Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.

A new magnum opus posits the existence of a hidden mathematical link akin to the connection between electricity and magnetism.

Eugenio Calabi, who died on September 25, conceived of novel geometric objects that later became fundamental to string theory.

Shor’s algorithm will enable future quantum computers to factor large numbers quickly, undermining many online security protocols. Now a researcher has shown how to do it even faster.

For decades, researchers have debated whether brain cells called astrocytes can signal like neurons. Researchers recently published the best evidence yet that some astrocytes are part of the electrical conversation.

What makes a quantum computer more powerful than a classical computer? It’s a surprisingly subtle question that physicists are still grappling with, decades into the quantum age.

A new analysis of ancient sediments fills a gap in the fossil record — revealing a massive dynasty of ancient eukaryotes, which may have reigned for 800 million years and shaped the history of life of Earth.

Alexei Efros has spent his career learning how machines see differently from humans. Now he’s helping to bridge the gap.

After identifying interlocking symmetries in mammalian cells, scientists can describe some tissues as liquid crystals — an observation that lays the groundwork for a fluid-dynamic theory of how tissues move.

New work attacks a long-standing barrier to understanding how prime numbers are distributed.

The discovery earlier this year of the “hat” tile marked the culmination of hundreds of years of work into tiles and their symmetries.

New research in social bats raises the intriguing possibility that evolution can reprogram the brain’s “place cells,” which are typically associated with location, to encode all kinds of environmental information.

Quadratic reciprocity lurks around many corners in mathematics. By proving it, number theorists reimagined their whole field.

The moons orbiting Jupiter and Saturn appear to have subsurface oceans — tantalizing targets in the search for life beyond Earth. But it’s not clear why these seas exist at all.

Three researchers have found a long-sought way to pull information from large databases secretly, moving us closer to fully private internet searches.

High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible.

In the rumbles and groans of underwater volcanoes, Jackie Caplan-Auerbach finds her favorite harmonies — and clues to the Earth’s interior.

Neuroscientists recently discovered that small numbers have a different neural signature than larger ones, offering a new look into the brain’s number system and its connections to memory and mathematics.

Scientists have recently discovered scores of free-floating worlds that defy classification. The new observations have forced them to rethink their theories of star and planet formation.

Cells in the placenta have an unusual trick for activating gentle immune defenses and keeping them turned on when no infection is present. It involves crafting and deploying a fake virus.

By bringing together disparate approaches, machines can reach a new level of creative problem-solving.