Explore a shape that can’t pass through itself, a teenage prodigy, and two new kinds of infinity.

Research into how a father’s choices — such as diet, exercise, stress, nicotine use — may transfer traits to his children has become impossible to ignore.

Try as they might, scientists can’t truly rid a space or an object of its energy. But what “zero-point energy” really means is up for interpretation.

Is the inside of a vision model at all like a language model? Researchers argue that as the models grow more powerful, they may be converging toward a singular “Platonic” way to represent the world.

A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, researchers have found a slew of new candidates in simpler versions of the problem.

The discovery that tissues use electricity to expel unhealthy cells is part of a surge of renewed interest in the currents flowing through our bodies.

In an unprecedented step, researchers crafted a detailed model compatible with the universe’s accelerated expansion.

The math of data structures helps us understand how different storage systems come with different trade-offs between resources such as time and memory.

The Bonnet problem asks when just a bit of information is enough to uniquely identify a whole surface.

Researchers documented the activity of neurons that shape directional navigation as bats explored a remote island off the coast of Tanzania.

Primordial black holes could rewrite our understanding of dark matter and the early universe. A record-breaking detection at the bottom of the Mediterranean Sea has some physicists wondering if we just spotted one.

Columnist Natalie Wolchover checks in with particle physicists more than a decade after the field entered a profound crisis.

Mathematicians are still trying to understand fundamental properties of the Fourier transform, one of their most ubiquitous and powerful tools. A new result marks an exciting advance toward that goal.

New experiments reveal how astrocytes tune neuronal activity to modulate our mental and emotional states. The results suggest that neuron-only brain models, such as connectomes, leave out a crucial layer of regulation.

Today’s observatories document every pulse and flash in the sky each night. To understand how the cosmos has changed over longer periods, scientists rely on a more tactile technology.

How physically magnifying objects using a key ingredient in diapers has opened an unprecedented view of the microbial world.

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues.

Machine learning is helping neuroscientists organize vast quantities of cells’ genetic data in the latest neurobiological cartography effort.

We describe electricity as a flow, but that’s not what happens in a typical wire. Physicists have begun to induce electrons to act like fluids, an effort that could illuminate new ways of thinking about quantum systems.

Columnist Philip Ball thinks the phenomenon of decoherence might finally bridge the quantum-classical divide.

Henry Yuen is developing a new mathematical language to describe problems whose inputs and outputs aren’t ordinary numbers.