What's up in

Mathematics

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"
geometry

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.

Illustration of a complex shape casting a shadow
geometry

Tinkertoy Models Produce New Geometric Insights

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

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

Art for "How Network Math Can Help You Make Friends"
Quantized Academy

How Network Math Can Help You Make Friends

Studying the structure of existing friendships in your community can help you forge the best connections when forming a new circle of friends.