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

What do you mean, as OpenAI employee, you cannot tell that his work has entered the training data ?

But also correct me if I'm wrong, if the two mathematician were really close to finish this problem, and their conversation were used by OpenAI, shouldn't the Agent have succeeded way faster/efficiently instead of using "4.9 million messages and used about 300 billion output tokens."

I’m not a mathematician so take this with a grain of salt. Apparently terry tao commented that the approach used for the Euler paper can “probably” be used for solving NS but it’s still technically challenging and can probably be done with an LLM with a lot of compute. To me the crux of the issue is whether the insight were stolen so that the problem becomes something that is in the domain of LLMs. This is much different than LLMs coming up with the insight. OpenAI wants everyone to think the LLM came up with the insight and solved the thing by itself even though they have perhaps an army of researchers.

Having the chat logs enter the training data and having them have a meaningful influence on the ultimate result the model produces are very different things.

The text for all the Goosebumps books are certainly in the training data and to some small amount influenced the solve. But their contribution was so vanishingly small it would seem absurd to say R L Stein should have recourse for contibuting to the solve.

It's almost as if it was actually found by manually written brute-force algorithm running on OpenAI's massive computer cluster.