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How Simple Math Can Cover Even the Most Complex Holes

January 8, 2020

No one knows how to find the smallest shape that can cover all other shapes of a certain width. But high school geometry is getting us closer to an answer.

Art for "Quanta’s Year in Math and Computer Science (2019)"
2019 in Review

The Year in Math and Computer Science

December 23, 2019

Mathematicians and computer scientists made big progress in number theory, graph theory, machine learning and quantum computing, even as they reexamined our fundamental understanding of mathematics and neural networks.

Animation of two rings of fluid approaching each other and colliding.
fluid dynamics

Famous Fluid Equations Spring a Leak

December 18, 2019

Researchers have spent centuries looking for a scenario in which the Euler fluid equations fail. Now a mathematician has finally found one.

Animated graphic showing different ways many numbers can arrive at 1 via the Collatz process
number theory

Mathematician Proves Huge Result on ‘Dangerous’ Problem

December 11, 2019

Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades.

insights puzzle

Does Natural Law Need Elegant Mathematics?

December 5, 2019

Many of us are drawn to beauty in mathematics. But is that the way nature really works?

An illustration of a woman sitting in a field embroidering a flower pattern. Around her grow wildflowers that appear to be randomly distributed but whose colors reveal a hidden pattern.
number theory

Mathematicians Catch a Pattern by Figuring Out How to Avoid It

November 25, 2019

We finally know how big a set of numbers can get before it has to contain a pattern known as a “polynomial progression.”

insights puzzle

Solution: ‘Randomness From Determinism’

November 22, 2019

Readers’ modifications of a bean machine showed how deterministic laws are capable of producing random-seeming behavior.

Neutrinos and matrices
mathematical physics

Neutrinos Lead to Unexpected Discovery in Basic Math

November 13, 2019

Three physicists stumbled across an unexpected relationship between some of the most ubiquitous objects in math.

Abstractions blog

Mathematicians Calculate How Randomness Creeps In

November 12, 2019

Mathematicians have figured out exactly how many moves it takes to randomize a 15 puzzle.