A Historic Achievement in Mathematics
In July 2026, the international mathematical community recognized Hong Wang, a 35-year-old professor at New York University and the Institute for Advanced Scientific Studies (IHES), with the Fields Medal. Widely regarded as the highest honor in mathematics, the award is presented to exceptionally accomplished mathematicians under the age of 40. Wang’s selection marks a historic milestone as she becomes only the third female recipient in the 90-year history of the prize.
The accolade follows her landmark 2025 collaboration with mathematician Joshua Zahl, in which the duo successfully proved the three-dimensional Kakeya conjecture. Their 127-page proof, finalized in February 2025, resolved a long-standing question at the intersection of harmonic analysis, geometric measure theory, and partial differential equations.
Resolving the Kakeya Problem
At the center of Wang’s research are “Kakeya-type problems,” which explore how sets of line segments pointing in different directions interact and overlap in space. The Kakeya set conjecture asks whether such sets, despite having no volume in the traditional sense, behave like solid objects in terms of their dimensionality. Proving the conjecture in three dimensions had been a significant challenge for decades, with implications for Fourier analysis and signal processing.
Wang’s approach utilized advanced techniques in multiscale analysis, building upon her previous work on the Falconer distance problem. Her ability to synthesize complex geometric patterns and apply them to wave equations has been described by colleagues as both creative and exceptionally disciplined. Jonathan Hickman of the University of Edinburgh noted that her early contributions as a doctoral student were surprisingly advanced, signaling her rapid rise to the forefront of the field.
Academic Trajectory
Wang’s journey to this honor began in Guilin, China, where she developed an early fascination with the permanence of mathematical theorems. After moving to France in 2011 to study at the École Polytechnique, she eventually transitioned to the Massachusetts Institute of Technology (MIT) for her doctoral studies under the mentorship of Larry Guth. Her career has been marked by a series of prestigious honors, including the Salem Prize, the Ostrowski Prize, and the Clay Research Award, culminating in the 2026 Fields Medal.