Why did mammals, grasses and some other groups of organisms explode in diversity only after millions of years? The evolutionary biologist Andreas Wagner plumbs the secrets of those “sleeping beauties.”

For a half century, mathematicians have tried to define the exact circumstances under which a black hole is destined to exist. A new proof shows how a cube can help answer the question.

How hard is it to prove that problems are hard to solve? Meta-complexity theorists have been asking questions like this for decades. A string of recent results has started to deliver answers.

In their jiggles and shakes, red giant stars encode a record of the magnetic fields near their cores.

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.

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

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.

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.

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

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

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

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

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

The preferred “handedness” of biomolecules could have emerged from biased interactions between electrons and magnetic surfaces, new research suggests.

Scientists have struggled to accurately forecast the strength of the sun’s 11-year cycle — even after centuries of solar observations.

A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.

Measurement and entanglement both have a “spooky” nonlocal flavor to them. Now physicists are harnessing that nonlocality to probe the spread of quantum information and control it.

On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics.

Because the areas around adult trees are selectively hostile to their seedlings, more tree species can be packed into tropical forests.

By using “classical shadows,” ordinary computers can beat quantum computers at the tricky task of understanding quantum behaviors.

Every species develops at its own unique tempo, leaving scientists to wonder what governs their timing. A suite of new findings suggests that cells use basic metabolic processes as clocks.