“The highest life is mathematics.”

The Artful Universe (1995)
Context: Where there is life there is a pattern, and where there is a pattern there is mathematics. Once that germ of rationality and order exists to turn a chaos into a cosmos, then so does mathematics. There could not be a non-mathematical Universe containing living observers.<!-- Ch. 5, p. 230

Letter to the Marquess of Northampton (June 17, 1838), in Robert Perceval Graves, Life of Sir William Rowan Hamilton Vol. 2 (1885) https://archive.org/details/lifeofsirwilliam02gravuoft, pp. 260-261.

La vie n'est bonne qu'à deux choses : à faire des mathématiques et à les professer.
quoted by François Arago in Notices biographiques, Volume 2 http://books.google.fr/books?pg=PA662&id=ZzNLAAAAYAAJ#v=onepage&q&f=false, 1854, p. 662.

Source: The (Mis)Behavior of Markets (2004, 2008), Ch. 7, p. 125
Context: Contrary to popular opinion, mathematics is about simplifying life, not complicating it. A child learns a bag of candies can be shared fairly by counting them out: That is numeracy. She abstracts that notion to dividing a candy bar into equal pieces: arithmetic. Then, she learns how to calculate how much cocoa and sugar she will need to make enough chocolate for fifteen friends: algebra.

Ideas and Opinions (1954), pp. 238–239; quoted in "Einstein's Philosophy of Science" http://plato.stanford.edu/entries/einstein-philscience/
1950s
Context: The theory of relativity is a beautiful example of the basic character of the modern development of theory. That is to say, the hypotheses from which one starts become ever more abstract and more remote from experience. But in return one comes closer to the preeminent goal of science, that of encompassing a maximum of empirical contents through logical deduction with a minimum of hypotheses or axioms. The intellectual path from the axioms to the empirical contents or to the testable consequences becomes, thereby, ever longer and more subtle. The theoretician is forced, ever more, to allow himself to be directed by purely mathematical, formal points of view in the search for theories, because the physical experience of the experimenter is not capable of leading us up to the regions of the highest abstraction. Tentative deduction takes the place of the predominantly inductive methods appropriate to the youthful state of science. Such a theoretical structure must be quite thoroughly elaborated in order for it to lead to consequences that can be compared with experience. It is certainly the case that here, as well, the empirical fact is the all-powerful judge. But its judgment can be handed down only on the basis of great and difficult intellectual effort that first bridges the wide space between the axioms and the testable consequences. The theorist must accomplish this Herculean task with the clear understanding that this effort may only be destined to prepare the way for a death sentence for his theory. One should not reproach the theorist who undertakes such a task by calling him a fantast; instead, one must allow him his fantasizing, since for him there is no other way to his goal whatsoever. Indeed, it is no planless fantasizing, but rather a search for the logically simplest possibilities and their consequences.

As quoted in Modern Political Ideologies, Third Edition, Andrew Vincent, West Sussex, UK, Wiley-Blackwell, 2010, p. 156

Bartlett's Familiar Quotations, 10th ed. (1919), Journal

Remark made by von Neumann as keynote speaker at the first national meeting of the Association for Computing Machinery in 1947, as mentioned by Franz L. Alt at the end of "Archaeology of computers: Reminiscences, 1945--1947", Communications of the ACM, volume 15, issue 7, July 1972, special issue: Twenty-fifth anniversary of the Association for Computing Machinery, p. 694.

The Fabric of Reality (1997)