Mathematics

Complex natural systems defy analysis using a standard mathematical toolkit, so one ecologist is throwing out the equations.

Using crowd-sourced and traditional mathematics research, Terence Tao has devised a solution to a long-standing problem posed by the legendary Paul Erdős.

A major advance in computational complexity reveals deep connections between the classes of problems that computers can — and can’t — possibly do.

In the drive to safeguard data from future quantum computers, cryptographers have stumbled upon a thin red line between security and efficiency.

A recent cryptographic breakthrough has proven difficult to put into practice. But new advances show how near-perfect computer security might be surprisingly close at hand.

The mathematician John Horton Conway’s myriad accomplishments — including the Game of Life, sprouts and the surreal numbers — are the product of a mind at play.

For more than 50 years, the mathematician Neil Sloane has curated the authoritative collection of interesting and important integer sequences.

A 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer.

Solve this variation of Thomas Kirkman’s famous 1850 puzzle by arranging girls in walking groups. And think fast — the clock is ticking.