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.

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.