The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum mechanics to infinitely intricate mathematical structures.

According to Einstein’s theory of gravity, black holes have only a small handful of distinguishing characteristics. Quantum theory implies they may have more. Now an experimental search finds that any of this extra ‘hair’ has to be pretty short.

An updated evolutionary model shows that living systems evolve in a split-and-hit-the-gas dynamic, where new lineages appear in sudden bursts rather than during a long marathon of gradual changes.

You’re carrying around in your head a model of how the world works. Will AI systems need to do the same?

Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, decomposes any function into its parts.

Recent progress on both analog and digital simulations of quantum fields foreshadows a future in which quantum computers could illuminate phenomena that are far too complex for even the most powerful supercomputers.

Scientists have identified tubulin structures in primitive Asgard archea that may have been the precursor of our own cellular skeletons.

In cellular automata, simple rules create elaborate structures. Now researchers can start with the structures and reverse-engineer the rules.

The James Webb Space Telescope has found a lonely black hole in the early universe that’s as heavy as 50 million suns. A major discovery, the object confounds theories of the young cosmos.

Over the past 60 years, scientists have largely succeeded in building a computer model of Earth to see what the future holds. One of the most ambitious projects humankind has ever undertaken has now reached a critical moment.

Earth’s radiation can send some molecules spinning or vibrating, which is what makes them greenhouse gases. This infographic explains how relatively few heat-trapping molecules can have a planetary effect.

Earth’s climate is chaotic and volatile. Climate change is simple and predictable. How can both be true?

Building an accurate model of Earth’s climate requires a lot of data. Photography reveals the extreme efforts scientists have undertaken to measure gases, glaciers, clouds and more.

Climate science is the most significant scientific collaboration in history. This series from Quanta Magazine guides you through basic climate science — from quantum effects to ancient hothouses, from the math of tipping points to the audacity of climate…

Two mathematicians have proved that a straightforward question — how hard is it to untie a knot? — has a complicated answer.

Naomi Saphra thinks that most research into language models focuses too much on the finished product. She’s mining the history of their training for insights into why these systems work the way they do.

Using a relatively young theory, a team of mathematicians has started to answer questions whose roots lie at the very beginning of mathematics.

A healthy brain maintains a harmony of neurons that excite or inhibit other neurons, but the lines between different types of cells are blurrier than researchers once thought.

“Anomalous” heat flow, which at first appears to violate the second law of thermodynamics, gives physicists a way to detect quantum entanglement without destroying it.

The V-JEPA system uses ordinary videos to understand the physics of the real world.

The amplituhedron, a shape at the heart of particle physics, appears to be deeply connected to the mathematics of paper folding.