Continuum hypothesis

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

Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core principles didn’t come easily.

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.

Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.

To determine the nature of infinity, mathematicians face a choice between two new logical axioms. What they decide could help shape the future of mathematical truth.