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 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, 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 others in 2025; 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.
When she isn't traveling, Wang works with the devotion and discipline of an 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 help relieve the stress and self-doubt that can accompany mathematical research.
Many Wonderful Things
In Guilin in the 1990s, Wang would come home from school and read — Greek myths, Harry Potter, The Lord of the Rings — or play table tennis or badminton. Her parents didn't pressure her academically, despite both being schoolteachers. 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 remembers one brainteaser that asked: How should you plant seven trees to get the greatest number of rows of three trees? Wang quickly worked out the answer. She was 6. "No one can come and say, 'Oh, actually, this is not true,'" she said of math's appeal. That permanence drew her in.
Wang skipped a couple of grades. She set her sights on Peking University's math program, but did not receive the highest entrance exam score. She attended as an earth sciences major and eventually transferred to math. Representatives from France's prestigious École Polytechnique held exams in Beijing; Wang moved to France in 2011. She later entered MIT's doctoral program and chose Larry Guth — whose clear, compelling seminar had first inspired her — as her adviser.
Strange Sets
Her specialty became Kakeya-type problems, a family of questions connecting harmonic analysis, geometric measure theory, and partial differential equations. The central question: How much space must a set of line segments pointing in every direction occupy? Mathematicians long suspected that such a set in 3D space must be fully three-dimensional — but proving it was another matter. The problem also connects to how waves traveling in different directions interact: can they concentrate energy, or must they spread out?
"All of these connections are why this area is considered so central and why Hong is celebrated so much," said Pablo Shmerkin of the University of British Columbia.
A Sticky Situation
Wang decided to tackle the 3D Kakeya conjecture directly. She contacted Joshua Zahl, and they pursued a proof strategy that Terence Tao and Nets Katz had sketched but never completed. Their approach: assume a hypothetical counterexample exists, then show it must have such a rigid structure that it contradicts established theorems — leaving the conjecture as the only possibility. The work took four years and produced 127 pages.
Even as the proof came together, Wang kept her doubts. "This is a difficult problem, and who am I to solve it?" she said. "You have doubt. But also the argument feels natural."
Finding Balance
As the proof was confirmed, it reshaped Wang's corner of mathematics. "It's a bit strange in the community because the holy grail has been achieved in some sense," Shmerkin said. New techniques have opened paths to many further problems.
Wang still worries about falling behind, and believes she must put in more hours than her colleagues. When told everyone considers her extremely talented, she seemed genuinely surprised and pleased.
"I always wish that I could come back to that time when I just feel like I had infinite time to read," she said. "I think that time was really nice."