Terence Tao writes about recent mathematical breakthroughs by Alpöge and Buckmaster regarding singularity formation in fluid dynamics. Building on previous work by Córdoba and Martínez-Zoroa, these researchers demonstrated finite-time blowup for the incompressible porous medium (IPM) equation, the two-dimensional Boussinesq equation, and the three-dimensional incompressible Euler equations using smooth forcing terms or initial data. Tao highlights that while full solutions to the Navier–Stokes global regularity problem remain unachieved by this method, it significantly increases their feasibility in the near future.
- The strategy involves iteratively constructing solutions by adding high-frequency corrections that cause singularities at a blowup time.
- Recent work from Ganeshram, Duruisseaux, and Anandkumar utilizes physics-informed neural networks (PINNs) to locate self-similar blowup profiles for Euler equations.
- A significant controversy exists regarding whether AI models may have "mined" human research results without proper attribution or credit.
- Tao describes the current status of some AI-generated proofs as being in a novel stage between a formally verified proof and a well-written, peer-reviewed paper.
- The strategy involves iteratively constructing solutions by adding high-frequency corrections that cause singularities at a blowup time.
- Recent work from Ganeshram, Duruisseaux, and Anandkumar utilizes physics-informed neural networks (PINNs) to locate self-similar blowup profiles for Euler equations.
- A significant controversy exists regarding whether AI models may have "mined" human research results without proper attribution or credit.
- Tao describes the current status of some AI-generated proofs as being in a novel stage between a formally verified proof and a well-written, peer-reviewed paper.
