Is there any evidence that the discovery was made by Claude and not by Levent Alpöge himself? The only sources listed in the wikipedia article are an X post and a news article that references the post.
He could have been paid by Anthropic to run a brute-force computer search. The counterexample looks short enough that, given a portion of Anthropic’s computing power and a sufficiently smart algorithm, it could be found by brute force.
Is your premise here that no other mathematician was ever equipped or motivated to do a "brute-force computer search"? Or is it instead that you think Anthropic dedicated an entire data center's worth of compute to the task of speculatively trying to disprove a conjecture that has stood for over 80 years?
This is a very well studied problem. Well-known mathematicians have spent a lot of effort on it - Yitang Zhang wrote his entire PhD thesis on it back in 1991.
It is deeply unlikely that a random guy at Anthropic just happened to solve it so they could pass it off as the LLM's work.