Often when describing patterns, they are placed in one of two categories: organic or geometric. Organic designs are ones ...

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 ...

Geometric objects take on different properties depending on the space in which you visualize them. Using techniques from an upstart field called tropical geometry — which analyzes complicated shapes ...

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 ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of the recent work by ...

These are not the kinds of objects that concern Scott Sheffield. Sheffield, a professor of mathematics at the Massachusetts Institute of Technology, studies shapes that are constructed by random ...