Hong Wang

fl. 1991, Guilin, Guangxi, China

AnalysisGeometryFields Medal 2026

Chinese mathematician who, with Joshua Zahl, proved the three-dimensional Kakeya set conjecture in 2025; awarded the 2026 Fields Medal.

Hong Wang works in harmonic analysis and geometric measure theory. After undergraduate study at Peking University and a master's at Université Paris-Sud, she earned her PhD at MIT in 2019 under Larry Guth. Following postdoctoral positions at the Institute for Advanced Study and UCLA, she joined the Courant Institute at NYU and later became a permanent professor at IHES. With Joshua Zahl she resolved the sticky Kakeya conjecture and then, in a 127-page 2025 preprint, the full three-dimensional Kakeya set conjecture, proving every Kakeya set in $\mathbb{R}^3$ has Hausdorff and Minkowski dimension 3. She has also contributed to the Fourier restriction conjecture, local smoothing for the wave equation, and Falconer's distance set problem. She received the 2026 Fields Medal.

Workplaces: Courant Institute, New York University, Institut des Hautes Études Scientifiques (IHES)

China, United States, France

Award-winning work

Fields Medal 2026Awarded for the proof, with Joshua Zahl, of the Kakeya set conjecture in three dimensions (2025). The conjecture asserts that any subset of three-dimensional Euclidean space containing a unit line segment in every direction must have Hausdorff dimension three; Wang and Zahl confirmed it by combining incidence estimates for tubes with a deep analysis of sticky configurations of tubes. Their result settles a central problem of geometric measure theory and strengthens the foundations underlying questions about the Fourier transform and partial differential equations. It is the first complete resolution of the Kakeya conjecture in a non-planar dimension.

Contributions, linked to the library

Great problemKakeya conjectureWith Joshua Zahl, proved the three-dimensional case of the Kakeya conjecture (2025).