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Do you know that from reading the proof, or are you just assuming this based on what you think LLMs should be capable of? If the latter, what evidence would be required for you to change your mind?

- Edit: I can't reply, probably because the comment thread isn't allowed to go too deep, but this is a good argument. In my mind the argument isn't that coding is harder than math, but that the problems had resisted solution by human researchers.

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1) this is a proof by example 2) the proof is conducted by writing a python program constructing hypergraphs 3) the consensus was this was low-hanging fruit ready to be picked, and tactics for this problem were available to the LLM

So really this is no different from generating any python program. There are also many examples of combinatoric construction in python training sets.

It's still a nice result, but it's not quite the breakthrough it's made out to be. I think that people somehow see math as a "harder" domain, and are therefore attributing more value to this. But this is a quite simple program in the end.

One of the possible outcomes of this journey is that “LLMs can never do X”. Another is that X is easier than we thought.

Or that some quixotic problems nobody cared about to the extent to actually work on them do have some solution.

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