Google DeepMind has made groundbreaking progress in fluid dynamics by using AI to discover new mathematical solutions to long-standing problems. In a new study, researchers introduced an entirely new family of unstable singularities—points where physical quantities like velocity or pressure become infinite—in some of the most complex equations governing fluid motion. These findings represent a major step forward in understanding the fundamental limits of fluid dynamics, a field that has puzzled scientists for centuries. The work, conducted in collaboration with mathematicians and geophysicists from Brown University, New York University, Stanford University, and other institutions, demonstrates how AI can be used not just to solve equations, but to uncover new mathematical phenomena. The team developed a novel method that transforms Physics-Informed Neural Networks (PINNs) into powerful tools for mathematical discovery, achieving unprecedented precision and interpretability. A key focus of the research was on the stability of singularities. While stable singularities are robust to small changes, unstable ones require extremely precise initial conditions. In the context of fluid dynamics, it is widely believed that no stable singularities exist for the 3D Euler and Navier-Stokes equations—two of the most important models in the field. Proving whether singularities can form in these equations is one of the six unsolved Millennium Prize Problems, carrying a $1 million reward. Using their AI-driven approach, the researchers systematically identified new families of unstable singularities across three major fluid equations: the Incompressible Porous Media (IPM), Boussinesq, and 3D Euler equations. Most notably, they observed a striking pattern in the data: when plotting the blow-up speed (represented by lambda, λ) against the order of instability—the number of ways a solution can deviate from the singularity—the points aligned along a clear line for the IPM and Boussinesq equations. This suggests the existence of a broader class of unstable solutions, with predicted lambda values extending along the same trend. Visualizations of these solutions reveal intricate three-dimensional structures and evolving vorticity fields, with one-dimensional slices showing how instability increases over time. These patterns provide strong evidence for deeper mathematical structures underlying fluid behavior. The study’s first author, Yongji Wang from NYU, emphasized that the success came from embedding deep mathematical insights into the AI framework, turning PINNs from mere solvers into tools for discovery. The results open new pathways for tackling complex problems in mathematics, physics, and engineering by combining AI with rigorous theoretical analysis. This work marks a turning point in how AI can be applied to fundamental science—moving beyond prediction to true discovery. The team plans to continue exploring the implications of these findings, particularly in understanding the limits of physical models and advancing the development of more accurate simulations for real-world applications.