Pencils Down

Donald Richards discusses the statistical rule-of-thumb he wishes everyone knew.

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, 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.

Goldman explains how “smarticles” work together to demonstrate collective behavior.

Kalai argues that limiting the noise in a quantum computer will also limit the computational power of the system.

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 explains how expansion microscopy could illuminate deep mysteries about how the brain works and improve cancer diagnosis, among other advances.

Mathematician Richard Schwartz talks about why he’s attracted to the hidden depths of simple problems.

Corina Tarnita argues that to fully appreciate nature, you must first understand its rules.