Breakthroughs in physics sometimes require an assist from the field of mathematics—and vice versa. In 1912, Albert Einstein, then a 33-year-old theoretical physicist at the Eidgenössische Technische ...

We are fond of saying things are symmetric, but what does that really mean? Intuitively we have a sense of symmetry as a kind of mirroring. Suppose we draw a vertical line through the middle of a ...

Jason Lotay explains how mathematicians studying special geometries are collaborating with physicists to explore M-theory, an 11-dimensional description of the world that unifies the various string ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...