Polynomials aren’t just exercises in abstraction. They’re good at illuminating structure in surprising places.

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.

How do black holes merge and make gravitational waves? Maybe with a little help from their friends.

Researchers agree it’s a long shot, but transmissible cancers could theoretically evolve into independent species. Certain weird parasites might be living proof.

Does objective, perfect randomness exist, or is randomness merely a product of our ignorance?

Mathematicians and neuroscientists have created the first anatomically accurate model that explains how vision is possible.

The theoretical particle physicist Ann Nelson, who died on August 4 at age 61, was a font of brilliant ideas and a champion of ending discrimination in the

Iyad Rahwan’s radical idea: The best way to understand algorithms is to observe their behavior in the wild.

In the “underground economy” for soil nutrients, fungi strike hard bargains and punish plants that won’t meet their price.

At stake are fundamental ideas about how black holes form — and a six-way bet.

Modern humans and more ancient hominins interbred many times throughout Eurasia and Africa, and the genetic flow went both ways.

While studying materials made from DNA-coated nanoparticles, researchers found a new form of this matter: lattices in which smaller particles roam like

Genetically identical bacteria should all be the same, but in fact, the cells are stubbornly varied individuals.

Since the 1970s, physicists have described black holes using borrowed versions of the laws of thermodynamics. But are black holes really thermodynamic systems? Craig Callender worries that the analogy has been stretched too far.

There are many different ways to think about probability. Quantum mechanics embodies them all.

Clues from fish diversity suggest that interbreeding between species could be a major mechanism of fast speciation.

A new measurement appears to have eliminated an anomaly that had captivated physicists for nearly a decade.

A giant star’s death throes may offer the first evidence of a pair-instability supernova, and a glimpse of the first stars in the universe.

Origin-of-life researchers have usually studied the potential of pure starting materials, but messy chemical composites may kick-start life more effectively.

In some ways, machine vision is superior to human vision. In other ways, it may never catch up.

Maintaining perfect stability through negative feedback is a basic element of electrical circuitry, but it’s been a mystery how cells could do it — until now.