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

‘Oh, I’ve been thinking about this business with your uncle. I wouldn’t want you getting any crazy ideas into your head about following family tradition and tackling —’ I laughed. ‘Goldbach’s Conjecture? Not bloody likely!’ Sammy nodded. That’s good. Because I have a suspicion that you Greeks are attracted to impossible problems.’ ‘Why? Do you know any others?’ ‘A famous topologist here, Professor Papakyri-akopoulos. He’s been struggling for years on end to prove the “Poincaré Conjecture” — it’s the most famous problem in low-dimensional topology, unproved

You Greeks are attracted to impossible problems

‘If multiplication is unnatural,’ he continued, ‘more so is the concept of “prime number” that springs directly from it.

Prime numbers are unnatural