In new work on graphs’ hidden structure, mathematicians probe the limits of randomness.

A new paper finds a faster method for determining when two mathematical groups are the same.

New modeling work suggests why nature is more diverse than niche-based ecological theory predicts.

Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.

Jellyfish and other aquatic creatures embody solutions to diverse problems in engineering, medicine and mathematics. John Dabiri, a fluid dynamics expert, talks with Steven Strogatz about what jellyfish can teach us about going with the flow.

Astronomers have found a background din of exceptionally long-wavelength gravitational waves pervading the cosmos. The cause? Probably supermassive black hole collisions, but more exotic options can’t be ruled out.

Physicists finally know where at least some of these high-energy particles come from, which helps make the neutrinos useful for exploring fundamental physics.

New research reveals how marine microbes use an extra membrane that once had digestive functions to boost their yield from photosynthesis.

Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.

Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?

For decades, physicists have struggled to develop a quantum theory of gravity. But what if gravity — and space-time — are fundamentally classical?

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.

Extreme microorganisms carpeting the Atacama Desert in Chile illuminate how life might have first taken hold on Earth’s surface.

Abnormal waves of electrical activity can cause a heart’s muscle cells to beat out of sync. In this episode, Flavio Fenton, an expert in cardiac dynamics, talks with Steve Strogatz about ways to treat heart arrhythmias without resorting to painful defibrillators.

A new algorithm brings together the advantages of randomness and deterministic processes to reliably construct large prime numbers.

In some deep subterranean aquifers, cells have a chemical trick for making oxygen that could sustain whole underground ecosystems.

By treating Earth as a topological insulator — a state of quantum matter — physicists found a powerful explanation for the movements of the planet’s air and seas.

A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

Quantum algorithms can find their way out of mazes exponentially faster than classical ones, at the cost of forgetting the path they took. A new result suggests that the trade-off may be inevitable.

Knowing a little about the local connections on flight maps and other networks can reveal a lot about a system’s global structure.

The proof establishes new conditions that cause connected oscillators to sway in sync.