Spanish Mathematician and Google DeepMind Tackle the Navier-Stokes Equations

Spanish mathematician Javier Gómez Serrano, born in Madrid 39 years ago, has joined forces with the artificial intelligence giant Google DeepMind to tackle one of the most challenging mathematical problems known to humanity: the Navier-Stokes equations. This enigma, part of the Millennium Prize Problems, comes with a $1 million prize from the Clay Mathematics Institute and the promise of “immortal fame,” as Gómez Serrano emphasizes.

The Navier-Stokes Enigma

The Navier-Stokes equations, formulated in the 19th century by French mathematician Henri Navier and Irish mathematician George Gabriel Stokes, describe the motion of fluids such as water and air. Despite their age, the equations remain unsolved, particularly concerning whether their solutions always maintain regularity or if they can suddenly change, akin to a tsunami in a calm sea. These equations are crucial for predicting phenomena like weather, catastrophic floods, airplane movement, and blood flow.

A Team of Experts

Gómez Serrano, who teaches at Brown University, is leading a team of five academics from various U.S. institutions. The team includes two geophysicists, Ching-Yao Lai and Yongji Wang, and three mathematicians: Tristan Buckmaster, Gonzalo Cao Labora, and Gómez Serrano himself. The team has been working discreetly for three years, aiming to solve the Navier-Stokes problem.

Using AI to Break New Ground

Previous attempts to solve the Navier-Stokes equations using traditional mathematics have failed. However, Gómez Serrano's team is leveraging artificial intelligence, specifically machine learning neural networks, to refine solutions and understand where and how singularities form. Their results, published three years ago, suggested that a solution to the million-dollar problem was imminent.

Competing Teams

Gómez Serrano believes there are only a few other groups seriously competing to solve the Navier-Stokes problem. These include Thomas Hou’s team at the California Institute of Technology, the tandem of Tarek Elgindi and Federico Pasqualotto, and Diego Córdoba’s team, which includes Gómez Serrano’s former PhD supervisor.

Recent Breakthroughs

Gómez Serrano has also been involved in another significant breakthrough with Google DeepMind: AlphaEvolve. This new AI system solves complex mathematical problems with unprecedented efficiency. Trained for four months on 50 puzzles, AlphaEvolve achieved a 95% success rate, matching or improving on the best human results.

The Future of AI in Mathematics

Demis Hassabis, the head of Google DeepMind, and his team have already made groundbreaking contributions with AlphaFold2, which predicts protein structures. Hassabis predicts that artificial general intelligence will arrive around 2030. Gómez Serrano, while more cautious, acknowledges the rapid progress in AI and its potential to revolutionize mathematics and other fields.

Optimism and Caution

Gómez Serrano believes that AI will change the world for the better, enabling more complex questions and better understanding of nature. However, he also acknowledges the need for responsible use of AI to avoid potential risks.

In the next year or year and a half, the world may witness a significant breakthrough in the Navier-Stokes problem, thanks to the collaboration between Gómez Serrano and Google DeepMind.