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.

A new technique for finding and characterizing microbes has boosted the number of known bacteria by almost 50 percent, revealing a hidden world all around us.

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.

Mathematicians have solved the century-old triangulation conjecture, a major problem in topology that asks whether all spaces can be subdivided into smaller units.

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