2025's Biggest Breakthroughs in Mathematics
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2025 marked a historic year in mathematics. Researchers solved a major case of Hilbert’s ambitious sixth problem, proved a sweeping new theorem about hyperbolic surfaces, and settled the longstanding three-dimensional Kakeya conjecture. Watch this year's Biggest Breakthroughs in Physics: https://youtu.be/CPoQkE9KaAY 00:00 - Hilbert's Sixth Problem Solved In a landmark achievement, mathematicians have put the laws of fluid dynamics on firmer mathematical footing. By proving how individual molecules create the complex motion of fluids, they've helped advance David Hilbert’s 125-year-old mathematical program. Read more at Quanta Magazine: https://www.quantamagazine.org/epic-effort-to-ground-physics-in-math-opens-up-the-secrets-of-time-20250611/ Associated paper: https://arxiv.org/abs/2503.01800 06:26 - Hyperbolic Geometry A powerful new proof extends the late Maryam Mirzakhani’s work on hyperbolic surfaces, showing that most of them have an important geometric property. The result great
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