Booklinks PAUl CoNlIN
Is God a Mathematician?
by MARIo lIvIo—(SIMoN & SCHUSTER, 2009)
FRoM 1984 To 1987, I attended the University of Massachusetts
at Amherst. The school’s defining architectural feature at the time was
the 26-story library (then the second-tallest college library in the na-
tion, after the University of Texas) at the center of the campus, which
provided stunning views of the surrounding Pioneer valley and berk-
shire Mountains of Western Massachusetts. These views made the
building, especially the upper floors, a popular studying location, even
more so than is standard for a campus library.
During a break from a study session
at some point in my undergraduate education, I stumbled across the 50-or-so
shelves of bound journals and periodicals
archived in the tower. Some of the journals had been continuously published for
decades, others for just a few years before
being discontinued. I recall my curiosity
drawing me to scan and randomly open
certain volumes. A bound periodical
isn’t quite a book (since, unlike a book,
it intends to provide current, new information each month or quarter) and isn’t
quite a newspaper (since, unlike a daily
newspaper, or even a magazine such as
Time or BusinessWeek, it’s printed on
sturdy paper that’s obviously intended
to sit on shelves indefinitely). The titles
of many of the sets that I picked up escape me now; I recall one dedicated to
Central European history, one covering
sociology and criminology, and a variety
of law reviews, etc.
But there was one, the opening of
which made a lasting impression on
me. Its title was innocent-sounding
enough: Journal of Finance. Never has
the gap been so wide between my expectation upon opening a text and my
realization of its contents. I expected
to find research and discussions on
corporate capital structure and the
cost of capital, perhaps stock price
movements and historical performance, maybe some banking and monetary economics. Instead, I was confronted with hundreds of pages of the
most dense, impenetrable mathematical formulas I’d ever encountered.
Bear in mind, I was pursuing a degree
in mathematical statistics, so I was thoroughly conversant in undergraduate-level
probability distribution functions, linear
regression analysis, and analysis of variance, partial differentiation, and multivariate integration. But as surprising as it
was for me to discover mathematics that I
couldn’t at least get my arms around after
a few minutes of consideration, for this to
originate from a financial periodical was
perplexing. (The Journal of Finance is still
in print, its six 2008 issues publishing more
than 3,000 pages of scholarly papers.)
It was only several years later, when
I began studying for the Society of Actuaries’ exam on asset management and
investments (at the time, SOA Course
220), that I was able to connect the dots
and comprehend the subject matter
upon which I had accidentally stumbled. That course covered the capital-asset pricing model, the Black-Scholes
option-pricing formula, and the fundamentals of subject matter that falls
under the rubric of financial economics. Financial economics was enjoying
wide and growing acceptance in many
circles, had generated a series of Nobel laureates, and was about to interact
with actuarial science. This interaction
has been, at times, graceful—by my informal count, approximately half of all
articles in the North American Actuarial
Journal have content related to financial
economics—and sometimes not. Actuary Jeremy Gold has argued forcibly
that financial economics conflicts with
both actuarial and GAAP prescriptions
for defined benefit pension plan accounting, triggering a series of actuarial
forums on the topic.
I bring up this personal history as a
means of explaining why I have problems with the structure of Mario Livio’s
latest book and yet believe he’s onto
a topic that has great implications for
all business professionals who work to
quantify financial phenomona. Livio’s
book gave me the ability to articulate to
myself the confusion that arose in me a
quarter century ago.
The Book’s Shortfalls
Livio is an unquestionably erudite and
curious author who is interested in
multidisciplinary topics. He’s an astrophysicist by profession and has written
three prior texts on the topics of pure
mathematics and mathematical physics. In this book, he covers mathematical puzzles and problems created by
almost every famous mathematician
