What does it mean that our data is used to improve model performance?

In year 2000, the Clay Mathematics Institute of Cambridge, Massachusetts established the Millenium Prize Problems. These are seven well-known complex unsolved mathematical problems, and the institute pledged to pay one million US dollars for the first correct sollution to each problem. Tristan Buckmaster, an NYU mathematics professor, had been collaborating with Levent Alpöge, a prominent mathematician, on solving the same problem for almost a year making extensive use of Claude and GPT 5.6 Sol. On August 15th, they had a breakthrough. They also got rummors that news of their solution, which had not been publicly announced, somehow had reached OpenAI. On September 8, 2026, OpenAI announced they had found a solution for the Navier-Stokes existence and smootheness problem, one of the Millenium Prize Problems. OpenAI used an internal advanced LLM for arriving at the solution. Buckmaster published a statement about the coincidence that OpenAI had solved the problem after having notice of…