Mathematics often feels straightforward, yet some results challenge the way people instinctively think about numbers. Certain paradoxes and probability problems produce answers that seem impossible at ...

Ambiguity and its cousins, contradiction and paradox, are everywhere in mathematics, both in content and thinking. Strangely, the subject that appears to be the very paradigm of reason, and that is ...

Humans are usually pretty good at recognising when they get things wrong, but artificial intelligence systems are not. According to a new study, AI generally suffers from inherent limitations due to a ...

Editor’s Note: Published in 1957, this article comes from Martin Gardner’s legendary Scientific American column Mathematical Games. Read more in our special digital issue, Fun and Games. A paradox is ...

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 ...