Uncle Petros and Goldbach's Conjecture: A Novel of Mathematical Obsession

by Apostolos Doxiadis

Turing knelt by his armchair, his finger stabbing excitedly at the arcane symbols filling Gödel’s article. ‘Here: this genius proved — conclusively proved! — that no matter what axioms you accept, a theory of numbers will of necessity contain unprovable propositions!’ ‘You mean, of course, the false propositions?’ ‘No, I mean true propositions — true yet impossible to prove!’ Petros jumped to his feet. ‘This is not possible!’ ‘Oh yes it is, and the proof of it is right here, in these fifteen pages: “Truth is not always provable!”’ My uncle now felt a sudden dizziness overcome him. ‘But … but this cannot be.’ He flipped hurriedly through the pages, striving to absorb in a single moment, if possible, the article’s intricate argument, mumbling on, indifferent to the young man’s presence. ‘It is obscene … an abnormality … an aberration …’ Turing was smiling smugly. ‘That’s how all mathematicians react at first … But Russell and Whitehead have examined Gödel’s proof and proclaimed it to be flawless. In fact, the term they used was “exquisite”.’ Petros grimaced. ‘“Exquisite”? But what it proves — if it really proves it, which I refuse to believe — is the end ofmathematics!’

Alan Turing Goedel's proof obscene exquisite