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Art for "With Ruler and Compass, Amateur Mathematician Tames Fiendish Problem"

Amateur Mathematician Finds Smallest Universal Cover

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.

abstractions blog

New Proof Shows Infinite Curves Come in Two Types

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.


Mystery Math Whiz and Novelist Advance Permutation Problem

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

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

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"

A Proof About Where Symmetries Can’t Exist

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

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

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

Belt trick illustration
Abstractions blog

The Strange Numbers That Birthed Modern Algebra

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