Daniel Tammet’s book Thinking in Numbers: On Life, Love, Meaning and Math is an engaging
tour through a multitude of sites where mathematics and numbers weave through
art, literature, history, and our daily lives. With lively, quick-reading
prose, Tammet encourages us to appreciate mathematical thinking both as an
imaginative art form and as a fundamental way we understand the world around
us.
The book describes its own structure as “eclectic,”
and indeed each chapter is a separate journey into some new permutation of memoir,
historical anecdote, and mathematical meditation. Tammet draws extensively on
his own personal experience to illustrate that mathematics is beautiful and
even life-affirming. The discussion spans from Archimedes’ estimation of the
number of grains of sand in the world to Tolstoy’s use of calculus to theorize
war and peace to the mathematics of income inequality to religion’s role in
helping mathematicians imagine the infinite. The book continues its path,
traversing through the history of mathematics, the distinct beauty or cultural
meaning of specific numbers, and many other ways that math intersects with
other parts of culture, society, and family.
In some ways, this book is part of the genre of
popular mathematics books whose main goal is to convince the non-mathematically-inclined
to take pleasure in mathematics and to appreciate it as an art form similar to
poetry or music (and, secondarily, to provide math-lovers with mathematical-historical-cultural
tidbits to relish, though one suspects this secondary goal is the more common
one). In this regard, this book is one of the better ones, though not
necessarily a stand-out.
Where Tammet’s book stands out is through its
persistent fascination with how personal experience shapes mathematical
thinking in diverse and often surprising ways. Tammet writes, for example, of
how growing up in a large family of nine children shaped his understanding of
sets and subsets, how his diagnosis of Asperger’s and savant syndrome helped him
think about the mathematics of individuality, and how his synaesthesia affects
his intimate connection to particular numbers. Tammet also speculates about the
role of personal experience in the mathematical or scientific thinking of
figures from the past and present, analyzing, for instance, the influence of
the new “zero” on Shakespeare’s understanding of nothingness. Other examples include wondering if Anne
Boleyn’s rumored 11th finger affected how she understood counting and
halves, or suggesting that growing up in a large city makes one more interested
in studying the very large numbers needed to consider the possibility of extraterrestrial
life. These speculations are only sometimes convincing but almost always
thought-provoking and original.
Indeed one of the strongest chapters, “Poetry of
the Primes,” begins with a conjecture about poet Arnaut Daniel, the inventor of
the sestina who was both admired by Dante and likely a gambling addict. Tammet
suggests that the importance of the number six may have had some connection to
Daniel’s lifelong devotion to dice, but then expands the discussion to include
poet Raymond Queneau’s calculation of which numbers allow for a sestina-like structure
(fewer than you’d think, and the reason relates to prime numbers). Tammet then
considers haiku and various other traditions where prime numbers play a special
role in poetry, all leading up to a riveting (if sometimes a bit confusing)
argument that poetry is like the prime numbers in its most essential qualities:
like poetry, the prime numbers are mysterious, knowable only in gaps and
fragments, “unpredictable, difficult to define” and containing a multitude of
meanings, just as life itself does.
Another stand-out chapter is “A Model Mother,” in
which the notion of abstraction and modeling are used to explore Tammet’s
relationship with his mother. Tammet recalls childhood experiences in which his
mother diverged from the way he imagined her to be as an example of how models
differ from observed data. But when his mother does not live up to his idealized
image, Tammet frames the experience not as a disappointment but as a
realization that allowed him to understand his mother better as a human being.
He ends this chapter on models with a meditation on the complexity and the
emotional highs and lows of identifying strongly with a parent, adding another
layer to what a mathematical “model” can mean.
The book does have some weaknesses. The structure
jumps from one anecdote to the next, touching on a myriad of issues but only
occasionally going in depth. I, for example, was eager to hear much more of his
opinion on whether mathematical proofs that rely on computers can be beautiful
or reflect the personal style of the mathematician. There are also a couple of
factual errors in the historical information (the claim that money was invented
by the ancient Greeks, for example). Most of the information about history and
even much of the waxing rhapsodic on mathematical beauty can be found more fully
developed in other books. Tammet’s book, however, is eminently readable and
contains some unique and chapters that discuss mathematics’ relationship to
life and art through captivating examples and provocative arguments. In all, it effectively conveys Tammet’s point:
that “often we are barely aware of it, but the play between numerical concepts
saturates the way we experience the world.”
More importantly, Tammet convinces us that this constant interplay of numbers in our lives is something
to be savored.
