You are here

Mathematical Demography

David P. Smith and Nathan Keyfitz
Publication Date: 
Number of Pages: 
Demographic Research Monographs
[Reviewed by
Susan D’Agostino
, on

Mathematical Demography, Selected Papers, 2nd Revised Edition is an updated version of the classic 514-page 1977 text of the same name that has long been out of print. At 335 pages, the second revised edition is shorter, due in large part to the omission of contemporary papers that are now readily available on the internet. This reviewer read the hardcopy of the text but readers should know that the entire book is available online as open access at

The text is divided into five parts: the life table (9 papers), stable population theory (12 papers), attempts at prediction and the theory they stimulated (3 papers), parameterization and curve fitting (8 papers), and probability models of conception and birth (3 papers). The span of the papers is impressive. For example, in the part concerning stable population theory, readers may enjoy an important paper by Euler titled, “A General Investigation into the Mortality and Multiplication of the Human Species” written in 1760, as well as a more modern paper by Samuelson titled, “Resolving a Historical Confusion n Population Analysis” written in 1976 specifically for the first edition. Many of the papers are prefaced with short notes from the authors, often providing context, clarification regarding notation, or full disclosure concerning omissions.

For mathematical demographers, this collection is an invaluable resource providing original works that showcase the history, depth, and breadth of the field. As such, mathematical demographers may be inclined to sit down and read the book beginning at page one and ending at page 335 (well, page 323 if you do not count the index). Doing so, I suspect, would provide for a dense but worthwhile read. This reviewer, however, is a mathematician whose subfield is not demography, but whose interest was piqued by the title. For such readers, Mathematical Demography, can be a highly enjoyable, even comprehensive, reading experience, though not necessarily linear. The casual reader will need a nontrivial amount of mathematical sophistication, including calculus and matrix algebra for most papers, with some papers requiring knowledge of stochastic processes.

As long as the reader possesses the requisite math skills, Mathematical Demography may be read out of order, based simply on the order of preference that the papers draw the reader in. This reviewer, for example, was first drawn to the older papers (regardless of the part in which they were organized) as they inspired thought concerning what it must have been like to develop a field. For example, in Graunt’s 1662 paper titled, “Natural and Political Observations Mentioned in a Following Index, and Made Upon the Bills of Mortality,” Graunt provides tables that include the number of deaths (from 229,250 people) resulting from “diseases” such as “cut of the stone,” “dead in the streets,” “lethargy,” and “lunatic,” or “casualties” such as “head-ache,” “excessive drinking,” “killed by several accidents,” and “smothered.” The exact words of those who were present and active at the beginning provide the reader with an appreciation of just how messy it might have been to organize their thoughts on the topic of life expectancy, as well as the imaginativeness that was likely required to move the field forward. Further, more recent papers are included in all parts, which this reviewer was drawn to read after digesting the earlier papers.

Overall, Mathematical Demography, Selected Papers, 2nd Revised Edition provides ample historical material to provide a broad context for the field. It is not, nor does it promote itself as, a math textbook in the traditional sense (i.e. with problems to solidify understanding). Rather, it is a collection of papers — carefully selected by capable authors who provide spare but important comments — that provides readers with a solid grounding in the field of mathematical demography.

Susan D’Agostino is an Associate Professor of Mathematics at Southern New Hampshire University. She is also an appointee on NH Governor Maggie Hassan’s STEM Education Task Force. Her essays have appeared in The Chronicle of Higher Education, and the Mathematical Association of America’s Math Horizons and MAA Focus magazines.