More than 50 years after Bob Paine’s experiment with starfish, hundreds of species have been pronounced “keystones” in their ecosystems. Has the powerful metaphor lost its mathematical meaning?

Using machine learning, string theorists are finally showing how microscopic configurations of extra dimensions translate into sets of elementary particles — though not yet those of our universe.

Topologists prove two new results that bring some order to the confoundingly difficult study of four-dimensional shapes.

A group of prominent biologists and philosophers announced a new consensus: There’s “a realistic possibility” that insects, octopuses, crustaceans, fish and other overlooked animals experience consciousness.

Researchers have shown how to find the simplest description of a data set faster than by simply checking every possibility.

Physicists and cosmologists will have a new probe of primordial processes when Europe launches the Laser Interferometer Space Antenna (LISA) next decade.

The work of the neuroscientist Ishmail Abdus-Saboor has opened up a world of insights into precisely how much pleasure and pain animals experience during different forms of touch.

Mathematicians think abstract tools from a field called symplectic geometry might help with planning missions to far-off moons and planets.

By apparently overtraining them, researchers have seen neural networks discover novel solutions to problems.