"All Cretans are liars", said Epimenides, a Cretan. But this means that his statement must be a lie too. But then it is false that Cretans are liars and the statement must be true. So what now?

GENEVA, SWITZERLAND - APRIL 19: A detailed view of the blackboard with theoretical physics equations in chalk by Alberto Ramos, Theoretical Physics Fellow and visitor, Antonio Gonzalez-Arroyo from the ...

The genius logician Kurt Gödel gave his name to his famous Incompleteness Theorems, which in the 1930s helped define the limits of both logic and mathematics. It might be thought that the ...

Last week I explained how a then 25-year-old logician, Kurt Gödel, overturned a basic assumption of many mathematicians in the early 20th century. Even as experts were building a seemingly firm ...

In 1931, the Austrian logician Kurt Gödel pulled off arguably one of the most stunning intellectual achievements in history. Mathematicians of the era sought a solid foundation for mathematics: a set ...

My friends and colleagues often ask me to help with number-related questions. After all, I know a lot about math. Ironically, I'm actually quite bad at mental arithmetic. What many people don't ...

When you purchase an independently reviewed book through our site, we earn an affiliate commission. In 1947, having left Nazi-occupied Vienna for the quaint idyll of Princeton, N.J., seven years ...

This article is from Proof Positive, our friendly math newsletter that's delivered to your inbox every Tuesday afternoon. Sign up today and read it first. My friends and colleagues often ask me to ...