In 1931, the Austrian logician Kurt Gödel published his incompleteness theorem, a result widely considered one of the greatest intellectual achievements of modern times. The theorem states that in any ...

Godel’s theorems on the incompleteness and undecidability of mathematical systems are among the deepest and most significant discoveries of the 20 th century. They represent a dramatic failure of one ...

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 ...

"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 ...

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Gödel's Incompleteness Theorem, which proved that no formal mathematical system can demonstrate every mathematical truth, is a landmark of modern thought. It's a simple but profound statement, but the ...

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. Last week I explained how a then 25-year-old ...

Earlier today I set you the puzzle below, which is based on Gödel’s incompleteness theorem. As I discussed in the original post, this theorem is one of the most famous in maths and states that in any ...