A Numerate Life, by mathematician John Allen Paulos, is memoir that uses the author’s autobiography primarily as a jumping off point for an exploration of a number of interesting concepts in mathematics, philosophy and psychology.  Paulos is an engaging writer who is able to explain a wide range of concepts in a way that is accessible while at the same time precise and informative.  Although a large part of the aim of the book is simply to introduce readers to ideas that Paulos finds interesting or important, a consistent thread throughout the book is an extended argument about the limits of biography. 

          Throughout his descriptions of his own experiences, Paulos self-consciously cautions his readers about the unreliability of biography.  He notes that much of his book is intended to show that “people in general and biographers in particular are often, to use a common slang expression, full of it.”  (pg. 163)  One might reasonably ask, however, whether most readers really need much convincing of this claim.  Surely the fact that many biographies are inaccurate, whether through intentional bias or simple error, is a well-established bit of folk wisdom.  In fact, though, his focus on biography undersells what’s really most interesting about Paulos’s arguments, which is that they serve to challenge popular preconceptions about personal identity and selfhood.

          His central argument is relatively simple.  He notes that memory is notoriously unreliable, even as regards deeply personal events, and suggests that much of what we think of as accurately describing  the past is in fact a kind of personal autobiographical storytelling.  All storytelling, he argues, involves the creation of a coherent and interesting narrative, and so our personal storytelling requires that some salient features of past situations be emphasized over others, some motivations exaggerated and others forgotten.  The result is that one’s notion of one’s “deepest self” is a kind of fiction that probably fails to reflect the more complicated and less coherent aspects of our actual lives. 

          One’s reaction to this realization, Paulos suggests, should be an increased humility about the limits of self-knowledge.  Far from being uniquely accurate reporters on our own lives, we are hopelessly self-interested interpreters of a vast complex of events, which we remember, if at all, only through a fog of bias and self-mythologizing.  This sort of skepticism about the essential self has a long philosophical pedigree (as Paulos readily acknowledges), but it is relatively rare to see it expressed outside of the philosophy classroom.  Given the prevalence of appeals to personal identity in popular discourse (“this is just who I am.  . .”, “you’ve got to be true to yourself”  etc.)  a thoughtful, accessible challenge to the coherence of such notions is a welcome development.   

          Throughout the book, Paulos illustrates his points and entertains his reader by telling stories from his own life.  However, anyone looking for a revelatory exploration of who John Allen Paulos really is will not find it in this book (and Paulos of course will say there is no such thing as “the real John Paulos” to be found).  The personal anecdotes largely serve to illustrate his points, a task at which they for the most part admirably succeed.   These stories are also invariably entertaining, whether they’re concerned with the shoplifting exploits of his grandmother, his youthful correspondence with Bertrand Russell or his grandson’s potty training.  Collectively they make reading the book something like having a friendly conversation at a bar with a very erudite drinking companion.  

          One of the anecdotes appearing near the end of the book provides a particularly striking example of how Paulos uses his own biography.  Having noted that biographers are likely to luck into accurate claims about their subjects, he relates this possibility to Edmund Gettier’s famous examples of beliefs that appear to be both true and justified and yet fall short of knowledge.  He illustrates this point with an example taken from his own childhood involving another child’s justified belief that Paulos had broken a window playing ball.  Having read most of a book-length discussion of the unreliability of biography, most readers are likely to wonder whether these events really occurred as Paulos remembers them.  How likely is it, really, that something happened to him as a child that so perfectly illustrates a famous philosophical argument?  I strongly suspect that Paulos expects and welcomes this kind of question, and they readily give substance his description of the book as a “meta-memoir, or even and anti-memoir.” (pg. 10)

          Paulos has spent much of his career actively engaged in teaching mathematics and evangelizing for the importance of his field, both in his capacity as a professor at Temple University and as a writer of books and articles intended for a general audience.  This book continues that mission by very effectively explaining a wide variety of mathematical ideas.  The connections between the particular mathematical examples Paulos discusses and his central thesis about biography are occasionally somewhat tenuous, but that is simply a product of the dual purposes of the book.  Paulos has substantial points to argue regarding biography, and he does so effectively, but he also obviously intends this book to further his readers’ understanding of the usefulness and beauty of mathematics, and in order to accomplish that he is often willing to stray away from discussion of biography in order to give proper due to the mathematical issues that he raises.

          Popular accounts of technical subjects invariably face a difficult task in balancing accessibility with rigor, but Paulos successfully meets this challenge.  His explanations avoid the tendency towards vague metaphor that frequently plagues popular writing on mathematics, but still remain accessible to readers with little background in mathematics.   Paulos makes the case for mathematics in at least two different ways.  He first of all shows how fluency with mathematical concepts is a key part of general good reasoning.    For instance, he argues that the ability to properly interpret statistics can increase our understanding of current events, and he discusses how conspiracy theories often result from misinterpretations of probability claims. The second way Paulos advocates for mathematics is by simply displaying the inherent beauty and interest of mathematical results, which he accomplishes in the course of covering topics including the continuum hypothesis, Kruskal’s card trick and Benford’s Law.

          A Numerate Life is worthwhile reading for anyone with a general interest in mathematics and philosophy.  It is consistently enlightening and entertaining, and it provides an accessible tour of topics of mathematical and philosophical interest that reflect the author’s wide and varied knowledge in a number of fields.  The central thesis of the book is well-argued and substantial, offering something for both the general reader unfamiliar with the traditional issues raised by personal identity and the philosopher looking for new perspectives on how to teach those issues. 

© 2016 T.G. Murphy

T.G. Murphy, Assistant Professor, Philosophy, SUNY Potsdam