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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.

An illustration of a mathematician staring up at an infinite pile of cubes of varying sizes and colors.
Quantized Academy

Why the Sum of Three Cubes Is a Hard Math Problem

November 5, 2019

Looking for answers in infinite space is hard. High school math can help narrow your search.

Animation showing two sets of tangrams cycling between identical squares and different shapes.

Mathematicians Cut Apart Shapes to Find Pieces of Equations

October 31, 2019

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

A fractal pattern.

A Power Law Keeps the Brain’s Perceptions Balanced

October 22, 2019

Researchers have discovered a surprising mathematical relationship in the brain’s representations of sensory information, with possible applications to AI research.