The book I chose to read for class was titled "Journey Through Genius" written by William Dunham. The first thing that stuck out to me was how closely this book followed our lectures and topics in class. It was not until our group book discussion that I found out that this book is used as the textbook for the other MTH 495 sections.
If you are someone that does not really enjoy reading and working through proofs of theorems and propositions, then I would not recommend this book for said person. However, if you enjoy that aspect of math, this is a great book in my opinion. With that being said, the book is not all "proofs". There is a great amount of historical information and stories that really describe and help distinguish many of the individual thoughts and minds of the greatest mathematicians the world has ever seen, and their thought processes and approaches to creating proofs.
This book flows smoothly in my opinion, and transitions to the next great mathematician/s according to either timelines of existence or particular work that they have done that somehow is introduced or is recognized to have something to do with the work that was described in the previous chapter. For example, the first chapter starts off with Egyptian mathematics ( speculated around 2000 B.C) and Thales (546 B.C) and the last chapter, chapter 12, ends with Cantor (1891), so the book does follow a somewhat chronological order of the history of mathematics dating back to the Egyptians.
Probably the one and only complaint I have with this book, which for me seems to be the same complaint I have for the few other proof-based or math-based books I have read, is that the author, like many others, will refer to a formula or drawing that is on a different page. For example, the section that discussed the Pythagorean Theorem: within the first couple of pages, the author referred to the very famous sketch, but the sketch was not visible until a few pages later. Or in other chapters, when working through some of the proofs, the author will refer to equations and formulas that were either several pages earlier or several pages ahead. I understand that this is probably a pretty common practice, but in my opinion, if you are going to explain something as in depth and as complicated as a mathematical proof, and you are going to right off the bat refer to a picture or formula, it should be visible on that page. Again, just my opinion.
I can also say that reading this book, along with the discussions in class, has really gotten me intrigued about many of these individuals that I might have heard of before in a previous math course, but did not really know anything about. The coolest part is seeing how these individuals thought about problems and their approaches to solving these problems. It is fascinating to realize that there are many areas of mathematics that have literally been created from people trying to solve or prove other propositions or postulates (for example, the creation of non-Euclidean Geometry, which was "invented" when people were attempting to prove Euclid's parallel postulate). If you like proofs, read this book.
