Mathematician Terence Tao has shared a new result concerning finite-time blowup with a smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equations, discussed in a post by Terry Tao. Additional commentary from Tao appeared on Mastodon. Tao, based at UCLA, is a Fields Medalist and one of the most widely followed mathematicians working today, which is part of why the post drew immediate attention across the mathematics community.

A shared ChatGPT conversation related to the work has also circulated, prompting discussion about the role AI tools may be playing in contemporary mathematical research.

Some observers are calling this "a Deep Blue moment" for AI, a reference to IBM's chess computer that defeated world champion Garry Kasparov in 1997. The links were passed along via T., a mathematician.

For background: the Navier-Stokes equations, which describe the motion of viscous fluids, are among the most famous open problems in mathematics. Proving the existence and smoothness of solutions in three dimensions is one of the seven Millennium Prize Problems established by the Clay Mathematics Institute in 2000, each carrying a $1 million prize. The incompressible Euler equations, which describe inviscid fluid flow, are closely related, and blowup results for related systems such as the Boussinesq and porous medium equations are often studied because they can shed light on the broader question of whether smooth Navier-Stokes solutions can develop singularities in finite time. A blowup result shows that a solution's derivatives become unbounded in finite time; demonstrating blowup even for related or forced systems is regarded as meaningful progress toward understanding the singularity landscape around Navier-Stokes itself. Whether the new result constitutes a genuine turning point for AI-assisted mathematics, as the "Deep Blue" framing suggests, remains a matter of debate, and further peer review and follow-up work will clarify its significance.