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Mathematics

An image with Lego blocks representing polynomials and their factors.
polynomials

Mathematicians Find Structure in Biased Polynomials

By Tamar Lichter Blanks
November 9, 2021
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New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.

A graphic of global air travel.
polynomials

Surprising Limits Discovered in Quest for Optimal Solutions

By Max G. Levy
November 1, 2021
Read Later

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

Insights puzzle

Where Transcendental Numbers Hide in Everyday Math

By Pradeep Mutalik
October 27, 2021
Read Later

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

topology

How Tadayuki Watanabe Disproved a Major Conjecture About Spheres

By Kevin Hartnett
October 26, 2021
Read Later

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.

an animation showing wavelets at different scales travel across a space
applied math

How Wavelets Allow Researchers to Transform, and Understand, Data

By Alexander Hellemans
October 13, 2021
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Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals.

A GIF of ice melting in a glass of water
mathematical physics

Mathematicians Prove Melting Ice Stays Smooth

By Mordechai Rorvig
October 6, 2021
Read Later

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.

Illustration showing yellow and green shapes over a blue background
topology

In Topology, When Are Two Shapes the Same?

By Kevin Hartnett
September 28, 2021
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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.

Quantized Academy

The Simple Math Behind the Mighty Roots of Unity

By Patrick Honner
September 23, 2021
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Solutions to the simplest polynomial equations — called “roots of unity” — have an elegant structure that mathematicians still use to study some of math’s greatest open questions.

combinatorics

Mathematician Answers Chess Problem About Attacking Queens

By Leila Sloman
September 21, 2021
Read Later

The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.


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