Ultrafinitism, a philosophy that rejects the infinite, has long been dismissed as mathematical heresy. But it is also ...

Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core ...

Neurons that fire together, wire together” is not the full story. A novel mechanism explains how the brain can learn across ...

Ice comes in more forms than what you’ll find in a freezer or a glacier. Since 1900, scientists have observed more than 20 ...

The bacterial flagellar motor is finally understood after 50 years. In its workings, columnist Natalie Wolchover finds the ...

Some quantum cryptographers want to find ways to keep messages secret even if the rules of quantum mechanics don’t hold. The ...

With a newly discovered mathematical tool, researchers are hoping to gain unprecedented insight into the structure of complex ...

Dozens of new discoveries reveal that defenses evolved by bacteria and viruses billions of years ago still define our own ...

Some 30 years ago, the mathematician Peter Shor took a niche physics project — the dream of building a computer based on the counterintuitive rules of quantum mechanics — and shook the world. Shor ...

Neutrinos have about as little influence as a particle can have. They have essentially no heft, no electric charge, and no “color” charge. As a result, the neutrino has no connection with most of ...

Last summer, a wedding photographer walked begrudgingly into a physics laboratory outside Rome. Feeling uninspired by the intricate machinery around him, he decided to turn off the lights. “I wanted ...