A quotation by Gerhard Gentzen


Mathematics is regarded as the most certain of all sciences. That it could lead to results which contradict one another seems impossible. This faith in the indubitable certainty of mathematical proofs was sadly shaken around 1900 by the discovery of the antinomies or paradoxes of set theory. It turned out that in this specialised branch of mathematics, contradictions arise without our being able to recognise any specific error in our reasoning.