Galileo Galilei, Dialogues Concerning Two New Sciences, 1638, translated by Henry Crew and Alfonso de Salvio, with an Introduction by Antonio Favaro (New York: Macmillan, 1914). Retrieved from Online Library of Liberty.
There is, in nature, perhaps nothing older than motion, concerning which the books written by philosophers are neither few nor small; nevertheless I have discovered by experiment some properties of it which are worth knowing and which have not hitherto been either observed or demonstrated. Some superficial observations have been made, as, for instance, that the free motion of a heavy falling body is continuously accelerated; but to just what extent this acceleration occurs has not yet been announced; for so far as I know, no one has yet pointed out that the distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity.
Richard Feynman, Lectures on Computation, edited by Tony Hey and Robin W. Allen (Boulder: Westview Press, 2000). Retrieved from Ryan Zezeski’s Zinascii.com.
It’s the way I study—to understand something by trying to work it out or, in other words, to understand something by creating it. The other way, which is also valuable, is to read carefully how someone else did it. I find the first method best for me, once I have understood the basic idea. If I get stuck I look at a book that tells me how someone else did it. I turn the pages and then I say “Oh, I forgot that bit”, then close the book and carry on. Finally, after you’ve figured out how to do it you read how they did it and find out how dumb your solution is and how much more clever and efficient theirs is! But this way you can understand the cleverness of their ideas and have a framework in which to think about the problem…. What one fool can do, so can another, and the fact that some other fool beat you to it shouldn’t disturb you: you should get a kick out of having discovered something. Most of the problems I give you in this book have been worked over many times, and many ingenious solutions have been devised for them. But if you keep proving stuff that others have done, getting confidence, increasing the complexities of your solutions—for the fun of it—then one day you’ll turn around and discover that nobody actually did that one!