Chinese Mathematicians Wang Hong and Yunqing Tang Win the Mathematics “Oscar”

Three‑dimensional Kakeya conjecture proved

In February 2025 Hong Wang (NYU) and Joshua Zahl published a 127‑page paper that resolves the three‑dimensional Kakeya conjecture. The conjecture asks for the minimal size of a set in ℝ³ that contains a unit line segment in every direction. In two dimensions the minimal area can be made arbitrarily small, but the three‑dimensional version predicts that any such set must have full Hausdorff dimension 3. Wang’s proof settles the conjecture, confirming the prediction. The paper is available at https://arxiv.org/pdf/2502.17655. Terence Tao described the result as “one of the most notable breakthroughs in geometric measure theory,” and NYU’s Eyal Lubetzky called it “one of the top mathematical achievements of the 21st century.”

Number‑theoretic breakthroughs by Yunqing Tang and Vesselin Dimitrov

Working with Frank Calegari, Yunqing Tang and Vesselin Dimitrov achieved two long‑standing results in the theory of modular forms. First, they proved the unbounded denominators conjecture, which asserts that Fourier coefficients of certain modular forms can have arbitrarily large denominators—a problem that had resisted resolution for decades. Second, they established the irrationality of a constant arising from a basic infinite series; this is the first irrationality proof of its kind since Apéry’s 1979 proof of the irrationality of ζ(3). Both results were highlighted as breaking a 45‑year stagnation in the field.

Differential‑geometric advances by Otis Chodosh

Otis Chodosh (Stanford) solved several central conjectures that had been open since the 1970s–80s. With Chao Li he proved a core conjecture concerning non‑spherical manifolds, establishing new rigidity properties for high‑dimensional spaces that are not diffeomorphic to spheres. In collaboration with Christos Mantoulidis he resolved a key problem in minimal‑surface theory, showing existence and regularity results for certain area‑minimizing hypersurfaces. These advances advance the broader field of variational analysis.