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