Mathematics

Does objective, perfect randomness exist, or is randomness merely a product of our ignorance?

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.

Answering these simple questions can give you an intuitive feel for the geometric properties behind the emergence of superconductivity in rotated graphene sheets.

The “sensitivity” conjecture stumped many top computer scientists, yet the new proof is so simple that one researcher summed it up in a single tweet.

Researchers are getting close to building a quantum computer that can perform tasks a classical computer can’t. Here’s what the milestone will mean.

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.

What do moiré patterns seen in optics, art, photography and color printing have to do with superconducting layers of graphene?