AI Just Solved a 100 Year Old Million Dollar Science Mystery

DeepMind's AI has solved a century-old mathematical mystery by uncovering new families of Navier-Stokes equation singularities, a problem previously deemed impossible and worth a million dollars.

• DeepMind's AI discovered new singularities for Navier-Stokes equations, solving a 100-year-old problem.

• Physics-informed neural networks provided extreme precision and uncovered previously unknown mathematical solutions.

• This breakthrough establishes AI as a vital partner in scientific discovery, with broad impacts across diverse fields.

An AI from DeepMind has made a groundbreaking discovery by identifying entirely new types of singularities in the Navier-Stokes equations, which describe fluid motion. This achievement addresses one of the seven Millennium Prize problems, providing solutions that human mathematicians later confirmed as correct. The implications of this breakthrough are vast, potentially revolutionizing fields from weather prediction and aircraft design to astrophysics by offering deeper insights into fluid behavior.

The Unsolvable Problem

• 00:00:26 For over a century, mathematicians struggled with certain equations related to fluid dynamics, leading them to be classified as one of the seven Millennium Prize problems, each carrying a million-dollar reward. These problems, including the Navier-Stokes equations, describe how fluids like air and water move and behave. The particular challenge centered on proving the existence of singularities, or 'blowups,' where values like velocity or pressure theoretically spike to infinity in the mathematical models, helping scientists understand the limits of these equations.

DeepMind's AI Approach

• 00:02:21 DeepMind employed a novel approach using graph neural networks and physics-informed neural networks (PINs) to tackle the Navier-Stokes problem. Unlike traditional neural networks, PINs are trained directly on the equations, constantly checking their output against physical laws and minimizing the residual error. This method allowed the AI to uncover entirely new families of singularities that had never been described before, with mathematicians from leading universities subsequently confirming their mathematical solidity.

Unstable Singularities & Precision

• 00:04:01 The AI discovered unstable singularities, which, despite requiring extremely precise conditions to manifest, offer profound insights into the equations' fundamental structure. This finding is significant because mathematicians had long suspected that stable singularities do not exist for the boundary-free, three-dimensional Euler and Navier-Stokes equations. The AI achieved an astounding level of accuracy, comparable to predicting Earth's diameter with an error of only a few centimeters, by utilizing advanced machine learning techniques like second-order optimizers to push networks to near machine precision.

AI as Research Partner

• 00:05:53 This breakthrough marks a historic shift, positioning AI as a crucial research partner that guides mathematicians to solutions they could not reach independently. Yang Jee Wang, a lead researcher, emphasized that by embedding mathematical intuition and driving extreme precision, PINs have transformed from problem-solving tools into 'discovery engines.' This ushers in a new era of computer-assisted mathematics, where AI explores complex equation landscapes and flags potential solutions for human experts to verify.

Broad Scientific Impact

• 00:06:43 The discovery extends far beyond theoretical mathematics, with significant implications for real-world applications across various scientific domains. In meteorology, it could lead to more accurate storm forecasts, while in aeronautics, it may help reduce turbulence and improve fuel efficiency. Furthermore, it offers new avenues for understanding astrophysical phenomena, demonstrating AI's ability to tackle long-standing fundamental scientific challenges and expanding the scope of what scientific research can achieve.