Hong Wang Wins 2026 Fields Medal, the Third Woman Ever

Key Points:

• Hong Wang specializes in Kakeya-type problems, which lie at the intersection of harmonic analysis, geometric measure theory, and partial differential equations, with connections to number theory and combinatorics; her work is highly regarded for its creativity and depth.
• Wang’s journey into mathematics began in childhood in Guilin, China, where she developed a passion for problem-solving and appreciated math for its certainty and permanence, eventually studying at Peking University and later moving to France and the U.S. for advanced study.
• During her doctoral studies at MIT under Larry Guth, Wang made significant progress on longstanding problems related to incidence geometry and harmonic analysis, including the Falconer distance problem and the local smoothing conjecture.
• Wang, together with Joshua Zahl, recently proved the 3D Kakeya set conjecture, showing that sets of line segments pointing in every direction in 3D space must occupy three dimensions; their proof involved analyzing “sticky” Kakeya sets and using advanced inductive arguments.
• This breakthrough reshapes the field’s landscape, opening avenues for tackling harder problems like the 4D Kakeya conjecture and 3D restriction problems, while Wang balances her rising fame with a desire to maintain personal well-being beyond mathematics.