alt Hacker News>It's unknowable and not possible to prove if any one specific conversation was the key to solving Navier–Stokes.
If the conversation was in the training set, there's a high likelihood that the small set of conversations related to solving Navier-Stokes was used by the model. I get Astra to still quote some of my friends' books or blogposts nearly verbatim on certain niche issues.
Much more importantly, we _can_ determine whether a conversation was used in the training data. And if it was, it gives us a great idea whether that logic was captured in reasoning for a novel problem never yet solved.
Given that you don't see any of this as below the belt according to your other comments, maybe your contribution here is more for yourself than a fair conversation about attribution.
The flaw with this line of reasoning is that Buckmaster and Alpöge only had a partially completed proof of a weaker version of the Navier-Stokes problem. OpenAI's internal model solved the full, harder problem. This means the key information needed to bridge the gap was not present in Buckmaster and Alpöge's chat history.
You might retort that ChatGPT used the training data to copy their approach, but the approach Buckmaster and Alpöge chose was already published by Luis and Diego in 2023 and in every frontier model's training set.