In the dozen years between the initial appearance of this book and today, two ongoing events have motivated us to prepare this revised edition. The first is the significant expansion of published scholarship in the history of mathematics, including many new books accessible to non-specialists. The second is the gratifying widespread use of this book, both here and abroad, and the continuing demand for it. In addition, several more topics, admittedly chosen by personal taste, seemed to merit sketches of their own.
Five new historical Sketches — on the tangent function, logarithms, conic sections, irrational numbers, and the derivative — have been added. We opted not to change the numbering of the original Sketches, so the new ones are numbers 26–30. Also new is the "When They Lived'' section just before the Bibliography. It replaces all the parenthetical birth/death dates that had appeared somewhat intrusively (and, alas, inconsistently) throughout the text, after the name of each mathematician or other prominent historical figure.
Parts of the "Nutshell" overview have been rewritten extensively to reflect recent scholarship. The "Books You Ought to Read" section and the Bibliography have been thoroughly reworked to reflect recent publications. The index has also been expanded and improved, and the "For a Closer Look" piece at the end of each Sketch has been revised to account for sources that have appeared in the past decade or so.
In preparing this revision we have tried to be mindful of the many college professors whose courses have been built, at least in part, around the first edition. To that end, Sketches 1–25 have remained substantially the same. To be sure, parts of some have been reworked a bit. In particular, there have been significant adjustments in Sketches 1, 5, 9, 15, 17, 18, and especially 19. Nevertheless, the "story lines" of all the Sketches are unchanged, so they are still compatible with the Questions and Projects of the first Expanded Edition. An Expanded Second Edition with Questions and Projects for the new Sketches is in the works.
Maine, August 2014