A type of chaos found in everything from prime numbers to turbulence can unify a pair of unrelated ideas, revealing a ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

The original version of this story appeared in Quanta Magazine. Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a ...

Quantum entanglement has a central role in many areas of physics. To grasp the essence of this phenomenon, it is fundamental to understand how different manifestations of entanglement relate to each ...

It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown. Mountain climbing is a beloved metaphor for mathematical research.

The starting point for rigorous reasoning in mathematics is a system of axioms. An axiom is a statement that is assumed, without demonstration, to be true. It is usually self-evident, for example, ...

For close to 40 years, a simple little hypothesis has been quietly sitting in a corner of graph theory, minding its own business. Known as the “bunkbed conjecture”, it always seemed kind of ...