Proof

"In the fourth part of the Discourse, Descartes returns to the main thrust of his development of a philosophy. He starts with his methodical doubt: I doubt, or negate, everything that cannot be proven in a mathematical way, he says. So what can Descartes prove? Everything is taken to be false. But Descartes, the person, is doing this doubting. So one thing can be deduced as true: Descartes exists. Otherwise, he could not doubt. Thus, from the negation of everything, a proof is derived of the existence of the person doing the doubting. This is the most brilliant deduction in the history of Western thought."

--Amir D. Aczel, Descartes' Secret Notebook: A True Tale of Mathematics, Mysticism, and the Quest to Understand the Universe, 2005