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mathematics

Photo of smoke
Abstractions blog

What Makes the Hardest Equations in Physics So Difficult?

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge.

520px photo of Richard Schwartz
Q&A

In Praise of Simple Problems

The mathematician Richard Schwartz finds the hidden depth lurking in simple mathematical puzzles.

Illustration: man using rulers stacked on a compass as a telescope
insights puzzle

How Triangulation Leads to Knowledge

What does measuring distances in sailing and astrophysics have to with motion sickness?

Simulation of Kelvin-Helmholz Instability
fluid dynamics

Mathematicians Find Wrinkle in Famed Fluid Equations

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense.

Photo of Corina Tarnita 520px
Q&A

A Mathematician Who Decodes the Patterns Stamped Out by Life

Corina Tarnita deciphers bizarre patterns in the soil created by competing life-forms.

Illustration of pentagon tiling
Quantized Academy

The (Math) Problem With Pentagons

Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?

Jennifer Balakrishnan and Sachi Hashimoto, plotted using SageMath
Abstractions blog

Mathematicians Crack the Cursed Curve

A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics.

Minhyong Kim in front of a whiteboard
number theory

Secret Link Uncovered Between Pure Math and Physics

An eminent mathematician reveals that his advances in the study of millennia-old mathematical questions owe to concepts derived from physics.

Edward Witten in his office at the Institute for Advanced Study in Princeton, New Jersey.
Q&A

A Physicist’s Physicist Ponders the Nature of Reality

Edward Witten reflects on the meaning of dualities in physics and math, emergent space-time, and the pursuit of a complete description of nature.