Everything You Wanted to Know About Math But....
Several weeks ago, I reviewed the text The Mathematics that Every Secondary School Math Teacher Needs to Know , designed, as expected, to answer almost everything a teacher might want to know about mathematics. This week, the recommended tome narrows in both size and focus, but widens its audience.
Though the Internet can answer many questions about mathematics (and most of them correctly), it is always comforting to have friendly reference books nearby. One I have had and used constantly for the past 40 years is James and James Mathematics Dictionary.
Another recent text trying to take up my "desk space" is Timothy Gower's (ed.) The Princeton Companion to Mathematics (2008). This 1008page tome is advertised as "An essential reference for every mathematician."
Editor Gowers is a respected mathematician, being the Rouse Ball Professor of Mathematics at the University of Cambridge and a Fields Medalist in 1998. He has done a commendable job coordinating and editing about two hundred entries, all written by worldclass mathematicians. Their overall goal was to:
 introduce basic mathematical tools and vocabulary
 trace the historical development of modern mathematics, including the discussion of open problems
 explain essential mathematical terms and concepts
 Identify and survey core themes in major areas of mathematics
 describe the achievements of almost 100 famous mathematicians
 explore the impact of mathematics on other areas such as biology, finance, and music
Overall, it "uncovers" topics in number theory, algebra, analysis, geometry, logic, probability, and more. All is supported by bibliographies, crossreferences, and a comprehensive index.
Consider this review comment from the American Scientist: "It has something for nearly everyone, from beginning students of mathematics who would like to get some sense of what the subject is all about, all the way to professional mathematicians who would like to get a better idea of what their colleagues are doing. . . . If I had to choose just one book in the world to give an interested reader some idea of the scope, goals and achievements of modern mathematics, without a doubt this would be the one. So try it. I guarantee you'll like it!"
Though I will not make the same guarantee, I do suggest you consider the text...knowing the cost is about $100. A good start is to browse the samples of text content, as provided via the link above. Personally, I have access to the text, have used it a few times (requires focused attention and some thoughful work)...but I am still waiting to make a commitment to it as a "new" fundamental resource on my desk, i.e. make it my "companion."
