My interest in mathematics was galvanized by what in retrospect seems to be horrible pedagogy bordering on child abuse. I mention the incident here and will describe it in less lurid tabloid terms a bit later, because it hints at a motivation for both my career in mathematics and my skeptical attitude toward biography and autobiography. I look back and wonder, Is the story true? Is it balanced? Is it representative? The answer is “yes, more or less,” but, although I am its protagonist, I still have reservations about its accuracy. I'm sure I'd have even more about your stories.

Whether because of my natural temperament, my training as a mathematician, or a late midlife reckoning, I look on the whole biographical endeavor, my own included, as a dubious one. Even George Washington's signature line about cutting down the cherry tree, “I cannot tell a lie,” is probably flapdoodle. More likely he said, “No comment” or “I don't recall the incident” or maybe “The tree was rotten anyway.” I tend to scoff when reading that a new biography has revealed that the great So-And-So always did X because (s)he secretly believed Y. I'm not particularly ornery, but I often react to such statements about the alleged actions or beliefs of well-known people with a silent “That's B.S.” A more likely reaction if someone makes the claim directly to me is a polite, but pointed “How do you know that?” or even “How could anyone know that?” or, in the case of autobiographies, “How could anyone remember that?”

Memories are often inaccurate or fabricated, perspectives biased, “laws” and assumptions unfounded, contingencies unpredictable; even the very notion of a self is suspect. (But like the nutritionist who secretly enjoys candy and donuts, I've always enjoyed reading [auto]biographies, ranging from James Boswell's The Life of Samuel Johnson, LL.D. to Mary Karr's Liars’ Club.1)

Given my skepticism of the biographical enterprise, it might seem I've taken a bold and/or foolhardy step to write a quasi-memoir of my own, but quasi- here means “not so much.”

True to my doubts, what I've written is a meta-memoir, even an anti-memoir. Employing ideas from mathematics (quite broadly and non-technically construed) as well as analytic philosophy and related realms, but requiring no special background in mathematics, I've tried to convey some of the concerns and questions most of us don't, but arguably should, have when reading biographies and memoirs or even when just thinking about our own lives. The “arguably” is the burden of this book; imparting a certain modicum of mathematical understanding and biographical numeracy is its presumptuous goal. (I say presumptuous because of the nebulousness of the notion of biography and the vast variety of different biographies. In a more concrete direction there is the specificity of the book's focus on conventional biographies, mine and probably yours.)

One of the first questions that comes to mind when considering a life is an abstract “What is its average length?” or perhaps a more visceral “How long have I got?” Quite relevant is evolutionary biologist Stephen Jay Gould's article “The Median Isn't the Message,” in which he describes his cancer diagnosis and the associated median life span of eight months that it allowed.² But the median, of course, is not the mean or simple average of patients’ life spans; it is the life span shorter than which half the patients survive and longer than which the other half do. Moreover, the statistical distribution of life spans is right-skewed, meaning many people live considerably longer than the median as did Gould (twenty years). Knowledge of statistics and distributions allayed his anxieties and, more generally, as I'll try to show, mathematical knowledge can shed much-needed light on many other life situations and life stories.

Let me illustrate with a somewhat disguised statistical point. Whatever else a biography may be, it is usually considered to be a story, the story of a person's life. And probably people's most common response to a story is a tendency to suspend disbelief when reading, hearing, or viewing one in order not to spoil its enjoyment. “Let's pretend. It'll be fun.” This mindset is quite opposed to that prevailing in mathematics and science where people typically suspend belief in order not to jump to conclusions until they have compelling evidence. “Wait. Why should we believe that?” These two different approaches are not unrelated to different tolerances for false-positive and false-negative conclusions, which I'll elaborate on later. Not surprisingly, perhaps, the latter show-me tentativeness is the approach I will adopt here. It's in line with the bumper sticker that counsels: Don't believe everything you think.

How did I come to write a book on such disparate realms as mathematics and biographies? After all, fish don't need bicycles, and flashlights don't use solar power, and biographies don't seem to need or use mathematics, hence this extended justification. One element of my biography (or psychology) that disposed me to write this book is that I've always liked the idea of rubbing together incongruous subjects, which seems to me almost a necessary condition for generating creative ideas. At times this habit of rubbing together has earned me a good number of eye rolls, sometimes even a bit of vituperation. People don't always like it when notions or relations they hold dear have reflections in domains such as mathematics that they consider reductive or somehow inappropriate.

That's too bad considering that mathematics is a most productive way of looking at the world. The philosopher Ludwig Wittgenstein once remarked that he looked forward to the day when philosophy disappeared as a subject but all other subjects were approached philosophically. I have a related but weaker wish for mathematics. I certainly don't wish for it to disappear as a subject, but I do wish that it, too, was more widely seen to be an adverb and that its insights and ideas could inform the approach to all other subjects, including biography. With this as a partial motivation, I have over the years written about the connections between mathematics and humor, journalism, the stock market, analytic philosophy, religion, and a number of other topics (but not fish and bicycles). Nonobvious but significant points of correspondence almost always arise if one searches for them.

Here I hope to show that the points of correspondence between mathematics and biography are, despite superficial appearances, quite profound. Carl Sagan, the astronomer, skeptic, and science writer, wrote that we—our DNA, our teeth, our blood—are starstuff, made out of the very same material as the stars. As naturally occurring entities in the universe, we are, in a sense, also “mathstuff”—changing and developing according to mathematically expressible relations, instantiating mathematical notions of all sorts, and illustrating mathematical principles from diverse fields. “Mathstuff,” I maintain, is a defensible neologism since patterns are, at least to mathematicians, nonmaterial stuff. It's thus eminently reasonable to try to obtain an understanding of this mathstuff of which, it can be maintained, we and everything else are made. In particular, how do these mathematical patterns express themselves in our life stories?

A less exalted factor in deciding to write this book is perhaps a bit too much self-reflection (a trait I share with all my fellow part-time solipsists). A while ago I had written a few short autobiographical sketches that I liked. Given my predilections, I wondered if a few of these personal vignettes might serve as jumping-off points, each providing a concrete illustration of general mathematically flavored insights about biographies—observations, perceptions, and experiences that would resonate widely.

For an early (and probably not uncommon) arithmetical example, I recall that even as a very young child I silently determined that the story of Santa Claus's exploits just had to be bogus on quantitative grounds alone—all those chimneys and hot chocolates in one night! Even then I wasn't very good at suspending disbelief. And as an adult I've found it all the more natural to wonder about the probability of certain reported events (not involving Santa) really occurring, whether because of purposeful lying or notoriously unreliable memories, or how to roughly quantify the strangeness of an event or the quirk of someone's personality, or what numbers and logic might intimate about both the quotidian happenings and the long arc of a life. So I've given myself the congenial task here of examining the structure of generic memoirs and biographies from a thoroughly skeptical and perhaps occasionally annoying perspective. I subject even the notion of a romantic crush to a mathematical analysis.

As mentioned, in some of my previous books, including Innumeracy, A Mathematician Reads the Newspaper and A Mathematician Plays the Stock Market, I tried to show how math (again, quite broadly construed) can help us understand and analyze certain areas of real life. I employ some of these same basic mathematical ideas here in an attempt to better comprehend our lives, in particular the enhanced, distorted, even imaginary narratives about ourselves that we all effortlessly create. I am repeatedly struck by recurring questions when I reread some of my brief remembrances or recall events from long ago. How did I get here from there—the psychological as well as the physical path? Not novelist Anne Tyler's “wrong life,”3 but certainly a different and unexpected one. Who was that kid, the one who, strangely to me now, loved playing with toy soldiers, tanks, and ships, and tacked model airplanes to the ceiling over his bed? How have I changed and how have I just gotten older? To what degree have I misremembered or embroidered events? Where'd my story of me come from?

But what is of much more universal interest are the constraints on any life story—mine, yours, his, hers. In particular, what are the ideas from mathematics that might clarify certain aspects of any biography?

How does one tell a life story or, more accurately, selected parts of it?

To what extent is the choice of incidents related likely to be biased—statistically, psychologically, otherwise?

How should we evaluate past decisions (or future ones)?

What kind of plastic, ephemeral, or nominal entity is the self?

What can one say of the general shape or trajectory of a life story?

And what roles do chaos, coincidence, probability, topology, social media such as Twitter, quantitative constraints, and cognitive delusions play in our lives and in their depiction in biographies?

Some of the specific questions addressed herein are:

How might the notion, borrowed from mathematical logic, of nonstandard models of axiom sets be relevant to the predicting of our futures?

How are our lives, in a profound sense, joke-like?

How does nonlinear dynamics explain the narcissism of small differences sometimes cascading into siblings growing into very different people?

How can simple arithmetic put lifelong habits into perspective?

How can higher-dimensional geometry help us see why we're all literally peculiar, far-out?

How can logarithms and exponentials shed light on why we tend to become jaded and bored as we age?

How can probability and card collecting tell us anything about our so-called bucket lists and the contingency of life's turning points?

How come I begin every question with How?

How can algorithmic complexity and Shannon entropy balance past accomplishments and future potential?

How can we find the curve of best fit that captures the path our lives have taken?

I will herein attempt to explain how these and other mathematical constructs say something of significance about biographies as well as all our unchronicled lives.

One obvious obstacle to the writing of somewhat truthful memoirs and biographies already alluded to is that people, especially the authors, tend to lie or at minimum embroider. And it's not just authors, of course. I remember my grandmother telling my grandfather that it was late and that he should stop playing cards with his friends. His reply was always the same, both humorous and slightly paradoxical, “We'll be through in a little while. We still have a few more lies to tell.” I'll discuss lies and the paradoxes to which they sometimes give rise in a bit, but they are not the most daunting obstacle.

As oddities from philosophy and psychology make clear, people's perspectives and evaluations of situations and others’ behavior not only differ greatly but change over time. For example, the comedian Louie C. K. rants about a fellow plane passenger who became irate because the Wi-Fi on the plane was so primitive—the plane, you know, that aluminum tube that was flying him through the air at five hundred miles per hour and an altitude of seven miles. Holding historical figures to a contemporary standard of political correctness also illustrates the phenomenon. Recently the life of the great physicist Richard Feynman has undergone reevaluation, and he's been adjudged quite sexist by contemporary mores.

I listen to golden oldies pop songs from the ’50s and ’60s on Sirius radio, songs Feynman might have listened to occasionally. I'm often shocked by the benighted sentiments implicit in the songs and doubly shocked by the way I can ignore the lyrics and still resonate with the songs.

Another personal example: In Once Upon a Number I recalled an event from my childhood that illustrates this change of evaluation. As kids, my brother and I would visit our grandparents and regularly make our way around the leafy neighborhood taking turns throwing darts at the large trees that were planted every twenty-five feet or so between the sidewalks and the streets. We kept meticulous score of how many of them we each hit. Once after he had beaten me, I convinced my brother to have this contest in our underwear. He never realized until we'd returned to our grandparents’ house that I was wearing swimming trunks under my underwear. In his anger and my gloating, we both accepted that I somehow had appeared less moronic than he during this escapade.

More generally—a phrase that appears often herein as I move from a personal incident or observation to a more abstract or universal rendering—how can we bring some mathematical muscle to the analysis and evaluation of common biographical anecdotes and stories?

I reiterate (reiterating being an occupational hazard of being a professor) that I take a singular approach: to simultaneously explore biography from a personal point of view and from the perspective of a mathematician interested in the no-man's land where my discipline comes within hailing distance of another domain—somewhere between Plato and Play-Doh, math and myth, Pythagoras and Plutarch. (More to the Play-Doh side is the observation that there is a fine line between numerator and denominator.) The book is terse, perhaps cloyingly self-indulgent in places, although very far from a tell-all and admittedly a somewhat weird amalgam.

Its progression will be episodic and nonlinear (although the autobiographical sketches will be roughly chronological), and connected by an introspective, mathematical sensibility leading to brief discussions of relevant theoretical matters, some distilled from previous works (my personal golden oldies). In a rough, approximate way the numbers and the narratives (if you'll allow the alliteration) will alternate throughout the book and, like life, will be a bit of a mishmash. But, as the Czech writer Milan Kundera asked, “Isn't that exactly the definition of biography? An artificial logic imposed on an ‘incoherent succession of images’?”4

To set the stage, a few simple facts crammed into a very long sentence to begin and moor this quasi-memoir: I was born in 1945; grew up in Chicago and Milwaukee; graduated from the University of Wisconsin; went into the Peace Corps to avoid the draft; returned to Madison where I met my beauteous wife, Sheila, and received my PhD in mathematics; moved to Philadelphia to teach at Temple University; had two wondrous children (who have recently begotten three grandchildren); wrote some books on mathematics, a couple of which were bestsellers;⁵ and gradually, as I became less intelligent, became more a writer than a mathematician. I'll begin with a couple of numerical childhood memories far enough in the past so that the golden gauze of nostalgia has settled over them.