First, OpenAI is not claiming that the model wasn't trained on those sessions. What they've said is “We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem.” and “We did not use their prompts or proofs to prompt our models or direct our agents.” and “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.”

They also said “Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge … and Tristan Buckmaster….” They say the rumor was that two Millennium Prize problems had been resolved, and that this prompted them to launch "an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems."

It's not obvious to me that's an unethical thing to do, if it happened as they described.

> we cannot rule out that de-identified data derived from their usage of our products helped improve our models.”

implied the humans sessions could have been (and probably were, why wouldn’t they be?) in the training set?

If I was trying to make a model smarter and I had transcripts from the smartest mathematicians in the world I’d make sure the model trained on them.