Three years ago, a solitary mathematician released an impenetrable proof of the famous *abc* conjecture. At a recent conference dedicated to the work, optimism mixed with bafflement.

A new breakthrough that bridges number theory and geometry is just the latest triumph for a close-knit group of mathematicians.

The polymath Christoph Adami is investigating life’s origins by reimagining life as self-perpetuating information strings.

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.

Next