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The mathematicians Günter Ziegler and Martin Aigner have spent the past 20 years collecting some of the most beautiful proofs in mathematics.

The computer scientist Barbara Engelhardt develops machine-learning models and methods to scour human genomes for the elusive causes and mechanisms of disease.

The mathematician Gil Kalai believes that quantum computers can’t possibly work, even in principle.

The neuroscientist Erich Jarvis found that songbirds’ vocal skills and humans’ spoken language are both rooted in neural pathways for controlling learned movements.

By developing new tools for visualizing subcellular structure and activity in molecular detail, Ed Boyden advances on his goal of understanding how the brain works.

The mathematician Richard Schwartz finds the hidden depth lurking in simple mathematical puzzles.

Corina Tarnita deciphers bizarre patterns in the soil created by competing life-forms.

Edward Witten reflects on the meaning of dualities in physics and math, emergent space-time, and the pursuit of a complete description of nature.

Federico Ardila opens up about his journey as a mathematician, teacher, Colombian transplant, DJ and creator of mathematical spaces.