Carl B. Boyer (1906–1976)

Everything you ever wanted to know about the rainbow, some things you didn’t realize you wanted to know about the rainbow, and a lot of stuff about the rainbow that will almost certainly fill you with indifference. There a short but enlightening introduction on rainbow mythology; however, author Carl Boyer was primarily a historian of mathematics, and it shows. Just about every Greek, Latin, Arabic, medieval, Renaissance, and Enlightenment philosopher and/or scientist had something to say show more about rainbows, and Boyer tracked every one down; as a result the book has more incorrect geometrical diagrams than anything I’ve ever seen. Boyer felt compelled to illustrate every wrong conception anybody came up with; thus there are carefully labeled illustrations, some from the original work and some redrawn, of light rays doing some jaw-dropping things. A sadist might assign this book to a geometry student to study the diagrams and explain what these people actually thought they were doing. The end result is something to be dipped into now and then rather than read through. show less

This book is probably a god-send for your average mathematician. But for the average reader, no matter how well versed in mathematics he/she is, this book is too esoteric to be more than occasionally interesting. In general, it's too comprehensive (and incomprehensible) for the cost of time/energy to read. I can understand the need for detail:

"Another paper of great influence in the trend to abstraction was Ernst Steinitz's work on the algebraic theory of fields, which appeared in the show more winter of 1909-1910 and had been motivated by Kurt Hensel's work on p-adic fields."
or
"Heesch thought that the four-color conjecture could be solved by considering a set of around 8,900 configurations."

I won't say that the book was never interesting [did you know that our "Arabic numbers" are really Indian inspired? Ever since my visit to Egypt many years ago I wondered why their numbers were different from ours.] Anyway, I have enough Science Fiction background that I recognized most of the buzz-words: Riemann fields, topology, tensors, pseudosphere(?), Hermitian matrices....

If I were an advanced student of Mathematics I would definitely give this book a 5-star rating. But, given that I actually was able to plow through the entire book, and comprehended so little, tells even me that the author was not intrinsically boring. There's a phenomenal amount of information in this book; it's just a shame that I understood so little of it. However, I may have been inspired to see if I can find an "advanced math for dummies" book. Just what is "non Euclidean geometry"? show less

This book reminds me of E.T. Bell's book, Men of Mathematics. It contains the history of mathematical discoveries as they are known to scholars. For instance, it shows that certain theorems were known to the oriental nations like China and India, and that a lot of things had to be rediscovered after the whole rigmarole with the fall of empires and nations and the destruction of ancient repositories of knowledge.

It starts with counting and goes on through the Egyptians, Babylonians, Greeks show more and Romans. After the Decline and Fall of the Roman Empire, we follow mathematical thought to India, China and Arabia. Throughout the book, it covers quadratics and how the ancients thought of them and goes on through the founding of Calculus and Analysis. The Giants are all covered, with Euler and Gauss each getting their own chapters. Basically, with every big name or thought in mathematics, the book is there, offering an opinion on stuff. Most of the stuff is priority of discovery, which is a huge thing to mathematicians.

This book is really interesting, but it takes a while for me to read the notation. I really wish I was better at that, but I am working on it. show less

A comprehensive survey of mathematics, from Babylonian number systems to 20th century analysis, with emphasis on the areas you'd expect: ancient Greek geometry, Arab work on polynomials, the development of analysis in Europe, etc. A tad dry in places, but very clear and thorough. The presentation doesn't assume a particularly high level of mathematical sophistication on the part of the reader, but on the other hand, why in the hell would you find this book interesting if you haven't already show more done some mathematical work?

The story proceeds chronologically in more or less self-contained chapters that focus on particular areas and eras, so this book can be used as a reference by people who don't want to read the whole thing. In addition to its general utility as a history, Boyer's book gives you an appreciation what a vast human undertaking mathematics has been. Even something like basic algebra, which now seems so obvious and common-sensical, represents a tremendous feat of intellectual innovation.

If you're looking for a good popular exposition of the ideas of mathematics rather than the history per se, a good place to start is The Mathematical Experience by Davis and Hersh. show less