2025's Biggest Breakthroughs in Mathematics

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 greatly advances our understanding of these exotic shapes. Watch our full Kakeya Conjecture explainer: https://www.youtube.com/watch?v=5J3tYU_-IZI
Read more at Quanta Magazine: https://www.quantamagazine.org/years-after-the-early-death-of-a-math-genius-her-ideas-gain-new-life-20250303/
Associated paper: https://arxiv.org/abs/2502.12268

12:27 - 3D Kakeya Conjecture
Two mathematicians have resolved a deceptively simple problem that had stymied researchers for decades, opening up new avenues in analysis and geometric measure theory.
Read more at Quanta Magazine: https://www.quantamagazine.org/once-in-a-century-proof-settles-maths-kakeya-conjecture-20250314/
Associated paper: https://arxiv.org/abs/2502.17655

Видео 2025's Biggest Breakthroughs in Mathematics канала Quanta Magazine