Examples are given which show the necessity of various hypotheses in the known finite dimensional complement theorems. In addition, several positive results are presented which improve one direction ...

For four decades, a quiet boundary in pure mathematics kept a powerful theorem locked inside the safe world of finite quantities. Now a new result known as Sebestyen’s theorem has pushed that boundary ...

This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...

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 ...

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 mathematics problem he solved had been lingering since 1637 — and he first read about it when he was just 10 years old. This week, British professor Andrew Wiles, 62, got prestigious recognition ...

Here's what the hairiest problem in math can teach us about wind, antennas and nuclear fusion. When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works.