maticians and scientists are keenly aware that nature may frustrate all
their efforts. Sometimes, there is no music out there.
Physics is currently embarked on a quest started by Albert Einstein,
who spent perhaps the last half of his life in search of a unified field the-
ory, which physicists now call a TOE, for theory of everything. Not all
great physicists search for a TOE—Richard Feynman once remarked
that, “If it turns out there is a simple ultimate law that explains every-
thing, so be it.... If it turns out it’s like an onion with millions of layers,
and we’re sick and tired of looking at layers, then that’s the way it is.”^5
Feynman may not have been looking for a TOE, but Einstein was, and
many top physicists are.
Nevertheless, Einstein was almost certainly aware that there may be no
TOE—simple and elegant, complicated and messy, or anything in be-
tween. During the latter portion of their careers, both Einstein and Gödel
were at the Institute for Advanced Study in Princeton, New Jersey. Gödel,
reclusive and paranoid, would talk only to Einstein. Given Gödel’s proof,
that some things are unknowable, it is a reasonable conjecture that they
discussed the possibility that there was no unified field theory to be dis-
covered, and that Einstein was chasing a wild goose. However, Einstein
could afford to spend his creative efforts chasing a tantalizing wild
goose—for he had made his reputation.
It may seem surprising that even those who work in mathematics and
science without the credentials of an Einstein do not live in fear of work-
ing on a problem that turns out to be unsolvable. Such problems have
occurred with some frequency throughout history—and quite often, even
though the wild goose escapes, the result has not been failure, but the
discovery of something new that is usually interesting and sometimes
immensely practical. The stories of those “failures,” and the surprising
developments that occurred because of them, form the subject matter of
this book.
Of Bank Robbers, Mathematicians, and Scientists
When asked why he robbed banks, Willie Sutton replied, “Because that’s
where the money is.” Every mathematician or scientist dreams of making
a remarkable discovery—not because that’s where the money is (although
fame and fortune do occasionally await those who make such discover-
ies), but because that’s where the fascination is: to be the first to observe,
or create, or understand something truly wonderful.
Even if that’s where the wild geese lurk, we have a desperate need to
solve some critical problems—and a strong desire to solve some intriguingIntroduction xvi