La Jornada: Mexican is getting closer to solving one of the seven mathematical challenges of the millennium

José Damián Espinosa, a graduate of the actuarial career from the University of the Americas Puebla (Udlap), developed a new mathematical approach to address the Riemann hypothesis, one of the seven problems of the millennium, the resolution of which would allow us to better understand the distribution of prime numbers.

Although he has heard about this challenge for years, it was during the last four years that he began to take it seriously and consider a way to approach it. Inspired by the work philosophy of physicists Albert Einstein and Richard Feynman, he dedicated much of his time to thinking about the root of the enigma and how to simplify it.

Between December 1, 2025 and January 2026, when he had a well-structured proposal, he presented it in Zenodo, a scientific repository developed by CERN, the largest and most famous particle physics laboratory in the world. He also posted it on MathOverflow, an online question-and-answer website for professional mathematicians and graduate-level students.

In a short time, his approaches received thousands of views, downloads and comments from experts. The case of Ravi Vakil, a specialist in algebraic geometry and president of the American Mathematical Society (AMS), stands out, who considered that Espinosa’s proposal opened a new avenue of analysis worth exploring.

“This sounds very good because it seems that you have found a nice translation of the problem and this seems to be enough to make it very interesting,” he wrote.

The Riemann hypothesis is one of the seven millennium problems, announced in 2000 by the Clay Mathematics Institute (a global organization dedicated “to promoting the beauty, power and universality of mathematical thought”), which offers a prize of one million dollars to whoever solves each of them. Until now, only the Poincaré conjecture has been proven by the Russian mathematician Grigori Perelmán.

Espinosa highlights that the value of these problems is that their resolution could build bridges between various branches of mathematics, deepen their connections and even give rise to new branches. “The important thing is not their solution itself, but the tools they create, the paths they open.”

He explained that when approaching the Riemann hypothesis, one of his main objectives was to reduce it to its most basic version and then he decided to link it with the Young lattice, a mathematical structure used to represent different ways of decomposing an integer into sums.

He specified that his proposal, although it is not the solution to the problem, but rather a reformulation, “opens a new path, a new promising approach, although this path still needs to be developed before reaching a possible demonstration.”

The positive feedback he has received since publishing his approach has encouraged the young mathematician to think about the next step. Now he plans to pursue a postgraduate degree that will enrich his knowledge and allow him to perfect a tool to get even closer to answering this challenge.

“You have to be willing to stumble”

“Devoting yourself to a difficult problem all the time, for a long time, is risky because there is no guarantee of victory. It is a risk, but I am willing to take it,” he commented.

To continue his work, Espinosa is inspired by the career and philosophy of mathematicians such as Andrew Wiles, who describes the process of doing mathematics as entering a dark mansion, tripping over the furniture, finding the light switch and moving to the next dark room.

“You have to be willing to go into the dark and bump into furniture, hoping to find the switch… by luck, by persistence, or by both,” he concluded.