Eric Weinstein proposes a Geometric Unity theory. It is presented to argue that the seemingly baroque features of the standard model of particle physics are in fact inexorable and geometrically ...

Arnold’s work was in an area of mathematics that concerns all the different configurations a physical system like bouncing billiard balls or orbiting planets can take. These configurations are encoded ...

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...

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 ...

Within mathematics, there is a vast and ever expanding web of conjectures, theorems and ideas called the Langlands program. That program links seemingly disconnected subfields. It is such a force that ...

One of the first collaborations Xinyi Yuan and Wei Zhang ever undertook was a trip to the Social Security office. It was the fall of 2004 and the two of them were promising young graduate students in ...