Marijn Heule turns mathematical statements into something like Sudoku puzzles, then has computers go to work on them. His proofs have been called “disgusting,” but they go beyond what any human can do.

Mathematicians have broken through a long-standing barrier in the study of “minimizing surfaces,” which play an important role in both math and physics.

The physics of mixing water layers — an interplay of wind, climate and more — makes lakes work. When it stops, impacts can ripple across an ecosystem.

Has the secret to understanding gravity been hiding in plain sight for nearly 50 years?

Encouraged by successes in understanding black holes, theoretical physicists are applying what they’ve learned to whole universes. What they’re finding has them questioning fundamental assumptions about how physics ought to be done.

Denoscriptive set theorists study the niche mathematics of infinity. Now, they’ve shown that their problems can be rewritten in the concrete language of algorithms.

The newly described microbe represents a world of parasitic, intercellular biodiversity only beginning to be revealed by genome sequencing.

The supercollider is now being used to explore quantum phenomena, including a “magic” form of quantum entanglement.

Researchers have used metamathematical techniques to show that certain theorems that look superficially distinct are in fact logically equivalent.

By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most powerful tools.

Is language core to thought, or a separate process? For 15 years, the neuroscientist Ev Fedorenko has gathered evidence of a language network in the human brain — and has found some similarities to LLMs.

A newly proposed explanation for the slipperiness of ice has revived a centuries-long debate.

Large language models such as ChatGPT come with filters to keep certain info from getting out. A new mathematical argument shows that systems like this can never be completely safe.

Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major problem in algebraic geometry. Other mathematicians had their doubts. Now he says he has a proof.

Take a jaunt through a jungle of strange neurons underlying your sense of touch, hundreds of millions of years of animal evolution and the dense neural networks of brains and AIs.

Explore the year’s most surprising computational revelations, including a new fundamental relationship between time and space, an undergraduate who overthrew a 40-year-old conjecture, and the unexpectedly effortless triggers that can turn AI evil.

Physicists spotted a “terribly exciting” new black hole, doubled down on weakening dark energy, and debated the meaning of quantum mechanics.

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.