Number theory

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.

A group of MIT undergraduates is searching for tetrahedra that tile space, the latest effort in a millennia-long inquiry. They’ve already made a new discovery.

Four mathematicians have cataloged all the tetrahedra with rational angles, resolving a question about basic geometric shapes using techniques from number theory.

A number theorist recalls his first encounter with the Riemann hypothesis and breaks down the math in a new Quanta video.

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.

Despite recent progress on the notorious Collatz conjecture, we still don’t know whether a number can escape its infinite loop.

For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.