My title is inspired by a passage I read, years ago, by the great British-American mathematician and philosopher, Alfred North Whitehead (1861-1947).

Alice B. Toklas (companion of the eccentric American writer, Gertrude Stein) once said that, in her many travels, she'd met exactly three geniuses. One was, of course, Gertrude Stein. One was the painter, Pablo Picasso. The third was Alfred North Whitehead.

With Bertrand Russell (1872-1970), Whitehead wrote the great logical classic, Principia Mathematica (not to be confused with Newton's work by the same name).

Whitehead's greatest (individually written) mathematical book is Universal Mathematics (1900), in which Whitehead compares (what I call) t-math with (what I call) o-math, and advocates their union, as I did before I became aware of Whitehead's notion.

Whitehead's greatest philosophical work is given in Process and Reality (1929, but corrected in 1978) -- a work understood (at best) superficially by all but a select few (not including moi).

My title is adapted from Whitehead's Science and the Modern World (1925), describing a vision which may surprise you:

"I will not go so far as to say that to construct a history of thought without profound study of the mathematical ideas of successive epochs is like omitting Hamlet from the play which is named after him. ... But it is certainly analogous to cutting out the part of Ophelia. ... For Ophelia is quite essential to the play, she is very charming -- and a little mad. Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings."

Countering the idea that we should study mathematics in order to learn how to think, Whitehead said, "Civiiisation advances by extending the number of importsnt operations which we can perform without thinkin about them."

Whitehead also said, "It is the business of the future to be dangerous.... The major advances in civilization are processes that all but wreck the societies in which they occur."