"What exactly is mathematics? Many have tried but nobody
has really succeeded in defining mathematics; it is always
something else."

STANISLAW ULAM ( 1909-1984) ¹

Our story, of course, is not complete. It cannot be, for however much
we learn there is still more beyond our view. That is because the
house of mathematics is so large we can never hope to visit all of its many
rooms. Humans have been steadily accumulating a body of mathematical
knowledge since the times of the ancient Greeks--for 2,500 years. How
long have we been accumulating knowledge on the human psyche or on
bacterial organisms? Most fields of study are incredibly young compared
to that of mathematics. It has been known for some time that recorded
mathematical knowledge is so extensive it is impossible for one person to
become an expert on the entire field. If an individual can become reason-
ably proficient in just one small area, this is considered a substantial
achievement.

The fact that the body of mathematical knowledge is immense is both
bad news and good news, yet the good outweighs the bad. The bad news
is that neither you nor I can grasp it all, even if we lived two or three
lifetimes. However, the good news is that in our lifetimes, we will never
exhaust all those beautiful equations that are waiting to charm and mystify
us. How fortunate we are!

Yet, not knowing all of mathematics does not preclude us from under-
standing much about mathematics--that is, understanding, at least to a
limited degree, what mathematics is and how it relates to the human

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