The devil says: “I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvelous machine.” —MICHAEL ATIYAH IF THERE ARE numbers and there are shapes in nature, which comes first? Common sense: neither. First in what? Although Euclid’s Elements is a treatise about geometry, some idea of the natural numbers 1, 2, 3, . . . is present as background. It could not be otherwise. Euclid talks of triangles, after all, meaning more than one, and there is one and only one line parallel to a given line specified by Playfair’s axiom. The natural numbers are among the common notions “on which all men base their proofs.” The reverse is true as well. No mathematician could study arithmetic if the numerals did not have stable geometrical properties. Imagine trying to prove that 2 plus 2 is 4 and seeing the numeral “2” undertake a sinuous deformation on the blackboard, or in the mathematician’s mind, vanishing, perhaps, at the very moment of intellectual triumph.
What do You think about The King Of Infinite Space?
