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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.
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David Deamer: How We’re Studying the Origins of Life
David Deamer explains how his laboratory mimics the extreme conditions found on volcanoes in the early Earth.
Michael Atiyah’s Imaginative State of Mind
Michael Atiyah discusses beauty in mathematics.
Are We Alone in the Universe?
David Kaplan explores the best ways to search for alien life on distant planets.
Leslie Valiant: Searching for the Algorithms Underlying Life
Leslie Valiant explains the term “ecorithm.”
Richard Dawid: Why Trust a Theory?
Richard Dawid discusses the fine line between science and speculation.
Christoph Adami: The Information Theory of Life
Christoph Adami explains how information theory can explain the persistence of life.
Joan Strassmann: The Woman Who Stared at Wasps
Joan Strassmann explains the benefits of studying social amoebas.
Gabriela González: Searching the Sky for the Wobbles of Gravity
Gabriela González explains how to measure black-hole collisions using gravitational waves.
What Is a Species?
David Kaplan explains why a simple definition of “species” is hard to come by.