This book, a sequel to the one with the same title with "Before" replacing "After", is just as good as the "predecessor." Eves has no peer in exploring the development of mathematics by identifying and describing some of the "inflection points" of mathematical progress. That is a term made famous by businessman Andrew Grove and is used to refer to a time when dramatic change is occurring.
Mathematicians, despite many conceptions to the contrary, work in a field where astonishing results sometimes occur. Eves, through his set of great moments selected from his series of lectures on the topic, ably describes some of those moments of astonishment. He also explains why the result was significant in a manner that almost everyone, including mathematically sophisticated high school students, can understand. Eves also includes problems at the end of each section, and these are excellent. They are well written and serve to solidify and expand the main points of the section. He also includes solution hints for most of the exercises.
A partial list of the topics includes the birth of probability, the invention of the calculus, the discovery of non-Euclidean geometry, the creation of group theory, the organization of set theory, and my favorite, transfinite numbers.
There is no better set of books available for courses in mathematical history than the two in this short series. Mathematics occasionally progresses in great bounds rather than small leaps and Eves gives detailed, understandable explanations of some of those of greatest length.
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