number at most two,... github.com/openai/math/blob/ma…
