Meet Hong Wang, one of the recipients of the 2026 Fields Medals.
In 1917, Japanese mathematician Sōichi Kakeya asked how little space is needed to turn a needle through every possible direction. More than a century later, that almost childlike puzzle sits at the heart of the work that helped earn Hong Wang a Fields Medal.
In 2025, Wang and Joshua Zahl proved the three-dimensional Kakeya conjecture. A set containing a unit-length line segment pointing in every direction can have zero volume, yet it cannot have a dimension below three. Their 127-page proof thickens the lines into narrow tubes, studies how those tubes can overlap across scales, and repeatedly sharpens a lower bound until it reaches three.
In July 2026, Wang became one of four Fields Medal recipients and only the third woman to receive the award. Read the full story of the proof, and why a set with no volume can still be three-dimensional: Can a Shape with No Volume Still Be Fully Three-Dimensional? The Math Behind a Fields Medal Breakthrough
Caption: Hong Wang. Image credits: HLFF / Badge.