Mathematics

In Topology, When Are Two Shapes the Same?

Quanta Magazine: Sorting a collection of shapes is child’s play. Circles here, squares there, triangles in their own pile. But if you take the task seriously, there’s a lot more to it. In fact, one of the largest subdisciplines in mathematics…

The Simple Math Behind the Mighty Roots of Unity

Quanta Magazine: If you’ve ever taken an algebra or physics class, then you’ve met a parabola, the simple curve that can model how a ball flies through the air. The most important part of a parabola is the vertex — its…

The Godmother of the Digital Image

New York Times: In the summer of 2010, while preparing for a long research trip to Madagascar, the mathematician Ingrid Daubechies bought a 50-inch flat-screen TV for her husband, so he could invite friends over to watch Premier League soccer games. After setting it up, the couple turned on a match,…

A Mathematician’s Guided Tour Through High Dimensions

Quanta Magazine: The notion of dimension at first seems intuitive. Glancing out the window we might see a crow sitting atop a cramped flagpole experiencing zero dimensions, a robin on a telephone wire constrained to one, a pigeon on the ground…