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‘Outsiders’ Crack 50-Year-Old Math Problem

Three computer scientists have solved a problem central to a dozen far-flung mathematical fields.

complex systems

Nature’s Critical Warning System

Scientists are homing in on a warning signal that arises in complex systems like ecological food webs, the brain and the Earth’s climate. Could it help prevent future catastrophes?


Theorists Draw Closer to Perfect Coloring

A theorem for coloring a large class of “perfect” mathematical networks could ease the way for a long-sought general coloring proof.


Networks Untangle Malaria’s Deadly Shuffle

By examining regions shared between some of nature’s most variable genes, malaria researchers are piecing together an understanding of a deadly parasite.


A Twisted Path to Equation-Free Prediction

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

number theory

A Magical Answer to an 80-Year-Old Puzzle

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

Computer Science

A New Map Traces the Limits of Computation

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


A Tricky Path to Quantum-Safe Encryption

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

Computer Science

A New Design for Cryptography’s Black Box

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.