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 ...

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

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

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 ...

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. Climate science is the ...

Erica Klarreich has been writing about mathematics and science for more than 15 years. She has a doctorate in mathematics from Stony Brook University and is a graduate of the Science Communication ...

Particle physicists in search of the next theory of reality are consulting a mathematical structure that they know will never fail: a table of possibilities known as the S-matrix. Matt von Hippel is a ...