It would be unthinkable for John Allen Paulos, noted mathematician and author, to write his memoir *A Numerate Life* without subjecting the form itself to a series of mathematical tests. Which is precisely what he has done.

How can simple arithmetic put lifelong habits into perspective? How can logarithms and exponentials shed light on why we tend to become jaded and bored as we age? On this foot, Paulos sets off to explore his own life story while taking on the building blocks of biography like memory (often inaccurate or fabricated), perspective (often biased), and the notion of a self (suspect at best). He returns with a trustworthy tale that answers a question steadily posed throughout the book: What ideas from mathematics might clarify certain aspects of a biography?

Upon sitting down to write your life story, the first subject to consider is, of course, yourself. You’ll need to describe you and you’ll need to do so while choosing how comprehensive to be. The more details you pinpoint, the more you’ll remove yourself from everyone else.

There are two kinds of people in the world, Paulos reminds us: those who are strange and those we don’t know very well.

To see this, he says, picture a straight line. Make it ten inches long and assign to it one area of interest or dimension. For instance: foods you like on a continuum from sweet to bitter. Those with more extremes tastes, like people who think sugar-coated maraschino cherries sound like a great idea and the ones who adore baker’s chocolate straight from the box, will fall within a half-inch from either end, so that normal tastes take up the middle nine inches. So far, more of us are alike than not.

Now take a second dimension, say musical tastes, ranging from vocals-free noise music to screaming bands. To measure people along both food and music dimensions, you’ll form a 10-by-10-inch square with these two lines, with a half-inch border for extremes. Recall that normal tastes fall upon nine inches of each side, creating an 81-inch area now that we’ve added the nine inches of “normal” musical tastes.

As you add dimension after dimension (forming what’s called a hypercube), that “normal” area become ever smaller, as the border of extremes increases in size (measured in number of people). To write a memoir that anyone will want to read, you’ll need to pick your biographical traits, or number of dimensions, wisely, so that you measure up as normal, with a touch of quirk.

Another tool you’ll need: the ability to think in numbers. *If you don’t understand arithmetic, how can you understand the world?* muses Paulos. He starts counting early: anything and everything, he reminisces, including the cigarettes in his father’s packs and the number of houses Santa Claus would have to visit in the few hours allotted to him, and comes up short on the latter. Santa’s “exploits just had to be bogus on quantitative grounds alone — all those chimneys and hot chocolates in one night,” Paulos realizes early on. When he tells unsuspecting students and neighbors that a football star once shook the hand of everyone in the stadium after a win, or that housing costs this year will top $3 billion, disbelief or belief follows quickly, but rarely with the analysis that based on a 4-second handshake the football player would have spent fifty-six hours shaking hands, or that the housing costs figure works out to about $10 per person.

When tracking down his memories, Paulos thinks of Benford’s law, a mathematical formalization of a strange numerical behavior that’s used to detect fraud in accounting departments and tax returns:

“In a wide variety of circumstances, numbers as diverse as the area of river deltas, physical properties of chemicals, figures in a newspaper or magazine, populations of small town, and the growth of money in an account all begin disproportionately with the number “1,” whatever units are used.”

Similarly, our memories show themselves at their most vivid and numerous when they come from our adolescence and early adulthood, and — after a long midlife gap — much later in life. Adulthood, with all of its changes and compromises, may not lend itself to memory at all, leaving memoirs to be told in light of only a certain period of your life: such “suspicious autobiographical reminiscences,” Paulos warns, could lead, however innocently, to biographical fraud.

Even fact-checking won’t hold up when scrutinized by the mathematical methods of probability. Imagine that a memoirist or a biographical subject tells the truth 1/4 of the time, and a source turned to for verification does so ¾ of the time: the events in question will turn out to be true only 3/16 of the time.

For more insight into what can affect accuracy, Paulos next asks us to ponder the word *intensional* — a technical term relied on in both logic and linguistics to mean the concept, the thing-ness, of a thing that springs to mind when we use words to represent it. What we “think, believe, and feel, and [interestingly] wager” will make it hard for, say, the word *dog*, to have equal meanings everywhere, thus allowing narrative logic to be stretched beyond reliability: one person’s hypocrite is another person’s nuanced, thoughtful protagonist. In mathematics, the fact that something can be shown to be equal to something else in the way that, say, the number four is equivalent to the “cube root of 64, the smallest integer bigger than pi, and 2 squared,” means that a statement can be true. How to qualify something as true in narrative logic remains at large.

There is as of yet no fix for these and many other pitfalls in tackling biographical writing, so often inadequate for the task of “getting at what a person is like,” yet so often compelling, beautifully written, and inspiring enough for us to read on regardless.

The way in which Paulos gets to his own life story in *A Numerate Life *should move us toward a new way to read this genre’s works. In place of something being “a biography of X,” in which only one narrative variable (the subject) is considered, Paulos suggests a two-variable approach, where something is “a biography of X written by Y.” Or, for those who wish for *even* greater accuracy, the three-variable approach: Something being “a biography of X written by Y at time Z,” to allow for change along the way.

It’s all in the name of a crucial kind of truth: who and how we really are.