Computer-assisted proofs

Two mathematicians have renewed a debate about the fundamental nature of some of math’s most important equations.

It was intuitive, even obvious. It was also wrong.

After decades of uncertainty, a motley team of programmers has proved precisely how complicated simple computer programs can get.

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer.

The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.