Mathematics
Hope Rekindled for Perplexing Proof
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.
Mathematics
Math Quartet Joins Forces on Unified Theory
A new breakthrough that bridges number theory and geometry is just the latest triumph for a close-knit group of mathematicians.
Q&A
The Information Theory of Life
The polymath Christoph Adami is investigating life’s origins by reimagining life as self-perpetuating information strings.
cryptography
A New Design for Cryptography’s Black Box
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.
Biology
At Tiny Scales, a Giant Burst on Tree of Life
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.
foundations of mathematics
Will Computers Redefine the Roots of Math?
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.
Mathematics
A Proof That Some Spaces Can’t Be Cut
Mathematicians have solved the century-old triangulation conjecture, a major problem in topology that asks whether all spaces can be subdivided into smaller units.