Javier Gómez Serrano collaborates with Terence Tao and DeepMind on an AI project to solve open mathematical problems

Researcher Javier Gómez Serrano, a former member of the Centre de Recerca Matemàtica (CRM) from 2020 to 2022, and currently a professor at Brown University, is part of a new project at the intersection between mathematics and artificial intelligence. Together with mathematician Terence Tao, form the University of California, and a team at Google DeepMind, Gómez Serrano is helping to develop AlphaEvolve, a pioneering tool that explores a new way of doing mathematics. We had the opportunity to speak with him during the recent Conference on Modern Trends in Fourier Analysis at the CRM.

AlphaEvolve, publicly announced on May 14, 2025, is an evolutionary coding agent based on language models like Gemini. Its core idea is simple but powerful: generate multiple candidate solutions in code and evolve them iteratively through a process similar to natural selection. This method has already shown its potential by tackling major open problems, such as matrix multiplication or the kissing number problem in 11 dimensions. In this last case, AlphaEvolve discovered a configuration of 593 spheres tangent to a unit sphere, setting a new lower bound for this longstanding geometric challenge.

A new way to do mathematics?

Gómez Serrano first came into contact with DeepMind through a previous collaboration on the Navier–Stokes equations. “I had already been working with them on that topic, and at the end of January 2025 we started this new project,” he explains. For him, the emergence of tools like AlphaEvolve signals a turning point in mathematical research: “I believe the way we do mathematics is going to change, at least for part of the community. These kinds of models or assistants will become more widespread and will help us reach results that now take one or two years in just a few days.”

This acceleration also transforms the kind of questions mathematicians can ask: “We’ll be able to tackle harder problems, because we’ll have more powerful tools,” he says. But he also adds a note of caution: “We still don’t know the best way to interact with these models. The community is figuring out how to get the most insight with the least computational cost.”

Unlike systems like ChatGPT, AlphaEvolve does not operate through natural language. “We don’t talk to it with plain text,” Gómez Serrano explains. “We ask it to write code that tries to solve the problem, and that code then evolves and improves over time.”

This raises new challenges, especially when it comes to extracting insight from the solutions. “When the model detects structure in a solution, how do we understand and translate that into mathematical intuition? That’s something we still don’t fully grasp.” As Terence Tao explained on Mastodon: “AlphaEvolve can attempt to extremize functions F(x) with x ranging over a high-dimensional parameter space, and can outperform traditional optimization algorithms when the function and space have non-obvious structure”.

When it comes to the role of AI in mathematics, Gómez Serrano is clear: it’s not a competition. “This isn’t about humans versus machines. The real value is in what humans and machines can do together. These tools allow us to go beyond our limits, not in competition, but in collaboration.”

As for the areas of mathematics most likely to be affected, he points to quantitative or concrete domains as natural early adopters. “It’s easier for a computer to handle numbers than to represent abstract concepts like groups. But with the speed these technologies are evolving, we don’t really know where the boundary will be.”

A message to young mathematicians

His advice to early-career mathematicians is simple: keep an open mind. “This landscape is evolving incredibly fast. The pace of results is no longer measured in years, but in months. Staying informed and open-minded is essential to understand how this new mathematical world will work.” He sees it not as a threat, but as an opportunity: “We’re starting from scratch in many ways. That gives us a chance to take the lead, not just in research, but in defining how mathematics is done in the future.”

New tools like AlphaEvolve are reshaping how we approach mathematical discovery. By combining human insight with AI-driven exploration, this project is opening new paths toward solving complex problems; faster, deeper, and with unexpected creativity.

The full interview with Javier is available on the CRM YouTube channel.