Proofs

At 25, Kurt Gödel proved there can never be a mathematical “theory of everything.” Columnist Natalie Wolchover explores the implications.

A graduate student recently harnessed the complexity of mathematical proofs to create a powerful new tool in cryptography.

AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning.

The quest to make mathematics rigorous has a long and spotty history — one mathematicians can learn from as they push to formalize everything in the computer program Lean.

Researchers have used metamathematical techniques to show that certain theorems that look superficially distinct are in fact logically equivalent.

Mathematicians have started to prepare for a profound shift in what it means to do math.

When pigeons outnumber pigeonholes, some birds must double up. This obvious statement — and its inverse — have deep connections to many areas of math and computer science.

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

Three researchers have figured out how to craft a proof that spreads out information while keeping it perfectly secret.