Albert Einstein’s ideas about space-time aren’t exactly intuitive, and they aren’t exactly Einstein’s, either.

New research in fish suggests that gut microbes can have a crucial early influence on the brain’s social development.

For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. A new computer-assisted proof marks a major breakthrough in that quest.

Two physicists have calculated that the universe has a higher entropy — and is therefore more likely — than alternative possible universes. The calculation is “an answer to a question that is yet to be fully understood.”

Proving that two polygons have the same area can be as easy as cutting them up and rearranging the pieces.

Wei Ho, the first director of the Women and Mathematics program at the Institute for Advanced Study, combines algebra and geometry in her work on an ancient class of curves.

Inspired by the results of a game-playing neural network, mathematicians have been making unexpected advances on an age-old math problem.

Researchers discover that to sharpen its control over precise maneuvers, the brain uses comparisons between control signals — not the signals themselves.

The work — the first-ever limit on how many whole numbers can be written as the sum of two cubed fractions — makes significant headway on “a recurring embarrassment for number theorists.”

The unprecedented experiment explores the possibility that space-time somehow emerges from quantum information, even as the work’s interpretation remains disputed.

Maintenance of the software that’s used for the hardest physics calculations rests almost entirely with a retiree. The situation reveals the problematic incentive structure of academia.

Wordle is a word game. But you can use math to optimize your chances of winning (without cheating).

Two new studies suggest that certain tetrahedral arrangements of galaxies outnumber their mirror images, potentially reflecting details of the universe’s birth. But confirmation is needed.

Mathematicians are finding inevitable structures in sufficiently large sets of integers.

A quantum approach to data analysis that relies on the study of shapes will likely remain an example of a quantum advantage — albeit for increasingly unlikely scenarios.

After decades in the shadow of the reigning model for Alzheimer’s disease, alternative explanations are finally getting the attention they deserve.

By using fluids to model inaccessible realms of the cosmos, Silke Weinfurtner is “looking for a deeper truth beyond one system.” But what can such experiments teach us?

Making sure our machines understand the intent behind our instructions is an important problem that requires understanding intelligence itself.

The neural representations of a perceived image and the memory of it are almost the same. New work shows how and why they are different.

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong.

The ecologist Holly Moeller studies microorganisms that expand their range by absorbing organelles and gaining new metabolic talents from their prey.