It’s an educated guess, not a proof. But a good conjecture will guide math forward, pointing the way into the mathematical unknown.

Mathematicians have found that materials conduct electricity when electrons follow a universal mathematical pattern.

Your expectations shape and quicken your perceptions. A new model that explains how that happens also suggests it’s time to update theories about sensory perception and decision making.

The sun radiates far more high-frequency light than expected, raising questions about unknown features of the sun’s magnetic field and the possibility of even more exotic physics.

The stunning emergence of a new type of superconductivity with the mere twist of a carbon sheet has left physicists giddy, and its discoverer nearly overwhelmed.

A strange glow coming from the Milky Way’s center was thought to be due to ordinary pulsars. But a new look at a years-old study shows that dark matter might still be responsible.

New work raises the estimated diversity of viruses in the seas more than twelvefold and lays the groundwork for a better understanding of their impact on global nutrient cycles.

Quantum computers can’t selectively forget information. A new algorithm for multiplication shows a way around that problem.

Promising efforts at disentangling the effects of genes and the environment on complicated traits may have been confounded by statistical problems.