NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge have publicly posted three preprints establishing finite-time blowup with smooth forcing for the incompressible porous medium equation, the two-dimensional Boussinesq system, and the three-dimensional incompressible Euler equations, alongside Lean formalizations of the proofs. In a statement posted with the preprints, Buckmaster also recounts contacts with OpenAI in which, he writes, the company told him an internal…