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2026 Fields medalist Hong Wang proved the three-dimensional version of a century-old problem that’s simple to explain, yet difficult to solve: How much space does it take to turn a needle so it points in every direction? Watch the full video about her work and learn more about this...

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When Hong Wang won the Fields Medal, everyone talked about the honor: her age, her journey, the history she had made. But the most interesting question was barely discussed: What did she actually solve? It begins with a needle. Turn it until it has pointed in every possible direction. How little space can that movement occupy? Almost none, strangely. And yet, that tiny set may still carry the full complexity of three-dimensional space. This is the Kakeya conjecture. It sounds like a puzzle, but it resisted mathematicians for more than a century and sits at the heart of how mathematics understands waves and their concentration—the same world of ideas behind MRI reconstruction, image compression, sound and quantum physics. In 2025, Hong Wang and Joshua Zahl finally solved the three-dimensional case. This video starts with that simple needle and slowly reveals the mathematics behind the medal. We celebrated the person. This is a chance to understand the work.
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When Hong Wang won the Fields Medal, everyone talked about the honor: her age, her journey, the history she had made. But the most interesting question was barely discussed: What did she actually solve? It begins with a needle. Turn it until it has pointed in every possible direction. How little space can that movement occupy? Almost none, strangely. And yet, that tiny set may still carry the full complexity of three-dimensional space. This is the Kakeya conjecture. It sounds like a puzzle, but it resisted mathematicians for more than a century and sits at the heart of how mathematics understands waves and their concentration—the same world of ideas behind MRI reconstruction, image compression, sound and quantum physics. In 2025, Hong Wang and Joshua Zahl finally solved the three-dimensional case. This video starts with that simple needle and slowly reveals the mathematics behind the medal. We celebrated the person. This is a chance to understand the work.

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Mathematician Hong Wang of New York University and Institut des Hautes Études Scientifiques - IHES has won the 2026 Fields Medal. Wang explored harmonic analysis and geometric measure theory, making major advances in Fourier restriction and the Kakeya problem in three dimensions. Watch her full video and see all of the Fields Medal winners: #math #ICM2026 #FieldsMedal
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A mathematician solved a problem that stood open for over 100 years, then explained it in an Italian lecture hall to a few dozen people. This is Hong Wang, professor at NYU's Courant Institute and at IHES in Paris, delivering the Colloquium Patavinum on Kakeya sets in 3 dimensions. The question is deceptively small: take a needle of length 1 and rotate it to point in every possible direction. How little space can the set of positions occupy. The conjecture says the answer must fill full dimension. Wang proved it in 3 dimensions. The Salem Prize followed in 2025, the Sadosky Prize in 2026, and an invitation to speak at the International Congress of Mathematicians. Watch how she frames the general statement about unions of tubes. The needle problem falls out as a corollary of something larger. A researcher I know rewatched the setup twice and said it was the clearest account of the result he had found anywhere. Free on YouTube from an Italian mathematics department. The problem was posed in 1917. She closed it, then took questions.
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