Courtesy of Yuan Li

After a space telescope disintegrated, astrophysicists had little hope of understanding how supermassive black holes agitate giant galaxies. Then they invented a hack.

Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades.

Machine learning and deep neural networks can capture and analyze the “language” of animal behavior in ways that go beyond what’s humanly possible.

New studies help to explain how microbes in the gut can shape a host’s fear responses.

New research makes a molecular connection between the brain and aging — and shows that overactive neurons can shorten life span.

We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”

A surprisingly youthful estimate of the age of the rings has stirred a backlash.

Barbara Liskov pioneered the modern approach to writing code. She warns that the challenges facing computer science today can’t be overcome with good design alone.

Many of us are drawn to beauty in mathematics. But is that the way nature really works?

Neural networks can be as unpredictable as they are powerful. Now mathematicians are beginning to reveal how a neural network’s form will influence its function.

In the late 1940s, Richard Feynman invented a visual tool for simplifying particle calculations that forever changed theoretical physics.

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