The company announced that an internal model had produced a proof addressing the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems established by the Clay Mathematics Institute.

Mathematicians at OpenAI showed that the Navier-Stokes equations, which describe how fluids flow, can sometimes “blow up.” But the massive result is not without controversy.

Think about placing dots on a flat surface. You want as many pairs as possible to be separated by the same distance. For any amount of dots, what is the greatest possible number of pairs that can be exactly that far apart? The question, what mathematicians ...