In the minds of mathematics teachers, calculus has long held the honor of being the gateway to college mathematics. But while many mathematics educators have wrestled with the vexing pedagogical questions posed by introductory calculus, in the meantime millions of college students — often sitting in courses taught by business and social science departments on the other side of campus — have been introduced to a college mathematics of a completely different sort. I'm talking, of course, about statistics. Just as calculus teachers have wrestled with the question of how to teach calculus more effectively, so too have statistics teachers wrestled with the question of how to re-invent statistics using the same tools. The particular question of how history and biography could play a role in this endeavor was on my mind when I picked up Statisticians of the Centuries.
This book, edited by Chris Heyde and Eugene Seneta and sponsored by the International Statistical Institute, consists of more than 100 biographies of individuals who have contributed to the development of probability and statistics. After a brief five-page introduction to the state of probability and statistics prior to the seventeenth century, the book begins in earnest with a biography of Fermat, the seventeenth century mathematician who was one of the first to seriously consider questions in probability when he wrestled with the problem of how to divide the stakes in an unfinished game of chance (a.k.a. the "problem of the points"). From there, the biographies follow a roughly chronological order until they end 490 pages later with a biography of William Edwards Deming, a modern statistician famous world-wide for his work in quality control and whose death in 1993 was (we are told in the preface) an impetus for undertaking this book. Though dozens of authors have contributed articles to the work, all of the biographies are formed from essentially the same mold. Each begins with a paragraph-long summary and ends with a brief bibliography. In between is a biography of 3-5 pages (with a few more pages being devoted to more important contributors).
There is not much mathematics to be learned from these biographies. The brief article format simply doesn't lend itself to presenting detailed mathematics. In fact, mathematical formulas appear only a handful of times throughout the entire book, and usually without justification. But this isn't really a criticism of the book. Rather, it's a warning about what to expect from it. As the editors themselves note in the preface, this book
aims to demonstrate the achievements of statistics to a broad audience . . . through short biographies that put the statistical work in its historical and sociological context, emphasizing contributions to science and society in broad terms rather than narrow technical achievement.
In other words, this isn't as much a book about mathematical thought processes as it is a book about the personal and social lives of those who discovered the mathematics. Instead of detailed mathematics, look for broad descriptions of mathematical ideas surrounded by information about personal milestones, positions held, interpersonal squabbles, and major publications.
Some of the mathematicians mentioned in the book will be familiar to anyone with even the slightest interest in the history of mathematics. In fact, many of those individuals who contributed to the foundations of probability — names such as Pascal, Huygens, Bernoulli, Laplace, and Gauss — also contributed in a fundamental way to many other branches of mathematics. For these mathematicians, Statisticians of the Centuries will provide a general introduction to a side of their mathematical work not usually treated in a typical history of mathematics. But this trip down the road of classical probability theory occupies only a small portion of the book. As the editors note in their preface, "statistics is interpreted broadly, and it is notable that many of the most important practitioners were major contributors to, and may be best remembered for, their work in other areas." So, for instance, sandwiched in between biographies of the well-known Christiaan Huygens and Jakob Bernoulli, we are given the biography of Caspar Neumann, a seventeenth century church pastor who "objected to the prevailing opinion of his time that human birth and death are determined by the position of the planets and comets, or governed by magic numbers" and set about compiling a record of births and deaths in his native Breslau in order to prove his point. These observations would later be used by Edmond Halley to derive some of the first actuarial tables.
But the classical contributions to probability and statistics occupy only a small portion of the book. Instead, the editors, while limiting themselves to individuals born before the twentieth century, are more interested in chronicling the explosion in statistical reasoning that modern times have brought. In fact, the sections devoted to the sixteenth, seventeenth, and eighteenth centuries are together covered in less than 100 pages. In contrast, biographies of those contributors who flourished in the twentieth century occupy more than half of the book.
And that's where my enthusiasm for Statisticians of the Centuries begins to wane. I was originally drawn to this book because I'm a true believer in the power of history and biography to enliven mathematics education. In a nutshell, by making use of history and biography, mathematics educators can show students that mathematics is not an insurmountable mountain of logical abstraction dealt with by a special class of people, but a fundamental and important human endeavor undertaken by ordinary people with real problems to solve. The problem is that many of the biographies presented in Statisticians of the Centuries — particularly those in the latter half of the book — just don't make this point. To be sure, there are interesting vignettes to be found. (Consider the story of William Sealy Gossett, who was drawn to statistics by his work at the Guinness brewery and who, using the nom de plume "Student", would eventually derive "Student's t-distribution".) Additionally, biographies of a handful of female contributors are also included, so the book could be used as a (somewhat limited) resource for understanding the accomplishments of women statisticians.
But by-and-large the typical biography of a modern statistician as seen in this book is, well, uninteresting. To begin with, while some of these later individuals will be familiar at least in name to just about anybody (e.g., John Maynard Keynes) or to any mathematician (e.g., Maurice Frechet), a great many of them (e.g., Edwin Pitman, or Gertrude Cox, or George Knibbs) may not even be familiar to practicing statisticians. There's nothing wrong with being obscure, but the question statistics teachers will ask is: How will these biographies interest my students? The answer won't be found here. In fact, a biography of a modern statistician as presented in Statisticians of the Centuries could often be summarized by something like: "Statistician Jones was born in X. While at the University of Y, he first began to consider the importance of mathematical theory A. After moving to the Institute of Z, he also began to look at the theory of B. However, Professor Jones is most known for his work in C..." For students with only a vague understanding of the mathematical importance of A, B and C, this is not material for an inspiring research project.
Don't get me wrong. This is an important book. It provides a broad historical introduction to one of the most important strands of mathematical thought in the twentieth century, and it does so by highlighting the contributions of key players from many disciplines. It's also a book that should be in the library of any institution that wants its students to have a well-researched and well-referenced alternative to the random biographical information that a typical Internet search engine will find out on the world wide web. But the tone and content of the book will make it interesting primarily to professional historians and statisticians looking to find their roots. Mathematical generalists hoping to find a Men of Mathematics for statistics will have to search elsewhere.
Andrew Leahy (firstname.lastname@example.org) is an Assistant Professor of Mathematics at Knox College.
Probability Prior to Pascal.- 17th Century: Pierre de Fermat (1601-1665). John Graunt (1620-1674). Blaise Pascal (1623-1662). Christian Huygens (1629-1695). Caspar Neumann (1648-1715). Jakob Bernoulli (1655-1705). John Arbuthnot (1667-1735). Abraham de Moivre (1667-1754). Pierre Remond de Montmort (1678-1719). Nicolaus Bernoulli (1687-1759). Daniel Bernoulli (1700-1782).- 18th Century: Thomas Bayes (1701-1761). Johann Peter Sussmilch (1707-1767). Georges-Louis Leclerc, Comte de Buffon (1707-1788). Rogerius Josephus Boscovich (1711-1787). D'Alembert (1717-1783). Marquis de Condorcet (1743-1794). Pierre-Simon Marquis de Laplace (1749-1827). Adrien-Marie Legendre (1752-1833). William Playfair (1759-1823). Thomas Robert Malthus (1766-1834). Sir Frederick Morton Eden (1765-1809). Carl Friederich Gauss (1777-1855). Simeon-Denis Poisson (1781-1840). Adolphe Quetelet (1796-1874). Irenee-Jules Bienayme (1796-1878). Stefano Franscini (1796-1857).- 19th Century: Gustav Theodor Fechner (1801-1887). Anton Meyer (1801-1857). Antoine Augustin Cournot (1801-1877). Augustus De Morgn (1806-1871). William Farr (1807-1883). George Boole (1815-1864). Florence Nightingale (1820-1910).