A discovery is like falling in love and reaching the top of a mountain after a hard climb all in one, an ecstasy not induced by drugs but by the revelation of a face of nature that no one has seen before and that often turns out to be more subtle and wonderful than anyone had imagined.

A mathematician who can only generalise is like a monkey who can only climb UP a tree. ... And a mathematician who can only specialise is like a monkey who can only climb DOWN a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise. ... There is, I think, a moral for the teacher. A teacher of traditional mathematics is in danger of becoming a down monkey, and a teacher of modern mathematics an up monkey. The down teacher dishing out one routine problem after another may never get off the ground, never attain any general idea. and the up teacher dishing out one definition after the other may never climb down from his verbiage, may never get down to solid ground, to something of tangible interest for his pupils.

I can assure you, reader, that in a very few hours, even during the first day, you will learn more natural philosophy about things contained in this book, than you could learn in fifty years by reading the theories and opinions of the ancient philosophers. Enemies of science will scoff at the astrologers: saying, where is the ladder on which they have climbed to heaven, to know the foundation of the stars? But in this respect I am exempt from such scoffing; for in proving my written reason, I satisfy sight, hearing, and touch: for this reason, defamers will have no power over me: as you will see when you come to see me in my little Academy.

If some race of quadrumanous animals, especially one of the most perfect of them, were to lose, by force of circumstances or some other cause, the habit of climbing trees and grasping the branches with its feet in the same way as with its hands, in order to hold on to them; and if the individuals of this race were forced for a series of generations to use their feet only for walking, and to give up using their hands like feet; there is no doubt, according to the observations detailed in the preceding chapter, that these quadrumanous animals would at length be transformed into bimanous, and that the thumbs on their feet would cease to be separated from the other digits, when they only used their feet for walking.

What can you conceive more silly and extravagant than to suppose a man racking his brains, and studying night and day how to fly? ... wearying himself with climbing upon every ascent, ... bruising himself with continual falls, and at last breaking his neck? And all this, from an imagination that it would be glorious to have the eyes of people looking up at him, and mighty happy to eat, and drink, and sleep, at the top of the highest trees in the kingdom.