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When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.

Computer scientists can prove certain programs to be error-free with the same certainty that mathematicians prove theorems.

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

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

When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the century-old rules underlying all of mathematics.

As the role of computers in pure mathematics grows, researchers debate their reliability.