Mathematician recognized with the highest prize in mathematics for resolving a long-standing problem in harmonic analysis and geometric measure theory—the three-dimensional Kakeya set conjecture

NEW YORK, July 23, 2026 /PRNewswire/ — New York University Professor Hong Wang has been awarded a Fields Medal, the highest honor in the field of mathematics, the International Mathematical Union announced in Philadelphia today.

Wang, Silver Professor of Mathematics at NYU’s Courant Institute School of Mathematics, Computing, and Data Science, was recognized for resolving a decades-old problem in harmonic analysis and geometric measure theory, the Kakeya conjecture in three dimensions, which tells how small a set can be while still containing a unit length needle in every direction.

“Moments like this never belong to just one person. They are the culmination of years of chance encounters and unexpected questions that steer you in the right direction. I have been so lucky to work alongside brilliant colleagues at every stage of my career, and this honor is theirs as much as it is mine. I am so grateful to the IMU for this award and so excited for what is to come,” said Hong Wang, Silver Professor of Mathematics at NYU.

“NYU is so proud of Professor Wang’s achievement. The world is recognizing what her NYU colleagues and students have known for years: she is one of the most remarkable minds in mathematics today. Resolving this century-old conjecture has opened new avenues of thought and inquiry that will be felt for decades to come,” said NYU President Linda G. Mills.

Wang is the first member of the NYU faculty to win a Fields Medal, which is awarded every four years to mathematicians under the age of 40. Wang is only the third woman to have won the prize. The 2026 recipients also included Yu Deng, a former Courant instructor now at the University of Chicago. Wang is also a professor at France’s Institut des Hautes Études Scientifiques (IHES).

“When Hong Wang joined IHES as a permanent professor, we knew we were welcoming an exceptional mathematician. What the international mathematical community has confirmed since then has exceeded all our expectations. The Kakeya conjecture is the kind of result that reshapes the landscape of an entire field of research. The awards she has received, from the Salem Prize to the Fields Medal, along with the Clay Research Award, simply reflect what her peers unanimously feel: Hong Wang is one of the most important mathematicians of her generation. We are proud and delighted that Hong Wang has chosen to pursue her work in France and at IHES,” said Emmanuel Ullmo, Director of IHES.

Wang, who was previously an assistant professor at UCLA, holds a bachelor’s degree from Peking University, master’s degrees from Université Paris Sud and École Polytechnique, and a doctorate from MIT. She joined the NYU faculty in 2023.

Earlier this year, Wang received the 2026 New Horizons in Mathematics Prize from the Breakthrough Prize Foundation. The foundation recognized her for “work in harmonic analysis, partial differential equations, and geometric measure theory, including the local smoothing conjecture, Furstenberg set conjecture, and the Kakeya conjecture.”

Her recognition coincides with the acceleration of NYU’s science and technology initiative, which includes the launch of cutting-edge computational assets, such as the Torch supercomputer, the recruiting and hiring of over 100 world-class faculty by 2031, and the establishment of the Courant Institute School of Mathematics, Computing, and Data Science.

Resolving the Three-Dimensional Kakeya Set Conjecture

The Kakeya conjecture was inspired by a problem asked in 1917 by Japanese mathematician Sōichi Kakeya: What is the region of smallest possible area in which it is possible to rotate a needle 180 degrees in a two-dimensional plane? Such regions are called Kakeya needle sets.

In a 2025 article, Wang, 35, and Joshua Zahl, a professor at the Chern Institute of Mathematics at Nankai University, showed that Kakeya sets, which are closely related to Kakeya needle sets, cannot be “too small”—namely, while it is possible for these sets to have zero three-dimensional volume, they must nonetheless be three-dimensional. Proving the Kakeya conjecture requires a fine understanding of the structure of the interaction of tubes in Euclidean—three-dimensional—space.

“There has been some spectacular progress in geometric measure theory: Hong Wang and Joshua Zahl have just released a preprint that resolves the three-dimensional case of the infamous Kakeya set conjecture!” wrote Terence Tao, a UCLA mathematics professor and a 2006 Fields Medal winner, at the time.

“This result was a major breakthrough in geometric measure theory and opened up a series of developments in harmonic analysis, number theory, and applications in computer science and cryptography,” explained former Courant Institute Professor Guido De Philippis last year.

Contact:

James Devitt

212.998.6808/914.522.3774

james.devitt@nyu.edu

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SOURCE New York University