“A bell cannot tell time, but it can be moved in just such a way as to say twelve o’clock – similarly, a man cannot calculate infinite numbers, but he can be moved in just such a way as to say pi.”

“With abstraction, birds become numbers. Men and maniocs, too. We can look at a scene and say, ‘There are two men, three birds and four maniocs’ but also, ‘There are nine things’ (summing two and three and four). The Pirahã do not think this way. They ask, ‘What are these things?’ ‘Where are they?’, ‘What do they do?’ A bird flies, a man breathes and a manioc plant grows. It is meaningless to try to bring them together. Man is a small world. The world is a big manioc.”

“Why learn a number like pi to so many decimal places? The answer I gave then as I do now is that pi is for me an extremely beautiful and utterly unique thing. Like the Mona Lisa or a Mozart symphony, pi is its own reason for loving it.”

“One particular aspect of Siddhartha’s revelation of the outside world has always struck me. Quite possibly he lived his first thirty years without any knowledge of number. How must he have felt, then, to see crowds of people mingling in the streets? Before that day he would not have believed that so many people existed in all the world. And what wonder it must have been to discover flocks of birds, and piles of stones, leaves on trees and blades of grass! To suddenly realise that, his whole life long, he had been kept at arm’s length from multiplicity.”

“Things were changing; I was changing. All swelling limbs and sweating brain, suddenly I had more body than I knew what to do with. Arms and legs became the prey of low desktops and narrow corridors, were ambushed by sharp corners. Mr Baxter ignored my plight. Bodies were inimical to mathematics, or so we were led to believe. Bad hair, acrid breath, lumpy skin, all vanished for an hour every Tuesday and Thursday. Young minds in the buff soared into the sphere of pure reason. Pages turned to parallelograms; cities, circumferences; recipes, ratios. Shorn of our bearings, we groped our way around in this rarefied air.”

“We know next to nothing with any certainty about Pythagoras, except that he was not really called Pythagoras. The name by which he is known to us was probably a nickname bestowed by his followers. According to one source, it meant ‘He who spoke truth like an oracle’. Rather than entrust his mathematical and philosophical ideas to paper, Pythagoras is said to have expounded them before large crowds. The world’s most famous mathematician was also its first rhetorician.”

“The human brain is like a memory system that records every thing that happens to us and makes intelligent predictions based on those experiences.”