“For reasons mathematical, psychological, and sociological, it is a good idea to use a money management system that is relatively forgiving of estimation errors.”

"The Mathematician", in The Works of the Mind (1947) edited by R. B. Heywood, University of Chicago Press, Chicago
Context: I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics. But, once they are conceived, the subject begins to live a peculiar life of its own and is … governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas.

Our America (1881)
Context: The youth of America are rolling up their sleeves, digging their hands in the dough, and making it rise with the sweat of their brows. They realize that there is too much imitation, and that creation holds the key to salvation. "Create" is the password of this generation. The wine is made from plantain, but even if it turns sour, it is our own wine! That a country's form of government must be in keeping with its natural elements is a foregone conclusion. Absolute ideas must take relative forms if they are not to fail because of an error in form. Freedom, to be viable, has to be sincere and complete. If a republic refuses to open its arms to all, and move ahead with all, it dies.

Source: Home

John D. Barrow, Between Inner and Outer Space: Essays on Science, Art and Philosophy (Oxford University Press, 2000, ISBN 0-192-88041-1, Part 4, ch. 13: Why is the Universe Mathematical? (p. 88). Also found in Barrow&#x27;s &quot;The Mathematical Universe&quot; http://www.lasalle.edu/~didio/courses/hon462/hon462_assets/mathematical_universe.htm (1989) and The Artful Universe Expanded (Oxford University Press, 2005, ISBN 0-192-80569-X, ch. 5, Player Piano: Hearing by Numbers, p. 250 <br class="br">Misattributed

The Artful Universe (1995)
Context: If a 'religion' is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.<!-- Ch. 5, p. 211

100 Years of Mathematics: a Personal Viewpoint (1981)

A New View of Society (1813-1816)
Context: All the measures now proposed are only a compromise with the errors of the present systems; but as these errors now almost universally exist, and must be overcome solely by the force of reason; and as reason, to effect the most beneficial purposes, makes her advance by slow degrees, and progressively substantiates one truth of high import after another, it will be evident, to minds of comprehensive and accurate thought, that by these and similar compromises alone can success be rationally expected in practice. For such compromises bring truth and error before the public; and whenever they are fairly exhibited together, truth must ultimately prevail.

Source: Systems theories (2006), p. 2.

Source: Education as a Science, 1898, p. 298.