Quote of the Day

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.

—John von Neumann, quoted in The Works of the Mind