Time was found to flow differently between the top and bottom of a single cloud of atoms. Physicists hope that such a system will one day help them combine quantum mechanics and Einstein’s theory of…

Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.

The transcendental number π is as familiar as it is ubiquitous, but how does Euler’s number e transcend the ordinary?

Years of conflicting neutrino measurements have led physicists to propose a “dark sector” of invisible particles — one that could simultaneously explain dark matter, the puzzling expansion of the…

Algorithms that zero in on solutions to optimization problems are the beating heart of machine reasoning. New results reveal surprising limits.

The computational biologist Anne Carpenter creates software that brings the power of machine learning to researchers seeking answers in mountains of cell images.

Over the past decade, researchers have completely rewritten the story of how gas giants such as Jupiter and Saturn form. They’re now debating whether the same process might hold for Earth.

A new study of gene expression in sponges reveals the complex diversity of their cells as well as some possibly ancient connections between the nervous, immune and digestive systems.

The brain not only helps to regulate immune responses, but also stores and retrieves “memories” of them.

New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.

In nonreciprocal systems, where Newton’s third law falls apart, “exceptional points” are helping researchers understand phase transitions and possibly other phenomena.

Results from neural networks support the idea that brains are “prediction machines” — and that they work that way to conserve energy.

Quantum bits are fussy and fragile. Useful quantum computers will need to use an error-correction technique like the one that was recently demonstrated on a real machine.

Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.

The Chinese remainder theorem is an ancient and powerful extension of the simple math of least common multiples.

Through his encyclopedic study of the electron, an obscure figure named Stefano Laporta found a handle on the subatomic world’s fearsome complexity. His algorithm has swept the field.

A mathematical model shows how a thermodynamic mechanism could have made protocells split in two.

By carefully constructing a multidimensional and well-connected graph, a team of researchers has finally created a long-sought locally testable code that can immediately betray whether it’s been…

The solution to our puzzle about Euler’s number explains why e pops up in situations that involve optimality.

The spate of furious wildfires around the world during the past decade has revealed to ecologists how much biodiversity and “pyrodiversity” go hand in hand.