Speaker: Péter Ván (Wigner RCP)
Title: The "Navier–Stokes Equation" Millennium Prize Problem: Mathematics and Physics, or How Smart Is Artificial Intelligence?
Date: Friday, 2. October 14:00
Place: Building 3, Council room
Abstract:
In this talk we explore the Clay Institute's Millennium Prize Problem on the Navier–Stokes equation. First, we review its origins, starting from the sixth of Hilbert's famous 23 problems, through the Lax–Friedrichs theorem, to the mathematical role of thermodynamic concepts. Then I will show what exactly would have to be solved on the mathematical side, and what the OpenAI team of machine-mind agents did and did not solve. It will become clear where the Navier–Stokes equation actually comes from, and why we expect that the solution of a dissipative equation with smooth initial conditions should not blow up by itself, nor develop shock waves and the like. From the physical point of view, however, the mathematical problem is strangely degenerate, and its real difficulty is revealed by the energy balance that necessarily accompanies the momentum balance. Finally, this leads us to reflect on what actually happened when mathematicians speak of mathematics' "Kasparov vs. Deep Blue" moment, and on when such a moment might come in physics. Reviewing the events and the priority dispute, one thing is certain: we are nowhere near the point where our natural intelligence becomes useless, and we may ponder how we ought to use it differently from the way we have so far.
