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

The physical nature of computers might reveal deep truths about their uniquely powerful abstract abilities.

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

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.

Computers can translate French and prove mathematical theorems. But can they make deep conceptual insights into the way the world works?

Researchers are uncovering the hidden laws that reveal how the Internet grows, how viruses spread, and how financial bubbles burst.

The Fields medalist Vladimir Voevodsky has died at 51. This 2015 article describes his computer-aided quest to eliminate human error and rewrite the century-old rules underlying all of mathematics.