I had the pleasure this weekend of devouring Daniel Tammet’s 2012 essay collection, Thinking in Numbers. Part mathematical inquiry, part memoir, Tammet’s wonderful collection offers a wonderfully creative window into a new vision of life – a vision in which we are able to separate ourselves from a rigid common view of life and find awe and beauty in the swirling patterns that we pass each day without notice.

Tammet was born in London in 1979, and experienced early childhood epileptic seizures and unusual behavior. In 2004, at the age of 25, he was diagnosed with high-functioning autistic savant syndrome. The same year, he set a European record at the Oxford Museum of the History of Science when he recited from memory the mathematical constant of pi to 22,514 places. It took him 5 hours and 19 minutes, and he made no errors in the process.

Tammet began writing in 2005 with the autobiographical account of his childhood and young life, Born on a Blue Day. He followed soon after with his overview of contemporary neuroscience, Embracing the Wide Sky. Thinking in Numbers is his first book of essays and draws inspiration to live a more complete and wide-open life from the mathematics he observes in subjects including snowflakes, chess problems, and Anne Boleyn’s sixth finger.

Tammet starts his collection with the essay “Family Values,” in which he describes his family relationships with his eight siblings as an example of set theory. Set theory is the branch of mathematics that is concerned with sets, or collections of objects. In describing his his siblings and himself together, Tammet described them as a set:

We are, my brothers, sisters, and I, in the language of mathematics, a “set” consisting of nine members. A mathematician would write:

S = {Daniel, Lee, Claire, Steven, Paul, Maria, Natasha, Anna, Shelley}

Put another way, we belong to the category of things that people refer to when they use the number nine.

In considering his familial set, Tammet ponders the number of potential combinations of different Tammet children in any given location at a random time. Mathematics tells us that a combination of two, three, or seven siblings is a subset of the Tammet family set, and that the number of subsets in any set is 2* ^{n}*, where

*n*represents the number of set members. The potential combinations of the author and his siblings in any place and time is 2

^{9}, or 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2, or 512. To Tammet, a visit to the bakery with one brother and one sister represents just one of a defined 512 combinations of family members that might show up in that store that day.

Tammet explains the significance of this mathematical representation of his family. Viewed through this lens, his family instantly shares some a communal aspect with other sets that have this characteristic. These include members of a baseball team (9), planets in the solar system prior to 2005, before Pluto’s demotion (9), and United States Supreme Court Justices (9). New commonality appears where before were only family boundaries.

Reminding us that “Our mind uses sets when we think and when we perceive just as much as when we count.” Tammet then marks a consistent theme of his book, that familiarity with mathematics can change one’s point of view in everyday life:

Defining a set owes more to art than it does to science. Faced with the problem of a near endless number of potential categories, we are inclined to choose from a few of those most tried and tested within our particular culture. Western descriptors of the set of all elephants privilege subsets like “those that are very large, and “those possessing tusks,” and even “those possessing an excellent memory,” while excluding other equally legitimate possibilities such as Borges’s “those that at a distance resemble flies,” or the Hindu “those that are considered lucky.”

Tammet’s point is that our descriptions, categorization, and even view of the objects and people in our lives are mechanical, when so many different and accurate points of view are available to us.

In “Eternity Within an Hour,” Tammet begins a discourse that spans several essays regarding the numerical mysteries that surround us during every waking moment. He recounts discovering that, as a child on his walk to school, that it took him eight seconds to travel from one lamppost to the next. These regular intervals repeated themselves, eight seconds to each lamppost. It occurred to Tammet that at four seconds, he was halfway to the next lamppost. He halved the distance again at six seconds. One second later – seven seconds had elapsed – he had cut the distance in half again. This would repeat itself infinitely, over and over again, with the intervals becoming half as long and taking half as much time. But the presence of infinity was obvious to Tammet, who marvels over this hidden dimension of the “infinity of fractions that lurked between the lampposts on my street.”

Tammet reveals observations like these to be much more than mere curiosities. They are, in Tammet’s view, moments in which we may find meaning as human beings. In his essay *Einstein’s Equations*, Tammet considers the explosion of meaning that comes from the analysis of whether a number – 75,007 – is a prime number. In wrestling with this question, Tammet processes the subject number, first to a sum of 74,900 and 107. As 74,900 is 10,700 x 7, 75,007 becomes 10,700 x 7 + 107. More precisely still, the number becomes 1o7 x 100 x 7 + 107. Tammet notes that the mathematician’s “blood leaps with joy to recognize the repeated factor: 107.” The problem solved, he writes 75,007 = 107 x 701. It is not a prime.

This is a moment of human meaning, revealing natural beauty:

Human beings’ quest for meaning is perpetual; lack of meaning is offensive to the mind, and whatever the scale of the problem, a solution is a thing of beauty. Einstein’s equations solved problems such as “What do we mean by the words ‘time’ and ‘mass’?” A mathematician could tell us that the number 75,007 means to travel from 0 to 107, and then repeat the same distance successively 701 times. Other meanings, like those found in music or cricket, while more intimate and inexpressible, can prove just as powerful. Where chaos is subdued and the arbitrary averted, there lies beauty, and it is all around us.”

This discovery of beauty in the natural order hearkens all the way back to Pythagorus and his followers, who believed that the identities of all objects depend on form and not substance, and could be described using numbers and ratios. Thus, Pythagorus taught that the “entire cosmos constituted some vast and glorious musical scale.” Tammet admires the group as “the first to understand the world not on tradition (religion), or observation (empirical data), but through imagination – the prizing of pattern over matter.”

Tammet’s greatest successes in this book is his ability to extrapolate these abstract appreciations of natural beauty to an application of mathematics to life. In *A Novelist’s Calculus*, he reminds us of Leo Tolstoy’s considered use of calculus as a metaphor for the story of history in *War and Peace*.

As geometers study shape, the student of calculus examines changes: the mathematics of how an object transforms from one state into another, as when describing the motion of a ball or bullet through space, is rendered pictorial in its graphs’ curves. In these curves, smooth and subtle, girding the infinitesimal movements behind every human life, Tolstoy thought he was the blindness of contemporary historians.

Specifically, Tammet explains how Tolstoy believed calculus’s ability to identify and analyze the rates of change of extremely small events was akin to study of history:

The movement of humanity, arising as it does from innumerable arbitrary human wills, is continuous. To understand the laws of this continuous movement is the aim of history… only by taking infinitesimally small units for observation … and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.”

Tammet summarizes, “Kinds and commanders and presidents did not interest Tolstoy. History, his history, looks elsewhere: it is the study of infinitely incremental, imperceptible change from one state of being (peace) to another (war).” Ultimately, “change appears to us mysterious because it is invisible.” Nonetheless, Tammet recognizes that the impact of change renders a writer powerless to control his or her message to an ever-shifting audience.

If Tolstoy is right, his book cannot be understood with prior assumptions, rules, and theories. Everything has its moment, its context. Earlier, in one state, you began this essay, and now later on, you finish it in another. What do you think? I cannot tell you. In everyone and everything, the process of change always asserts its own meaning.

Tammet’s ultimate point is that mathematics simultaneously offers a reminder of our own finite capacities, and an opportunity to discover new beauty in patterns within our reach. “Properly understood,” Tammet writes, “the study of mathematics has no end: the things each of us does not know about it are infinite.” He closes his opening essay on his family and siblings with these fine words:

Like works of literature, mathematical ideas help expand our circle of empathy, liberating us from the tyranny of a single, parochial point of view. Numbers, properly considered, make us better people.