Archive

Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

New research finds that the memories useful for future generalizations are held in the brain separately from those recording unusual events.

Astronomers are scouring the cosmos for fingerprints of the invisible — tiny clumps of pure dark matter that might solve a long-standing cosmic mystery.

Sticking out your tongue while doing delicate work with your hands reveals a history of evolutionary relationships.

Quantum computing is still really, really hard. But the rise of a powerful class of error-correcting codes suggests that the task might be slightly more feasible than many feared.

A five-year “adversarial collaboration” of consciousness theorists led to a stagy showdown in front of an audience. It crowned no winners — but it can still claim progress.

Researchers have discovered ways around a fundamental trade-off between accuracy and beauty in digital images.

The telescope conjecture gave mathematicians a handle on ways to map one sphere to another. Now that it has been disproved, the universe of shapes has exploded.