God Created the Integers


The book God Created the Integers: The Mathematical Breakthroughs That Changed History is an anthology released originally in 2005 that was edited by Stephen Hawking. It consists of excerpts from thirty-one curated works from some of the most important minds in mathematics. The book’s title is derived from a quote by Leopold Kronecker, famous mathematician, who once said “God made the integers; all else is the work of man.” Grouped by author and set in chronological order, each of this book’s sections are prefaced by some of the notes about the particular mathematician’s life, experience, and work. Among the famous mathematicians included are Euclid, Archimedes, Diophantus, René Descartes, Isaac Newton, Leonhard Euler, Pierre-Simon Laplace, Joseph Fourier, Carl Friedrich Gauss,, Augustin-Louis Cauchy, Nikolai Ivanovich Lobachevsky, János Bolyai, Évariste Galois, George Boole, Bernhard Riemann, Karl Weierstrass, Richard Dedekind, Georg Cantor, Henri Lebesgue, Kurt Gödel, and Alan Turing. Some works by Euler, Bolyai, Lobachevsky, and Galois were included in the book’s second edition, but could not make it into the first.

Coming off of the success of his book On the Shoulders of Giants, published back in 2003, Stephen Hawking again used the same format of collecting selections of the work of great mathematicians and/or physicists, all of which are preceded by biographies that Hawking wrote himself. This book differs in that it’s slightly shorter in length, making the excerpts used slightly shorter in length as well. One of the most interesting aspects of this collection is that the works curated are presented in total chronological order, so in the process of reading the book, the reader will also be covering 2,500 years of history in mathematics. The vast majority of the text actually deals with events that occurred even before the sixteenth century. While some might not be happy with the final list of mathematicians used, ultimately tough choices had to be made for the sake of brevity, so only those deemed most influential by Stephen Hawking were included.

One critical sticking point for the book is that for some reviewers it appears to be difficult to nail down who the particular audience for this book would actually be. While some critics contend that it’s not written for the mathematics historian, some would argue that the bare bones biographical works add little to the established canon of what is known in regards to some of the greatest minds to ever grace the field of mathematics. One critic even asserts that whenever a mathematician appears in both texts, there’s next to nothing biographically new offered in God Created the Integers that does not also already appear in E. T. Bell’s work Men of Mathematics. Notwithstanding these critical points to be made, this book does provide three new sources translated into English for the first time, which have never before appeared in the literature.

God Created the Integers: The Mathematical Breakthroughs That Changed History is definitely not for the layman, or even your average student of mathematics. Most of the text is actually devoted to excerpts that can be found from the published works of the mathematicians included here. Reviewer Eugene Borman, writing for the Mathematical Association of America, notes that few layman will benefit from “reading Gödel’s ‘On Formally Undecidable Propositions of Mathematics’, Gauss’ ‘Disquisitiones Arithmeticae’, or even Newton’s ‘Principia’ unless the entries are extensively footnoted, which they are not.” However, it’s entirely possible that someone who is studying something such s Number Theory might enjoy reading exposition on this topic previously written by Gauss. As such, this text can be considered useful as more of a resource for an entire course on the history of mathematics as a subject.

Others have also noted that the book can be appreciated at varying levels of experience in mathematics, depending on whether you’re reading only the introductions or are delving full bore into the mathematics in detail. Another benefit in the presentation of this particular book is that individual chapters can be studied independently of each other, which would make this book perfect for those who might be seeking postgraduate degrees who are studying for exams, or even for those who would like to study the works of a particular mathematician or mathematicians without having to arduously locate the text in question. Yet another reviewer considers that the text ending with philosopher and mathematician Alan Turing’s work on computable numbers is a bit premature, though Turing’s work has already been considered by many experts in the field to have been groundbreaking and revolutionary. But again, the historical perspective is yet to be cemented on the subject. One reviewer also notes that William Dunham’s Journey Through Genius: Great Theorems of Mathematics and The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities are similar in content and presentation. However, this book is still recommended for larger public and academic libraries.

Stephen Hawking’s ability to condense very complicated scientific ideas into understandable and digestible chunks of information was first cemented in Hawking’s book A Brief History of Time, which has since sold 10 million copies and been translated into 40 separate languages. Hawking has also either himself authored or participated in the publication of numerous science and mathematics related books. Aside from On the Shoulders of Giants, he also participated in the publication of The Illustrated On the Shoulders of Giants.

As can be easily seen, Stephen Hawking has extensive knowledge and experience not just in the fields of science and mathematics, but also in the scientific and mathematic book publishing industry. While his latest offering, God Created the Integers: The Mathematical Breakthroughs That Changed History, is a bit polarizing and divisive for some critics, it remains clear that few people are as well qualified as Hawking to talk about the subjects and viewpoints he espouses. And for a succinct summary of some of the leading minds in mathematics, this is really a very fine collection indeed.