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Mathematics

An illustration of a mathematician on a ladder stringing red and blue beads against a tiled red backdrop dotted with blue circles.
combinatorics

Mathematician Hurls Structure and Disorder Into Century-Old Problem

By Erica Klarreich
December 15, 2021
Read Later

A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”

geometry

Mathematicians Transcend Geometric Theory of Motion

By Kelsey Houston-Edwards
December 9, 2021
Read Later

More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective.

Insights puzzle

Why e, the Transcendental Math Constant, Is Just the Best

By Pradeep Mutalik
November 24, 2021
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The solution to our puzzle about Euler’s number explains why e pops up in situations that involve optimality.

information theory

Researchers Defeat Randomness to Create Ideal Code

By Mordechai Rorvig
November 24, 2021
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By carefully constructing a multidimensional and well-connected graph, a team of researchers has finally created a long-sought locally testable code that can immediately betray whether it’s been corrupted.

Quantized Academy

What Hot Dogs Can Teach Us About Number Theory

By Patrick Honner
November 18, 2021
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The Chinese remainder theorem is an ancient and powerful extension of the simple math of least common multiples.

Color photo of Ana Caraiani in a black coat standing on a bridge
Q&A

The Mathematician Who Delights in Building Bridges

By Steve Nadis
November 17, 2021
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Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.

Closeup photo of an automated two-wheeled robot on a wooden table
mathematical physics

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

By Stephen Ornes
November 11, 2021
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In nonreciprocal systems, where Newton’s third law falls apart, “exceptional points” are helping researchers understand phase transitions and possibly other phenomena.

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


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