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mathematics

Two red loops connected by a ghostly tube.
topology

How Complex Is a Knot? New Proof Reveals Ranking System That Works

By Leila Sloman
May 18, 2022
Read Later

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

A red-headed man in a purple suit runs alongside a white rabbit against a bright teal background. Large white numbers are falling out of his top hat.
Insights puzzle

Think of a Number. How Do Math Magicians Know What It Is?

By Pradeep Mutalik
May 4, 2022
Read Later

Mathematical magic can seem like mind reading. Your job is to reveal the secret behind these four tricks.

A ring of bubbles in blue water.
fluid dynamics

Mathematicians Coax Fluid Equations Into Nonphysical Solutions

By Leila Sloman
May 2, 2022
Read Later

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

Three circles that have dots connected by lines, as in a graph.
graph theory

Elegant Six-Page Proof Reveals the Emergence of Random Structure

By Jordana Cepelewicz
April 25, 2022
Read Later

Two young mathematicians have astonished their colleagues with a full proof of the Kahn-Kalai conjecture — a sweeping statement about how structure emerges in random sets and graphs.

A mathematical graph with plant roots.
number theory

New Proof Illuminates the Hidden Structure of Common Equations

By Leila Sloman
April 21, 2022
Read Later

Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.

Simulated water particles swirl in an upward vortex.
mathematical physics

Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations

By Jordana Cepelewicz
April 12, 2022
Read Later

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near.

Insights puzzle

The Secrets of Zugzwang in Chess, Math and Pizzas

By Pradeep Mutalik
April 8, 2022
Read Later

Learn the magic and math of how to win games when your opponent goes first.

Illustration of a figure standing between broken orange walls and a blue unbreakable wall with a broken sledgehammer beside it
computational complexity

Researchers Identify ‘Master Problem’ Underlying All Cryptography

By Erica Klarreich
April 6, 2022
Read Later

The existence of secure cryptography depends on one of the oldest questions in computational complexity.

An illustration of a polyhedral shape being folded flat.
geometry

Father-Son Team Solves Geometry Problem With Infinite Folds

By Rachel Crowell
April 4, 2022
Read Later

The result could help researchers answer a larger question about flattening objects from the fourth dimension to the third dimension.


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