Fields Medal Winner Hong Wang Once Quit Math for Architecture

She graduated in 2011 and moved to France through a postbaccalaureate program at École Polytechnique. Her courses went well. She did not believe she was capable of original research. So she left. She switched to architecture and took an internship at a Paris firm. The pressure of mathematics lifted, and her sense of purpose went with it. She returned within the semester, having decided to stop asking whether she would be good enough.

A research internship at MIT in 2013 put her in a seminar given by the analyst Larry Guth. His explanation of his own recent proof she found clear enough to follow in part. She earned a master's degree at Université Paris-Sud in 2014, entered MIT's doctoral program the same year with Guth as her adviser and finished in 2019. She then held a postdoctoral position at the Institute for Advanced Study, joined the UCLA faculty in 2021 and moved to NYU in 2023.

The problem she is best known for dates to 1917, when the Japanese mathematician Soichi Kakeya asked how little area a needle needs in order to turn and point in every direction. Abram Besicovitch showed by 1928 that the area can be made arbitrarily close to zero. The modern conjecture concerns dimension rather than area. Roy Davies proved the two-dimensional case in 1971. The three-dimensional version resisted every serious attempt for the next half century, defeating Jean Bourgain and Guth among others.

Wang and Joshua Zahl, then at the University of British Columbia, posted a 127-page proof of that case in February 2025. A Kakeya set in three-dimensional space can occupy zero volume, they showed, and still have dimension exactly three. "If you change it to three-dimensional complex space, the statement we proved is false," Wang told the Centre de Recerca Matemàtica. Most familiar tools cannot distinguish real numbers from complex ones, she said. The proof drew on Bourgain's discretized sum-product theorem, which rules out fractal sets of real numbers approximately closed under both addition and multiplication.

Wang had read a 2014 blog post by Tao setting out a strategy he and Nets Katz devised but never pursued. She contacted Zahl to attempt it, Quanta reported. The work took four years. Katz has called the solution a once-in-a-century achievement in which Wang played the central role. Guth, her former adviser, has since posted two expository papers on the arXiv preprint server walking other mathematicians through the argument.

"The Kakeya conjecture was the first major obstacle to solving many other problems," Tao wrote in an IHES newsletter. Its resolution opens the restriction, Bochner-Riesz and arithmetic Kakeya conjectures, he said. NYU mathematician Guido De Philippis said the result opens developments in harmonic analysis, number theory, computer science and cryptography. The South China Morning Post has reported possible implications for imaging, data processing and wireless communication.

The proof brought the Salem Prize, the Ostrowski Prize and the International Congress of Chinese Mathematicians Gold Medal in 2025. The Clay Mathematics Institute named Wang among four recipients of a Clay Research Award on April 14 this year. The Breakthrough Prize Foundation announced her $100,000 New Horizons in Mathematics Prize four days later. She also won the Maryam Mirzakhani New Frontiers Prize in 2022, named for the first woman to win the medal she has now been given.

The restriction and local smoothing conjectures remain open in three dimensions, as does Kakeya in four dimensions and above.