# A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours

John Allen Paulos is mathematics professor at Temple University, a columnist, media figure, often invited for public lectures, an intensive twitter, and author of several popular books on mathematics. His first book *Innumeracy* (1988) in particular is well known in which he exposes the dangers of mathematical illiteracy and misconceptions among common people. Other books deal with mathematics in relation with stock markets, humor, and religion.

From reading the introduction, it was already clear to me that I was in for something different, something besides the ordinary of a popular math book slash autobiography. And indeed after I finished reading, it is difficult to classify or characterize the contents. Perhaps it could be defined as a book about an attempt by a mathematician to write a partial autobiography, and perhaps somewhere the word numerate should also be smuggled in too. There are some chunks of an autobiography indeed, and they are in a rather chronological order. And then there are also almost philosophical reflections upon what it is like to write a biography or an autobiography. Is it even possible to tell a life story? How reliable can a biography be? In fact, as he did in his previous books: apply mathematics to unmathematical questions, he applies here mathematics to questions that can (and should) be asked when writing a biography. There are excursions about mathematics too of course, often drawing parallels between mathematics and some other event or situation or concept. At the end of the introduction he gives his cv in about 10 lines. These are the facts, and although we learn something about the personality behind these facts, there are not many essential facts added while reading the rest of the book.

While telling some anecdotes from his childhood, he applies his mathematics like in *Innumeracy* to several of the items like for example the probability of obtaining a missing baseball card. Or think about this problem: Cut 1/2 inch from all sides of a 10 inch cube and the remainder is? Only about 73%! Most people would spontaneously estimate a much larger part. This trick of smuggling in the numerics is repeatedly applied in other chapters too. He has a particular fascination for the number e. Problems whose result is related to e keep showing up. Paulos also displays his sense of humor. Sometimes the joke is mathematical or logical, style Groucho Marx, who is one of his favorites. When Paulos was a guest in a tv-show, he was interviewed by a model (more beautiful than numerate), she was reading the question from a poster behind him, he waited till the text disappeared and then asked her to repeat the question. Mumbling and stumbling she tried to reformulate it. Afterwards the producer thanked him for exposing something to the manager that he himself had suggested several times before. .

There is some mathematics is every chapter. Several chapters deal largely with statistics. For example, it is observed in practice that the normal distribution does not hold near the pass/don't pass grades but shows some discontinuous drop. The average person does not exist, in fact everybody is abnormal. More statistics in a later chapter on dating (a well known rule says that you have to take the next best after rejecting the first 37% of the candidates and he notes that 37% is approximately 1/e). And when after dating you decide on living together you might wonder what is most effective, leaving the toilet seat up or down?. More statistics are needed to analyze the probability of (seemingly unlikely) coincidences.

And there is more math stuff. There is the problem of self-reference in an autobiography. Writing the autobiography affects the author, leading to problems of infinity and the continuum hypothesis. Life is also very complex, depending on a zillion of parameters, so that a biography is automatically an approximation problem. The butterfly effect may result in a completely different outcome of anybody's life. Here he attaches the anecdote that he wrote in one of his columns that the margin of error was larger than the margin of election referring to the balance of the votes in Florida during the presidential election in 2000. A judge cited him and ordered re-counting the votes, resulting in the election of George W. Bush, which he still regrets.

How come there seems to be some tendency to have more memories from your childhood than from the central part of your life. Is that a kind of Benford's law? But there are some turning points in his middle life and these he surely remembers: marriage, becoming a father, Bertrand Russell who answers to one of his letters, the publication of his first book etc.

For the biographer, there is also the problem of quantitative information. With a quantified selver like Stephen Wolfram, numbers is no problem at all. Paulos doesn't even have a Facebook account, but he belongs to the Twitter community, an occasion to do some mathematics again: he compute the number of possible tweets, and he explain some network analysis defining hubs and authorities and explains the small world phenomenon as a result of network distances like Erdős and Bacon numbers.

Paulos had a bad experience with stock markets because he lost a lot of money through the WorldCom debacle. He wrote a book *A Mathematician Plays the Stock Market* about it and also here this episode is represented. Just like also his other books are shimmering through in this one at several places.

Perhaps lives are too complex, too fractal, too multilayered, and a person cannot be completely understood (a digression on Chaitin's algorithmic information theory), hence can not be caught in a biography. Life goes on in his children and grandsons and after thinking about mortality (Gompretz' law), he reflects on topology (lives can be very different and yet still be conformal) and Brouwer's fixed point theorem (completely different lives may still have a common fixed point where they meet). As life tends to its end, it approaches a steady state, meaning that highlights become less frequent. After some reminiscences about his father, he concludes with the empty set, a set from which all the integers, and rationals and reals and in fact all mathematics can be created.

I really did enjoy reading this book. Paulos writes very eruditely, although his thoughts sometimes wander away from the main line, there are wonderful things said in many of his excursions. He is philosophical, charming, and funny in a gentle way. I don't know if all the mathematical puns will be understood by non-mathematicians, but for mathematicians, it is a wonderful and playful (self-)reflection on mathematicians, their mathematics,... and their biographers.

**Submitted by Adhemar Bultheel |

**30 / Jul / 2016