In the Encyclopedia of Philosophy (Edwards, 1967, 348–49), the article by Jean van Heijenoort titled “Gödel's Theorem” begins with the following terse paragraphs:

By Gödel's theorem the following statement is generally meant:

Despite its forbidding technicality, the Gödel (1931) theorem has never stopped generating enormous interest. Much of that interest has been piqued because with the proof of the Gödel theorem, the human mind has succeeded in proving that – at least in any fixed, consistent system with a fixed, finite set of axioms that are at least minimally adequate for number theory and in a system that has the usual logic as the instrument with which deductions are to be made from those axioms – there has to be a mathematical statement the human mind cannot prove.