The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.

New research finds that chaos plays a bigger role in population dynamics than decades of ecological data seemed to suggest.

Everybody gets older, but not everyone ages in the same way. In this episode, Steven Strogatz speaks with Judith Campisi and Dena Dubal, two biomedical researchers who study the aging process.

Perineuronal nets, rigid structures that hold certain neurons in place, affect a surprising amount of brain activity, including some associated with chronic pain.

Readers balanced logical reasoning and mathematical insights to find phony coins with a double-pan balance scale.

A hidden link has been found between two seemingly unrelated particle collision outcomes. It’s the latest example of a mysterious web of mathematical connections between disparate theories of physics.

Christopher Kanan is building algorithms that can continuously learn over time — the way we do.

Partnerships between engineers and biologists have begun to reveal how birds evolved their superb maneuverability.

The solutions to Einstein’s equations that describe a spinning black hole won’t blow up, even when poked or prodded.

The biochemist Nick Lane thinks life first evolved in hydrothermal vents where precursors of metabolism appeared before genetic information. His ideas could lead us to think differently about aging and cancer.

The key to understanding the origin and fate of the universe may be a more complete understanding of the vacuum.

Ever since Archimedes, mathematicians have been fascinated by equations that involve a difference between squares. Now two mathematicians have proven how often these equations have solutions, concluding a decades-old quest.

Quantum field theory may be the most successful scientific theory of all time, but there’s reason to think it’s missing something. Steven Strogatz speaks with theoretical physicist David Tong about this enigmatic theory.

Self-supervised learning allows a neural network to figure out for itself what matters. The process might be what makes our own brains so successful.

Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers.

In exploring a family of two-dimensional crystals, a husband-and-wife team is uncovering a potent variety of new electron behaviors.

A statistical analysis of chemical tags on DNA may help unify disparate theories of aging.

In honor of the actor and activist Nichelle Nichols, this month’s puzzle imagines a Star Trek adventure in which her character, Lieutenant Uhura, faces a life-and-death conundrum.

By studying how electric organs arose in different lineages of fish, scientists gain new insights into a long-standing question of evolutionary biology.

Supermassive black holes have come to the fore as engines of galactic evolution, but new observations of the Milky Way and its central hole don’t yet hang together.

Two researchers have broken an encryption protocol that many saw as a promising defense against the power of quantum computing.