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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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Jay Pasachoff: Eclipse Hunter Reveals the Science That Can Only Be Done in the Dark
Jay Pasachoff explains what scientists can learn during a total solar eclipse.
Andrea Ghez: Black-Hole Hunter Takes Aim at Einstein
In this 2017 interview, the UCLA astrophysicist Andrea Ghez explains how tracking the movement of stars revealed the existence of a supermassive black hole at the center of the Milky Way galaxy.
Jessica Flack: How Nature Solves Problems Through Computation
Jessica Flack describes the special challenges of applying collective computation to the understanding of complex biological systems.
Purvesh Khatri: More Data — the Dirtier the Better
Purvesh Khatri learned that by working with ‘messy’ clinical data sets, he could find genes that the human body expresses in response to diverse forms of a disease.
Journey to the Birth of the Solar System
Join David Kaplan on a virtual-reality tour showing how the sun, the Earth and the other planets came to be.
Tim Maudlin: A Defense of the Reality of Time
Tim Maudlin explains how math has led physicists to believe some very strange things about the nature of time.
John Novembre: A Map of Human History, Hidden in DNA
John Novembre explains how he uses genomic data to map human history.
Sharon Glotzer: ‘Digital Alchemist’ Seeks Rules of Emergence
Sharon Glotzer explains how emergence, entropy and order can all fit together.
Sylvia Serfaty: In Mathematics, ‘You Cannot Be Lied To’
Sylvia Serfaty explains why you don’t have to be a genius to become a mathematician.