Stephen Hawking’s 50-year-old theorem on how black holes merge together has been successfully tested thanks to huge advances in gravitational wave astronomy, which helped astronomers catch the waves ...

Daniel Liberto is a journalist with over 10 years of experience working with publications such as the Financial Times, The Independent, and Investors Chronicle. Robert Kelly is managing director of ...

The original version of this story appeared in Quanta Magazine. In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last ...

The Pythagorean theorem, a cornerstone of mathematics for millennia, provides a method for determining unknown sides in right-angled triangles using the formula a² + b² = c². Its applications extend ...

Nernst's theorem—a general experimental observation presented in 1905 that entropy exchanges tend to zero when the temperature tends to zero—has been directly linked to the second principle of ...

In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last Theorem, a central problem in number theory that had remained open ...

A mathematician will turn a groundbreaking 100-page proof into computer code. The proof tool, Lean, lets users turn proofs written in prose into rules and logic for testing. Kevin Buzzard already uses ...

The Pythagorean Theorem is an ancient theory that states that in a right triangle, if the length of the hypotenuse is c, and the lengths of the two sides that sandwich the right angle are a and b, ...