a two-digit number, reversed the digits, and subtracted one from the
other, the result was always divisible by 9.^1
Seeing as I wasn’t going to be able to toss a football around for a while, I
got a piece of paper and started checking my father’s statement. Every
number I tried worked; 72 27 45, which was divisible by 9. After a
while, my father found the error; or at least decided that maybe he should
play football with me. But the idea that there were patterns in numbers
took root in my mind; it was the first time that I realized there was more
to arithmetic than the addition and multiplication tables.
Over the years, I have learned about mathematics and related subjects
from four sources. In addition to my father, who was still attending Sun-
day-morning mathematics lectures when he was in his seventies, I was
fortunate to have some excellent teachers in high school, college, and
graduate school. When the Russians launched Sputnik in 1957, schools
scrambled desperately to prepare students for careers in science and engi-
neering; the Advanced Placement courses took on added importance. I
was in one of the first such courses, and took a wonderful course in calcu-
lus my senior year in high school from Dr. Henry Swain. One of my re-
grets is that I never got a chance to tell him that I had, to some extent,
followed in his footsteps.
In college I took several courses from Professor George Seligman, and I
was delighted to have the opportunity to communicate with him as I was
writing this book. However, the greatest stroke of good fortune in my ca-
reer was to have Professor William Bade as my thesis adviser. He was not
only a wonderful teacher, but an inspired and extremely tolerant mentor,
as I was not the most dedicated of graduate students (for which I blame
an addiction to duplicate bridge). The most memorable day of my gradu-
ate career was not the day I finished my thesis, but the day Bill received a
very interesting and relevant paper.^2 We met at two and started going
over the paper, broke for dinner around 6:30, and finished, somewhat
bleary-eyed, around midnight. The paper itself was a breakthrough in the
field, but the experience of going through it, discussing the mathematics
and speculating on how I might use it to develop a thesis, made me real-
ize that this was something I wanted to do.
There are a number of authors whose books had a profound effect on
me. There are too many to list, but the most memorable books were
George Gamow’s One, Two, Three... Infinity, Carl Sagan’s Cosmos, James
Burke’s Connections, John Casti’s Paradigms Lost, and Brian Greene’s The
Elegant Universe and The Fabric of the Cosmos. Only two of these books
were published during the same decade, which attests to a long-standing
vii Preface