Hong Wang, former student at École Polytechnique, receives the 2026 Fields Medal

It all began in 1917, when Japanese mathematician Soichi Kakeya asked what the minimum surface area required to fully rotate a needle would be. Intuition suggests a disk with a diameter equal to the length of the needle. However, other shapes were quickly discovered, such as inwardly curved triangles.

Eleven years later, another scientist—Abram Besicovitch—turned conventional wisdom on its head by proving that it is possible to create a figure containing every possible needle direction while having zero area. Equipped with tools to measure the dimensions of objects—that is, the way they occupy space—mathematicians showed that the set described by Besicovitch occupies the entirety of the available 2D space due to its dense geometric texture. In other words, it contains a multitude of lines pointing in all directions, giving it the maximum geometric consistency allowed in a two-dimensional plane.

Unlocking the 3D barrier

In the 1970s, extending the Kakeya conjecture to three-dimensional space emerged as the natural next step. For over 50 years, researchers tackled the problem, but it was not until the 2020s that Hong Wang (who devoted her PhD thesis to the subject) and Joshua Zahl finally broke through this bottleneck.

Just as in 2D, the two scientists demonstrated that if a space is filled with very thin tubes representing all possible needle directions, the entanglement of these tubes possesses the maximum geometric thickness allowed in a three-dimensional space.

In doing so, they pave the way for further breakthroughs, particularly in harmonic analysis (the study of waves and signals), to which the Kakeya conjecture is intimately linked. Indeed, understanding how these needle-like tubes intersect sheds new light on the way waves propagate and interfere.

A fourth Fields Medal for IP Paris

Hong Wang, who was recently awarded an honorary doctorate recipient from École Polytechnique, is also a permanent professor at the Institut des Hautes Études Scientifiques (IHES) in Bures-sur-Yvette, as well as a professor at the NYU Courant Institute of Mathematical Sciences. She joins Alessio Figalli*, Pierre-Louis Lions, and Laurent Schwartz*** on IP Paris's list of Fields Medal laureates.

*Former holder of the Hadamard Chair at École Polytechnique, 2018 Fields Medalist

**Former professor at École Polytechnique, 1994 Fields Medalist

***Former professor at École Polytechnique, 1950 Fields Medalist