On Whose Shoulders Does Wang Hong Stand? Mapping Her Mathematical Lineage

Introduction

In 2017 an article highlighted the only female Fields Medalist, Maryam Mirzakhani, who died at 40, and noted Maryna Viazovska’s 2022 award. The piece then celebrated the 2026 Fields Medal awarded to Chinese mathematician Wang Hong, expressing hope for peace amid ongoing wars in Iran and Ukraine.

Academic Paths of Recent Fields Medalists

Mirzakhani: Sharif University of Technology → Harvard University (PhD, advisor Curtis McMullen) → Stanford University.

Viazovska: Kyiv University → University of Kaiserslautern and University of Bonn (Germany) → École Polytechnique Fédérale de Lausanne (EPFL).

Wang Hong: Peking University → École Polytechnique & Paris‑Saclay → MIT (PhD, advisor Larry Guth) → Institute for Advanced Study (postdoc) → UCLA → NYU/IHES.

Resolving a Century‑Old Problem

The article asserts that Wang Hong solved a problem that has challenged mathematicians for a hundred years. Many masters, especially Terence Tao, made partial progress.

1. Tao’s Contribution

Tao’s 2014 blog post suggested a promising direction. Earlier, Katz–Łaba–Tao (2000) identified three structural properties required for a three‑dimensional Kakeya counterexample: planiness, graininess, and stickiness. Bennett–Carbery–Tao (2006) later proved the planiness property using the multilinear Kakeya inequality, reducing the open conditions to two.

2. Guth’s Contribution

Larry Guth (2014) applied the polynomial method to establish the graininess property, leaving stickiness as the remaining obstacle. This exact obstacle is the focus of Wang Hong and Joshua Zahl’s 2022 paper, which directly addresses the “sticky Kakeya” conjecture.

3. Wang Hong’s Synthesis

Wang Hong combined insights from multiple mathematical lineages, requiring deep expertise. Influential figures cited include:

Elias Stein – a founder of harmonic analysis and Tao’s PhD advisor, who cultivated Tao’s broad perspective on function decomposition.

Donald Sarason – an operator‑theory specialist whose student Wolff later contributed to Kakeya results.

Tomasz Mrowka – a geometric‑topology expert whose mentor Larry Guth transferred polynomial‑method intuition from topology to combinatorial geometry.

Over six years, Wang Hong focused on selected collaborators, achieving a series of breakthroughs:

2022: Sticky Kakeya theorem with Joshua Zahl.

2023: Furstenberg set conjecture with Kevin Ren.

2024: Assouad dimension work with Zahl.

2025: Released a 127‑page proof of the three‑dimensional Kakeya problem; received the Salem Prize, Ostrowski Prize, ICCM Gold Medal, and later the Clay Research Award, New Horizons in Mathematics Award, and the Fields Medal.

In June 2025, she joined the Chen‑Sheng‑Shen Mathematics Institute at Nankai University as a full‑time chaired professor.

Lineage Intersection

Wang Hong’s advisor, Larry Guth, recruited Joshua Zahl—one of Tao’s former students—creating a direct link between the Tao and Guth lineages. This intersection places Wang at the crossroads of two major mathematical traditions, which themselves trace back to Mrowka’s geometric intuition and Stein’s harmonic‑analysis foundation, and further to the century‑long work of Besicovitch, Wolff, and Bourgain.

Conclusion

The article concludes that Wang Hong’s ability to navigate historical mathematical figures and her sustained effort allowed her to both honor and extend a century of research, ultimately securing her place among the giants of mathematics.