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Luis Martínez Zoroa, researcher at CUNEF Universidad, gains global recognition for major advances in the Navier-Stokes problem
9 September 2026
The research paper co-authored in 2023 by CUNEF Universidad professor Luis Martínez Zoroa and Diego Córdoba (ICMAT-CSIC) has been recognised as one of the intellectual foundations driving breakthroughs in the Navier-Stokes problem, one of the greatest mathematical enigmas of the 21st century. This challenge stands as one of the six Millennium Prize Problems that remain unsolved since they were formulated by the Clay Mathematics Institute in 2000.
The scientific journal Quanta Magazine reports that recent breakthroughs achieved by AI-assisted teams, which include OpenAI among other international researchers, rely heavily on the previous findings by CUNEF Universidad’s Luis Martínez Zoroa and ICMAT’s Diego Córdoba. The Spanish researchers proposed a novel strategy to address the problem that broke away from the mainstream methods used by a large part of the mathematical community.
The Navier-Stokes problem concerns a set of fundamental differential equations used to model fluid dynamics, ranging from ocean currents to airflows. Although these equations were formulated in the 19thcentury as a core tool in fluid mechanics, a key question remained unanswered: Do their solutions always remain smooth, or can they develop a singularity under certain conditions, leading to extreme behaviours where an infinitesimal part of the fluid evolves uncontrollably?
The article explains that the findings published by Martínez Zoroa and Córdoba were pivotal because they unlocked a different analytical pathway, based on the construction of an infinite sequence of “layers” or non-singular solutions that combine into what Martínez Zoroa calls an “infinite cascade” to produce a new solution exhibiting a singularity. Although their study alone did not fulfil all the conditions set for the Millennium Prize Problem, particularly the requirement of ensuring specific smoothness conditions, it did lay down a strategy that has subsequently been used by the teams behind the latest advances.
“This recognition underscores the power of mathematical research and the critical need for original knowledge that can unlock new pathways into problems that, for decades, were considered virtually unapproachable,” states CUNEF Universidad’s Luis Martínez Zoroa.
“For CUNEF Universidad, having researchers like Luis Martínez Zoroa and backing work with this level of international prominence highlights how university research can contribute original and rigorous approaches to some of the greatest scientific challenges of our time,” says Ana I. Fernández, Rector of CUNEF Universidad.
International acclaim
The relevance of Martínez-Zoroa’s work has been acknowledged by prominent members of the mathematical community. The scientific journal Quanta Magazine cites Princeton University’s Charles Fefferman, author of the official description of the Navier-Stokes problem for the Clay Mathematics Institute, who states that Córdoba and Martínez Zoroa are “the heroes in this story”. In the same vein, Tristan Buckmaster, a researcher at New York University, maintains that, in view of this work, Luis Martínez-Zoroa “deserves a Fields Medal.”
The breakthrough announced by OpenAI consists of a proof coded in Lean, a language designed for mathematical proof verification, that suggests the presence of singularities in 3D Navier-Stokes equations. If this proof is confirmed following the necessary scrutiny by the scientific community, it would be one of the most significant mathematical achievements enabled by AI models to date.
CUNEF Universidad views this global recognition as a clear result of its commitment to mathematical research. Since its foundation in 2023, CUNEF Universidad’s Department of Mathematics has assembled a team of 45 PhD researchers, 29 of whom pursue their research under the university’s tenure-track scheme. The purpose of this initiative, which includes Luis Martínez Zoroa, is to consolidate early-career researchers. Its ranks already feature recipients of Ramón y Cajal grants, funding from the BBVA Foundation’s Prisma and Leonardo initiatives or the Knowledge Generation Program of the State Research Agency, among others. The department’s research areas encompass partial differential equations, algebra and computational geometry, geometric and combinatorial optimisation, scientific calculus, computational mathematical physics and topological data analysis.
New studies
Alongside this line of research, Luis Martínez Zoroa is currently conducting new studies on mathematical analysis and differential equations, targeting highly complex, globally relevant problems. These active projects aim to continue exploring some of the unresolved questions at the forefront of the mathematical community’s attention, with specific findings set to be presented soon.
