It has long been a mystery why pure math can reveal so much about the nature of the physical world. Antimatter was discovered in Paul Dirac’s equations before being detected in cosmic rays. Quarks ...

Two weeks ago, a modest-looking paper was uploaded to the arXiv preprint server with the unassuming title "On the invariant subspace problem in Hilbert spaces". The paper is just 13 pages long and its ...

This article is the first part of a series about quantum field theory published by Quanta Magazine. Other stories in the series can be found here. Over the past century, quantum field theory has ...

Mathematics is full of weird number systems that most people have never heard of and would have trouble even conceptualizing. But rational numbers are familiar. They’re the counting numbers and the ...

Physicists searching for a better understanding of quantum gravity stumbled upon something unexpected: the defining signatures of string theory.

Breakthroughs in physics sometimes require an assist from the field of mathematics—and vice versa. In 1912, Albert Einstein, then a 33-year-old theoretical physicist at the Eidgenössische Technische ...