The first assumption [1. AI really did solve a problem in mathematics] is wrong because to really solve a mathematical problem, providing a mere answer (even if formally certified) is not sufficient.
This subjective attitude turns mathematics into nothing more than number-poetry.
That would reduce mathematics to something very pathetic.
Focus instead on attribution. Yes, OpenAI took the last tiny step in the process of solving this problem (= proving it). But it cannot attribute credit to all the mathematicians whose chat logs from the past few months were fed into its training data. Unlike a human, it can't even remember where it learned things from! For many theorems, I can still recall which exposition was the one that "sank in" for me (often not the first one!) a decade after grad school.
In my mind, this makes current LLMs unfit to deserve any credit at all -- they cannot give credit to others, so they and their owners deserve no credit themselves. OpenAI's LLM took the last tiny step, but not any of the important ones.
This subjective attitude turns mathematics into nothing more than number-poetry.
That would reduce mathematics to something very pathetic.
Focus instead on attribution. Yes, OpenAI took the last tiny step in the process of solving this problem (= proving it). But it cannot attribute credit to all the mathematicians whose chat logs from the past few months were fed into its training data. Unlike a human, it can't even remember where it learned things from! For many theorems, I can still recall which exposition was the one that "sank in" for me (often not the first one!) a decade after grad school.
In my mind, this makes current LLMs unfit to deserve any credit at all -- they cannot give credit to others, so they and their owners deserve no credit themselves. OpenAI's LLM took the last tiny step, but not any of the important ones.