For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

The Standard Model is a sweeping equation that has correctly predicted the results of virtually every experiment ever conducted, as Quanta explores in a new video.

Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.

The root of today’s quantum revolution was John Stewart Bell’s 1964 theorem showing that quantum mechanics really permits instantaneous connections between far-apart locations.

Scientists have reported large DNA structures in some archaea that defy easy categorization.

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

Theorists are in a frenzy over “fractons,” bizarre, but potentially useful, hypothetical particles that can only move in combination with one another.

A centuries-old concept in soil science has recently been thrown out. Yet it remains a key ingredient in everything from climate models to advanced carbon-capture projects.

Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

Like a perpetual motion machine, a time crystal forever cycles between states without consuming energy. Physicists claim to have built this new phase of matter inside a quantum computer.

Showy male competitions over mating privileges have grabbed scientists’ attention more often, but new work hints that sexual selection is also widespread among females.

By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.

Brown dwarfs such as “The Accident” are illuminating the murky borderlands that separate planets from stars.

A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.

Crows recently demonstrated an understanding of the concept of zero. It’s only the latest evidence of animals’ talents for numerical abstraction — which may still differ from our own grasp of numbers.

The mechanism behind leopard spots and zebra stripes also appears to explain the patterned growth of a bismuth crystal, extending Alan Turing’s 1952 idea to the atomic scale.

When Steven Weinberg died last month, the world lost one of its most profound thinkers.

The unambiguous discovery of a Wigner crystal relied on a novel technique for probing the insides of complex materials.

The evolution of a defensive gland in beetles shows how organs can arise from novel cells carving out new functional niches for their neighbors.

The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult computational problem.

By showing that even large objects can exhibit bizarre quantum behaviors, physicists hope to illuminate the mystery of quantum collapse, identify the quantum nature of gravity, and perhaps even make…