Javier Gómez-Serrano receives the 2025 R. E. Moore Prize

Javier Gómez-Serrano, professor at Brown University, has been awarded the 2025 R. E. Moore Prize for Applications of Interval Analysis, together with Tristan Buckmaster (Courant Institute of Mathematical Sciences, New York University) and Gonzalo Cao-Labora (École Polytechnique Fédérale de Lausanne). The award recognises their article Smooth imploding solutions for 3D compressible fluids, published this year in Forum of Mathematics, Pi.

The R. E. Moore Prize was created in 2002 by the editorial board of the journal Reliable Computing to honour the legacy of Ramon E. Moore, a pioneer in interval arithmetic. The prize, awarded every two to four years, celebrates outstanding contributions where interval analysis makes a decisive impact.

“It is the highest distinction within this community, and I feel very proud and fortunate to have received it,” says Gómez-Serrano. He is also quick to stress the collective nature of the award, underscoring the key role of Tristan Buckmaster and Gonzalo Cao-Labora: “This article began as Gonzalo’s undergraduate thesis between Princeton and the UPC, which gives his contribution extraordinary value and deserves recognition.”

Gómez-Serrano studied Mathematics and Telecommunications Engineering at the Universitat Politècnica de Catalunya, and obtained his PhD in Mathematics from the Universidad Autónoma de Madrid in 2013. He later held positions at Princeton and the Universitat de Barcelona before joining Brown University in 2022. His work sits at the crossroads of analysis, partial differential equations, fluid mechanics, spectral geometry, numerical computation, machine learning, and rigorous computer-assisted proofs.

Smooth implosions that trigger singularities in 3D fluids

In their prize-winning paper by Buckmaster, Cao-Labora and Gómez-Serrano (which also carries the affiliation of the CRM), construct the first smooth self-similar imploding solutions to the 3D Euler equations for all adiabatic exponents γ > 1, and show that these profiles can also be used to build asymptotically self-similar imploding solutions to the Navier–Stokes equations (for γ = 7/5). This represents the first rigorous example of singularity formation in compressible fluids with density bounded away from zero and constant at infinity.

“Singularities are the central piece of any differential equation. By understanding how singularities form, we also gain a deeper understanding of the model itself and its connection with the natural world around us.”

Singularities, Gómez-Serrano explains, are “the central piece of any differential equation, in fluids or beyond. The fact that a singularity appears tells us whether a problem has a solution or not, one of the most basic questions one can ask mathematically. By understanding how singularities form, we also gain a deeper understanding of the model itself and its connection with the natural world around us.”

“For example, with a simple quadratic equation, we know that if b² – 4ac < 0 there is no real solution. For partial differential equations there is no such criterion, and all studies are very complex and must be carried out equation by equation, not always successfully. By understanding the formation of singularities, we gain a much better understanding of the mathematical model and its relationship with the nature that surrounds us.”

To establish these results, the authors combined deep mathematical analysis with rigorous computer-assisted proofs based on interval arithmetic. “The classical pencil-and-paper approach is very limited when some quantity is not perturbative (for example, when the solutions are not small) and the calculations have to be done quantitatively,” says Gómez-Serrano. “A modern approach, mixing classical analysis with highly precise quantitative estimates, can make the difference between proving a result or not.”

Opening paths for future mathematics

Beyond its specific results, the paper also highlights the growing role of computer-assisted methods in mathematics. “This research helps bring computer-assisted proofs closer to the mathematical mainstream and shows how synergy produces stronger theorems. Our methods are already being reused in other contexts, and I believe this kind of approach will be very successful in the future, especially now that AI models have made programming much faster and easier.”

This is not Javier’s first step into the frontier between mathematics and computation. Just a few months ago, we reported on his collaboration with Terence Tao and DeepMind on AlphaEvolve, an AI tool for exploring open mathematical problems. In that piece, and in a video interview available on the CRM YouTube channel, he reflected on how AI is reshaping the way mathematicians work, opening faster and more collaborative paths to discovery.

The award ceremony will take place during SCAN’2025 (International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations), held in Oldenburg, Germany, from 22 to 26 September 2025.

This is the second time the award goes to a researcher affiliated with the CRM, following Àlex Haro, professor at the Universitat de Barcelona, who was previously distinguished with the same prize in 2018.

Citation

Buckmaster T, Cao-Labora G, Gómez-Serrano J. Smooth imploding solutions for 3D compressible fluids. Forum of Mathematics, Pi. 2025;13:e6. doi:10.1017/fmp.2024.12