As researchers race to cultivate more of the intriguing cells from the deep seafloor, the few cells now growing in labs are giving us our best glimpses of the forerunners of all complex life.

In 50 years of searching, mathematicians found only one example of a “subspace design” in a vector space. A new proof reveals that there are infinitely more out there.

By imbuing enormous vectors with semantic meaning, we can get machines to reason more abstractly — and efficiently — than before.

On Mount Everest and in the Peruvian Andes, Tracie Seimon uses DNA to study how species and ecosystems respond to climate change, pathogens and other influences.

So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.

In all bilaterally symmetrical animals, from humans down to simple worms, nerves cross from one side of the body to the opposite side of the brain. Geometry may explain why.

All infinities go on forever, so how is it possible for some infinities to be larger than others? The mathematician Justin Moore discusses the mysteries of infinity with Steven Strogatz.

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer.

A new analysis argues that ubiquitous eruptions in the sun’s corona explain the vast flow of charged particles seen streaming out through the solar system.

A new, deeper understanding of how the breeding structure of species affects their genetic diversity is giving conservationists better tools for saving animals.

It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.

Cynthia Rudin wants machine learning models, responsible for increasingly important decisions, to show their work.

After decades of frustration, researchers have determined how an airborne scent molecule links to a human smell receptor.

Four mathematicians have found a new upper limit to the “Ramsey number,” a crucial property describing unavoidable structure in graphs.

When he invented Turing machines in 1936, Alan Turing also invented modern computing.

A new phase of matter called a “time crystal” plays with our expectations of thermodynamics. The physicist Vedika Khemani talks with Steven Strogatz about its surprising quantum behavior.

If we want to understand complex constructions, such as ourselves, assembly theory says we must account for the entire history of how such entities came to be.

A new genetics study of ant “social parasites” shows how complex sets of features can emerge rapidly and potentially split species.

In two landmark experiments, researchers used quantum processors to engineer exotic particles that have captivated physicists for decades. The work is a step toward crash-proof quantum computers.

Minhyong Kim is leading a new initiative called Mathematics for Humanity that encourages mathematicians to apply their skills to solving social problems.