In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

Brain-imaging techniques have made it possible to explore the neural foundations of logical and mathematical cognition. These techniques are revealing more than simply where these high-order processes ...

On a recent train trip from Lyon to Paris, Vladimir Voevodsky sat next to Steve Awodey and tried to convince him to change the way he does mathematics. Voevodsky, 48, is a permanent faculty member at ...

“This tattoo is the Zermelo-Fraenkel with Choice axioms of set theory. These nine axioms are the basis for ZFC set theory, which is the most commonly studied form of set theory and the most well known ...

No less a mind than Bertrand Russell, of Principia Mathematica fame, was responsible for this paradox, which opened a hole in math. It’s those barbers. The Barber Paradox shows that barbers are not to ...

When I started as a K–8 STEM coach at Amesbury Public Schools, I noticed that the math and science lessons we were teaching in elementary school weren’t vertically integrated with what we were ...

If you enjoyed this article, I’d like to ask for your support. Scientific American has served as an advocate for science and industry for 180 years, and right now may be the most critical moment in ...

When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the ...

The claim is often made that mathematical results are immutable. Once proven, they remain forever valid. But things are not so simple. There are problems at the very core of mathematics that cast a ...