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Mathematics

combinatorics

Mystery Math Whiz and Novelist Advance Permutation Problem

November 5, 2018

A new proof from the Australian science fiction writer Greg Egan and a 2011 proof anonymously posted online are now being hailed as significant advances on a puzzle mathematicians have been studying for at least 25 years.

number theory

Without a Proof, Mathematicians Wonder How Much Evidence Is Enough

October 31, 2018

A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof?

Quantized Academy

The (Imaginary) Numbers at the Edge of Reality

October 25, 2018

Odd enough to potentially model the strangeness of the physical world, complex numbers with “imaginary” components are rooted in the familiar.

Art for "A Proof About Where Symmetries Can’t Exist"
geometry

A Proof About Where Symmetries Can’t Exist

October 23, 2018

In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.

Art for "Titans of Mathematics Clash Over Epic Proof of ABC Conjecture"
number theory

Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

September 20, 2018

Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.

Art for "Why Mathematicians Can’t Find the Hay in a Haystack"
Abstractions blog

Why Mathematicians Can’t Find the Hay in a Haystack

September 17, 2018

In math, sometimes the most common things are the hardest to find.

Belt trick illustration
Abstractions blog

The Strange Numbers That Birthed Modern Algebra

September 6, 2018

The 19th-century discovery of numbers called “quaternions” gave mathematicians a way to describe rotations in space, forever changing physics and math.

Illustration of a complex shape casting a shadow
geometry

Tinkertoy Models Produce New Geometric Insights

September 5, 2018

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.

Art for "The Universal Pattern Popping Up in Math, Physics and Biology"
In Theory

The Universal Pattern Popping Up in Math, Physics and Biology

August 23, 2018

Quanta’s In Theory video series returns with an exploration of a mysterious mathematical pattern found throughout nature.