The 30th International Congress of Mathematicians (ICM) was held from July 23 to July 30, 2026, in Philadelphia, United States. Joshua Zahl, Chair Professor at the Chern Institute of Mathematics, Nankai University, was invited to attend the congress and delivered a 45-minute invited lecture on the afternoon of July 28.
Joshua Zahl's lecture was entitled "The Kakeya Set Conjecture in R³", centering on the three-dimensional Kakeya set conjecture. A Kakeya set is a compact subset of Euclidean space that contains a unit line segment pointing in every direction. The Kakeya set conjecture says that every Kakeya set in n dimensional Euclidean space has Hausdorff and Minkowski dimension n. In his lecture, Professor Zahl systematically traced the conjecture's research history and highlighted the complete proof of the three-dimensional Kakeya set conjecture. This groundbreaking achievement was obtained jointly by Professor Zahl and the Chinese mathematician Hong Wang, who is this year's Fields Medalist.
Delivering an invited lecture at the ICM represents an exceptionally high academic honor, signifying that a scholar's outstanding research contributions have earned high recognition from the international mathematical community. Following Academician Yiming Long, Academician Weiping Zhang, and Professor Jiangong You, Joshua Zahl has become another NKU scholar to deliver an invited lecture at the ICM.
Organized by the International Mathematical Union (IMU), the ICM is the world's largest and most influential academic event in mathematics. The inaugural congress was held in Zurich, Switzerland, in 1897, and it is convened every four years. Centered on academic exchanges, the ICM also presents a series of prizes: the Fields Medal (first awarded in 1936), the Rolf Nevanlinna Prize (first awarded in 1982, now renamed the IMU Abacus Medal), the Gauss Prize (first awarded in 2006), and the Chern Medal (first awarded in 2010). Approximately 200 mathematicians were invited to deliver lectures at this year's congress to share key findings and cutting-edge advances across diverse research fields. Their presentations represent the highest level of contemporary international mathematical research.
Born in 1986, Joshua Zahl earned his bachelor's degree from the California Institute of Technology and his Ph.D. from the University of California, Los Angeles. He previously worked at the Massachusetts Institute of Technology and the University of British Columbia. In June 2025, he joined Nankai University as a Chair Professor at the Chern Institute of Mathematics. His research centers on classical harmonic analysis and discrete geometry, with particular interests in the Kakeya conjecture, sum-product problems, and the Erdős distance problem. His highly original contributions have been published in top-tier journals such as Inventiones Mathematicae and the Journal of the American Mathematical Society, earning him extensive recognition from the international mathematical community.
In February 2025, Joshua Zahl and Hong Wang jointly completed a 127-page proof that fully resolved the Kakeya conjecture in three-dimensions. In April 2026, Joshua Zahl received the Clay Research Award. It is the first time the award has been given to a mathematician working full time in China.
At the opening ceremony of this year's ICM, Hong Wang was awarded the 2026 Fields Medal for her outstanding mathematical achievements. Joshua Zahl was present at the congress to witness this historic moment. The award citation specifically mentioned the three-dimensional Kakeya conjecture, a problem that had challenged mathematicians for more than half a century. As featured in the award-winner video screened at the ceremony, this conjecture was fully solved by Hong Wang and Joshua Zahl using a refined multiscale inductive method.
The Chern Institute of Mathematics was founded in 1985 by Professor Shiing-Shen Chern, known as the "father of global differential geometry", at his alma mater, Nankai University. His vision was to foster a congenial environment for mathematical researchers and help early-career scholars develop an appreciation of what constitutes "good mathematics". In 1986, Nobel laureate Chen-Ning Yang established the Theoretical Physics Division at the CIM, laying a solid foundation for the institute's international academic development. Since its foundation, the institute has adhered steadfastly to Professor Chern's guiding principle: Based at Nankai, Serving the Country, and Embracing the World. Dedicated to cultivating home-grown mathematical talents, the institute regularly hosts lectures by world-leading mathematicians and organizes a series of international academic conferences. It has built an outstanding reputation for mathematical research at Nankai University, both nationally and internationally.
In recent years, NKU has established positions such as Chair Professor to attract a number of top-notch scholars from China and abroad. Internationally renowned scholars, including Shaoming Guo, Xiaonan Ma, and Joshua Zahl, have successively joined the Chern Institute of Mathematics as full-time members, fueling the thriving development of the discipline.
Source: NKU News
Translated by CIM
