There are reasons to suspect that OpenAI may have intentionally or unintentionally trained on chat logs from mathematicians--mathematicians who were actively using OpenAI to try to to solve the same problems themselves.[1] If those mathematicians were on the right track, and getting close to a solution, that could be classified as finding "better training data somewhere."
[1] https://cybernews.com/ai-news/openai-accused-stealing-anothe...