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mathematics

Art for "Scientists Learn the Ropes on Tying Molecular Knots"
chemistry

Scientists Learn the Ropes on Tying Molecular Knots

As chemists tie the most complicated molecular knot yet, biophysicists create a “periodic table” that describes what kinds of knots are possible.

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 "How Equality and Inequality Shape the Birds and the Bees"
insights puzzle

How Equality and Inequality Shape the Birds and the Bees

Two dynamic, seemingly opposing forces likely played an important role in the evolution of reproduction and child rearing in social animals like bees and humans.

Photo of Urmila Mahadev
quantum computing

Graduate Student Solves Quantum Verification Problem

Urmila Mahadev spent eight years in graduate school solving one of the most basic questions in quantum computation: How do you know whether a quantum computer has done anything quantum at all?

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.

Art for "Evolutionary Math and Just-So Stories"
insights puzzle

Solution: ‘Evolutionary Math and Just-So Stories’

How much stock should we put in mathematical models of evolution that have not been validated by rigorous empirical data?

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.