Videos
The Biggest Breakthroughs in Mathematics: 2025
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.
Read related article
Explore All Videos
Lisa Manning on the Dynamics of Glasses and Embryos
Lisa Manning, a physicist at Syracuse University, describes how the physics of glassy materials helps to explain how some organs assume their correct shape during embryonic development.
Michela Massimi: Defending the Philosophy of Science
Michela Massimi argues that the philosophy of science doesn’t have to be useful to scientists for it to be useful to humanity.
Donald Richards: A Revealer of Secrets in the Data of Life and the Universe
Donald Richards discusses the statistical rule-of-thumb he wishes everyone knew.
Günter Ziegler Seeks God’s Perfect Math Proofs
Günter Ziegler describes one of the most famous and beautiful proofs in Proofs From THE BOOK, a book he co-authored with Martin Aigner.
Barbara Engelhardt on How to Improve Statistical Analyses of Genomes
Barbara Engelhardt, a computer scientist at Princeton University, explains why traditional machine-learning techniques have often fallen short for genomic analysis, and how researchers are overcoming that challenge.
Daniel Goldman and His Smart Robots
Goldman explains how “smarticles” work together to demonstrate collective behavior.
Gil Kalai: Why Quantum Computers Won’t Work
Kalai argues that limiting the noise in a quantum computer will also limit the computational power of the system.
Erich Jarvis on Theories About the Origin of Vocal Learning
Neuroscientist Erich Jarvis discusses how the brain circuitry for vocal learning in songbirds and humans evolved from systems for controlling body movements and why so few species have this ability.
Ed Boyden on the Promise of Expansion Microscopy
Ed Boyden explains how expansion microscopy could illuminate deep mysteries about how the brain works and improve cancer diagnosis, among other advances.