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 ...

Emmy Noether showed that fundamental physical laws are just a consequence of simple symmetries. A century later, her insights continue to shape physics.

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 ...

In a year filled with sweet new observations in astronomy and tantalizing breakthroughs in condensed matter physics, the brand-new space telescope takes the cake.

Imagine if our skies were always filled with a thick layer of opaque clouds. With no way to see the stars, or to view our planet from above, would we have ever discovered that the Earth is round? The ...