During today's #ICM2026 opening ceremonies, the IMU announced the 2026 Fields Medals recipients:
@UChicago's Yu Deng, @stonybrooku's John Pardon, @UofT's Jacob Tsimerman, and Hong Wang of @nyuniversity and @Institut_IHES.
Read more: https://t.co/oJARAI8I8j
Hong Wang (MIT PhD 2019, now Associate Professor at NYU Courant & Permanent Professor at IHES) together with Joshua Zahl has achieved a major breakthrough in geometric measure theory.
In February 2025, they posted a 127-page preprint proving the long-standing three-dimensional Kakeya set conjecture.
A Kakeya set in ℝ³ is a compact set that contains a unit line segment in every possible direction. For over a century, mathematicians wondered how “small” such a set could be. Wang and Zahl proved that these sets must have full Minkowski and Hausdorff dimension 3; they cannot hide in lower-dimensional space, even though they can have zero volume.
This result settles a fundamental question with deep connections to Fourier analysis, the restriction problem, PDEs, and incidence geometry. Their work builds on years of incremental progress (including their own earlier papers from 2022 onward) and introduces powerful new volume estimates for unions of tubes and convex sets.
@alexolegimas way more android flagships pricier than iPhones… and also plenty of budget android phones capable of running IOS smoothly. Ever heard of hackintosh?
@krisgulati 😈 lack of info is to blame. Let’s force everyone to use AI to help disclosure every meeting between coauthors, record who is responsible for every idea, every word and every line of code. We will find an equilibrium
@alz_zyd_@cherylwoooo {people want to show off the upgrades brought by AI} & {many economists only want understand abstractions at the level of py and R}. Nonbinding advice: stick w stata, or go for cpp/rust/julia😈
@alz_zyd_ This appears to be empirically true. In 2021, when China implemented a ban on K12 after-school tutoring, it was followed by a surge of *home* tutors
An icon’s final flight! 🐳 After 25 years of loyal service, our #BelugaST №5 flew its last mission to Broughton, UK, where it will rest, with plans to transform it into an education facility to inspire future generations.
The mission continues with the 6 #BelugaXL fleet, keeping our sites around Europe connected!