Although this may seem a paradox, all exact science is dominated by the idea of approximation.
W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.
Mathematics Emerging: A Sourcebook 1540 - 1900
Mathematics Emerging: A Sourcebook 1540-1900, edited by Jacqueline Stedall, 2008, 653+xxi pages, $100.00, ISBN 978-019-922690-0. Oxford University Press, New York, NY http://www.oup.com/us/
This is an excellent addition to the current selection of mathematical sourcebooks that includes Calinger’s Classics of Mathematics, Fauvel and Gray’s The History of Mathematics: A Reader and older works such as Struik’s and Smith’s sourcebooks. Almost all of the translations in this book are new and provided by Stedall. Stedall takes a minimalist approach to the translations; she is quite literal (as long as readability is served) and does not use modern equivalents. (That would spoil the fun for readers like me!) However, and this distinguishes it from other sourcebooks, every source is also given in its original form. This also adds to the fun by allowing the reader to supply his or her own translation (if one is so inclined). This also has historical and pedagogical merit. When reading sources it is important to take the mathematics as it was, not as we want it to be.
Even though the stated time frame is 1540-1900, the book begins with a chapter on the known mathematics at the start of the sixteenth century. This allows the reader to approach the original sources with an eye to what the “original readers” knew. After that is a run through seventeenth century analytic geometry and number theory, early probability, calculus from Cavalieri to Lebesgue, complex analysis (Cauchy-style), linear and abstract algebra, and it ends with the foundations of arithmetic and geometry at the dawn of the twentieth century. Before each entry is a brief description of the work in the context of the time period.
There is a quite a bit here that is not in a standard (at least in the U.S.) first course in the history of mathematics, but this book allows instructors and students to follow along with their upper level courses. This book is written for those with some background and knowledge of mathematics. However, there is nothing here that a typical undergraduate math major will not see in her curriculum. This is a strength of the book, provided instructors and students are willing to turn to history for background and motivation. In fact, with many schools turning to capstone courses for majors, this book could find an audience there as well.
What sets this anthology apart? My favorite parts are the original facsimile pages, the new, original translations, and the author’s choice of source material. As with Calinger’s anthology, undergraduate mathematics instructors will find foundational papers in the usual core courses. For those who use original sources for background, motivation, or for sheer fun, this is definitely a book you should have on your shelf next to your Calinger and Fauvel/Gray.
Gary S. Stoudt, Professor of Mathematics, Indiana University of Pennsylvania