The prize-winning geometer feels most fulfilled when exploring the fertile ground where constraint meets creation.

There once was a cosmic seed that sprouted the Milky Way galaxy. Astronomers have discovered its last surviving remnants.

The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

A novel type of “jumping gene” may explain why the genomes of complex cells aren’t all equally stuffed with noncoding sequences.

Unpredictability can help computer scientists solve otherwise intractable problems.

The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way.

The first large-scale comparison of mutation rates gives insights into how quickly species can evolve.

Should Covid-19 vaccines be judged by how well they prevent disease or how well they prevent death? Anna Durbin, a public health expert and vaccine researcher, talks with Steven Strogatz about the science behind vaccines.

In the math of particle physics, every calculation should result in infinity. Physicists get around this by just ignoring certain parts of the equations — an approach that provides approximate answers. But by using the techniques known as “resurgence,” researchers…

If the electron’s charge wasn’t perfectly round, it could reveal the existence of hidden particles. A new measurement approaches perfection.

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.