Mathematics

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.

Polynomials aren’t just exercises in abstraction. They’re good at illuminating structure in surprising places.

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

Mathematicians have proved that a random process applied to a random surface will yield consistent patterns.

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.

Amie Wilkinson searches for exotic examples of the mathematical structures that describe change.

Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.

A little high school geometry can help you understand the basic math behind movie recommendation engines.

Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.