Hong Wang Wins 2026 Fields Medal, the Third Woman Ever | Quanta Magazine
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Living Fully in the Math World Means Threading the Needle
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2026 Fields and Abacus Medals
Living Fully in the Math World Means Threading the Needle
By
Natalie Wolchover
July 23, 2026
Focus, commitment, and insight resulted in a “once in a century” proof. Hong Wang is now just the third woman to win a Fields Medal.
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Hong Wang, pictured here working on a new article at the Institute for Advanced Scientific Studies (IHES) in France, is just the third woman to receive a Fields Medal in the award’s 90-year history.
Julien Pebrel/M.Y.O.P.
Introduction
By Natalie Wolchover
Columnist
July 23, 2026
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2026 Fields and Abacus Medals
Fields Medal
fractals
geometry
harmonic analysis
mathematics
partial differential equations
All topics
One might imagine that, for a mathematician, proving a monumental theorem is a blissful experience. It wasn’t so for Hong Wang. In February 2025, Wang and her collaborator Joshua Zahl presented a 127-page proof of a long-standing conjecture at the intersection of multiple branches of math. The duo had been checking their work for months and had sent it to select colleagues for review before finally mustering the courage to post it publicly. Wang worried less that the arguments were flawed than that they might be imperfectly expressed and therefore unclear.
No error was found, the proof’s logic was digested and streamlined, and everyone became convinced of its soundness. Wang and Zahl had proved the three-dimensional Kakeya conjecture.
The proof triggered a succession of prizes for Wang: the Salem Prize, the Ostrowski Prize, and the International Congress of Chinese Mathematicians’ Gold Medal of Mathematics in 2025; the Antonio Ambrosetti Medal, Sadosky Prize, Clay Research Award, and New Horizons in Mathematics Prize in the first half of 2026; and finally a 2026 Fields Medal, widely regarded as math’s highest honor, given to exceptionally accomplished mathematicians under 40. Wang, 35, a professor of mathematics at New York University who comes from Guilin, China, is just the third female winner in the Fields’ 90-year history.
The attention has meant more speaking invitations and travel and interview requests that she struggles to refuse, which impinge on the time she can spend trying to understand how long, thin tubes pointing in different directions can overlap.
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Early morning walks help Wang handle the stress and self-doubt that come with her mathematical research.
Julien Pebrel/M.Y.O.P.
This is the issue at the heart of the “Kakeya-type problems” that are Wang’s specialty, a family of mathematical questions and conjectures that lies at the center of the Venn diagram of harmonic analysis (the study of how signals break up into constituent frequencies), geometric measure theory (pertaining to the shapes and sizes of non-smooth things), and partial differential equations (which describe systems that change in multiple ways simultaneously), with further connections to number theory, combinatorics, and beyond. “All of these connections are why this area is considered so central and why Hong is celebrated so much,” said Pablo Shmerkin, a mathematician at the University of British Columbia.
She is always very kind and acknowledges that some of the ideas came from my work, but she was able to apply them in these fantastic ways that I couldn’t have envisioned.
Pablo Shmerkin
When she isn’t traveling, Wang works with the devotion and discipline of a cloistered nun or elite athlete. “She’s crazy into math,” said Shukun Wu of Indiana University, a collaborator. “She’s definitely one of the most dedicated people I’ve seen.” She denies herself time-consuming indulgences like reading books or having a dog, though she does make time for friends, yoga, and early-morning walks to see the dogs at Washington Square Park, which all help relieve the stress and feelings of self-doubt that, for her, can accompany mathematical research.
The desire to feel confident in her knowledge and ability seems to have shaped Wang’s life. It is, for example, what draws...