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The Mathematician Who Delights in Building Bridges

November 17, 2021

Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.

A New Theory for Systems That Defy Newton’s Third Law

November 11, 2021

In nonreciprocal systems, where Newton’s third law falls apart, “exceptional points” are helping researchers understand phase transitions and possibly other phenomena.

Mathematicians Find Structure in Biased Polynomials

November 9, 2021

New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.

Surprising Limits Discovered in Quest for Optimal Solutions

November 1, 2021

Algorithms that zero in on solutions to optimization problems are the beating heart of machine reasoning. New results reveal surprising limits.

Where Transcendental Numbers Hide in Everyday Math

October 27, 2021

The transcendental number π is as familiar as it is ubiquitous, but how does Euler’s number e transcend the ordinary?

How Tadayuki Watanabe Disproved a Major Conjecture About Spheres

October 26, 2021

Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.

How Wavelets Allow Researchers to Transform, and Understand, Data

October 13, 2021

Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals.

Mathematicians Prove Melting Ice Stays Smooth

October 6, 2021

After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.

In Topology, When Are Two Shapes the Same?

September 28, 2021

As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.

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