Hong Wang Wins 2026 Fields Medal, the Third Woman Ever | Quanta Magazine

SERIES Living Fully in the Math World Means Threading the Needle 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. 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 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, who comes from Guilin, China: 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 and the Institute for Advanced Scientific Studies (IHES) in France, 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. 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. 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 her to mathematics: to her, the least doubtful thing. Even though she never took the time to celebrate her landmark proof — nor felt any consequent ego boost — at least Wang can now say with utter certainty that tubes pointing in every direction in 3D space can’t overlap very much. Many Wonderful Things Reserved at first but easily loosened up, Wang wears tortoiseshell panto glasses and rings on both index fingers, which would occasionally dart into the frame of video calls — silver on the left and gold on the right. From the West Coast, where she was spending a few months visiting collaborators and friends, she explained that her life started out a lot more carefree. In Guilin in the 1990s, she would come home from school and read (Greek myths, Harry Potter, The Lord of the Rings), or watch television, or play table tennis or badminton. Her parents didn’t pressure her academically, despite both being schoolteachers. The three of them enjoyed evening walks around Guilin, often called China’s most beautiful city, situated amid steep emerald hills with a river running through it. During Wang’s childhood in Guilin, China, math was just one pastime among many, but she clearly showed an early aptitude for it. Julien Pebrel/M.Y.O.P. Math began as one hobby among all the others. Whenever she got a new textbook, she’d complete all the exercises before the semester started. She’d get more math books from the bookstore and solve all their problems as well. She remembers one brainteaser at the end of a chapter that asked: How should you plant seven trees to get the greatest number of rows of three trees? Like the Kakeya-type problems she would study later, the puzzle is about “incidence geometry,” or how objects overlap — in this case, lines (rows of trees) and points (trees). Wang quickly figured out that you should plant the trees in the shape of an equilateral triangle, with a tree at each corner, a tree at the midpoint of each side, and the seventh tree in the center. This forms six rows of trees: three along the sides and three through the middle. She got the answer faster than her father, a math teacher. She was 6. Wang came to appreciate math for its permanence. History is forever being revised; learning English was frustrating because it seemed to have as many exceptions as rules. Only theorems seemed reliable. “No one can come and say, ‘Oh, actually, this is not true,’” she said. Both parents wanted her to live as normal a life as possible, Wang recalled. She just wanted to learn as much as possible, so she skipped a couple of grades. Toward the end of middle school, her grades started to matter for getting into a good high school in Guilin. Wang set her sights on studying math at Peking University in Beijing, one of the most prestigious universities in China. According to her, Peking reserved a single spot in its math program for a student from her province in 2007, with admission based on a standardized test. She did not receive the highest score. But she did well enough to attend the university as an earth sciences major and hoped to transfer to math once there. Her geophysics professor encouraged her, affirming the importance of math to science, for instance in the way seismic waves are used to map Earth’s interior (math that, in fact, relates to the Kakeya problem, though she didn’t know it at the time). She worked hard and was eventually allowed to switch majors. She recalled an offhand remark by her father that analysis, the type of math concerned with evolving quantities, limits, measures, and approximations, is much easier than algebra, with its symbolic equations and exact solutions. Wang rebelled by focusing on algebra. A detour into architecture while studying in France was short-lived. The tangible goals of math drew Wang back to analysis. Julien Pebrel/M.Y.O.P. She didn’t have top grades and doubted she would get into graduate school. Then representatives from the École Polytechnique near Paris, one of France’s prestigious, highly selective grandes écoles, held exams in Beijing for its postbaccalaureate program. In 2011 she moved to France. All her courses were taught in French, which she didn’t speak. Fortunately, she already knew much of the math in her first-semester classes. She shared meals with her French-speaking classmates, quietly listening, politely asking for clarification, gradually understanding more. She took classes in analysis and found that it came more naturally to her than algebra. She was faring well in her classes, but she didn’t think she was good enough to do mathematical research. For a semester, she switched to architecture and interned at a Paris firm. “I didn’t have much stress,” she said. “But I didn’t know the goal.” So she recommitted to math. “I decided not to worry about whether I would be good or not and just work on understanding better,” she said. Strange Sets In 2013, during a research internship at the Massachusetts Institute of Technology, Wang attended a seminar by an analyst named Larry Guth. Guth discussed his recent proof, with the mathematician Nets Katz of Rice University, of the Erdős distinct distances problem, which asks: For any finite set of points on a plane, how many distances are there between pairs of points? Guth explained the problem and his solution so clearly that Wang felt she could grasp part of the proof well, and this motivated her. She learned that it was closely related to many other problems of a similar character, all with incidence geometry at their heart. She was admitted to the doctoral program at MIT the next year and chose Guth as her adviser. The “Kakeya-type problems” Wang focuses on are connected to harmonic analysis, geometric measure theory, and partial differential equations, as well as number theory, combinatorics, and more. Julien Pebrel/M.Y.O.P.