Mathematics

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?

Pure, verifiable randomness is hard to come by. Two proposals show how to make quantum computers into randomness factories.

Neven’s law states that quantum computers are improving at a “doubly exponential” rate. If it holds, quantum supremacy is around the corner.

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.

The universe of problems that a computer can check has grown. The researchers’ secret ingredient? Quantum entanglement.