Since the main thread of my blog is going to have some ongoing entries concerning the history of mathematics, I am including some books on the subject here to let you do a deeper dive, if you wish. You can also judge how much of my blog has been directly stolen from these references.
Otto Neugebauer - The Exact Sciences in Antiquity heads the list only because I had the privilege of having the author for a professor. It is written in a stilted form and is difficult to read. That being said, it still remains one of the primary sourcebooks on early (1700 BCE and forward) Egyptian/Babylonian mathematics and astronomy. It signs off during the twilight of Greek mathematics, around 50 CE, with a discussion of Ptolemy.
Morris Kline – Mathematical Thought from Ancient to Modern Times remains the classic book on the history of mathematics, but beware – here be dragons. This little (~1200 pages) contains actual equations, up to and past the partial differential equation level. The good news – the book is still eminently readable even if you don’t understand the math. Enough context is given to keep the story coherent even though the math is not necessarily comprehended. Update 6/2014 – This is now available as a three-volume set, to save on the schlepping energy. And there is always the Kindle option.
Carl B. Boyer – A History of Mathematics keeps the math to an Algebra II level while still describing the development of more advanced topics. (and weighs in at only ~600 pages.) The book is oriented heavily toward the people involved and kind of scrimps on the description of the flow of increasing knowledge, treating the progress discretely by tying discoveries to individuals rather than a continuous process. Not wrong, just not my personal preference for how to treat the topic. De gustibus …
John Stillwell – Mathematics and Its History is truly written for a mathematician, or at least a college student pursuing a degree in Mathematics. In addition, it comes from the Springer Press, historically a publisher of deeply intensive books. (Also, Springer-Verlag). In graduate school we would learn to dread these yellow books, as they signify we were in for a rough semester. However, if you have any mathematical training, say Advanced Calculus and maybe Modern Algebra (group theory, etc.), and the bucks to spend, you will find this an engrossing read.
So many books, so little time ..
Luke Hodgkin – A History of Mathematics, my penultimate suggestion, is a fine middle ground for readers who can tolerate some mathematical rigor, but who not possess advanced training. There are also examples for the reader to solve, using the techniques available at the time covered in the period under discussion. It is also one of the few books on this subject that discuss the crisis due to modernity (you’ll have to read the book, or Google it).
David Burton – The History of Mathematics: An Introduction – Hey, if you like lots of pictures, this is for you. The mathematics is not intense, but the impact of the principles are brought out clearly. It, too, has problems to while away those cold winter nights.
And, of course, all the above contain references to other books, which, in turn …
“All science, logic and mathematics included, is a function of the epoch – all science, in its ideals as well as its achievements.” E. H. Moore (~1920)