A "Reader's Digest" Version of Mathematics History?
This summer P.L. (Portland) wrote to me with the suggestion "...it came up on someone's response card after reading a piece by Hiebert et al that it would be nice to have an easy reading 'Reader's Digest like' resource that catalogs a 'brief history of most mathematical concepts so that it might make it easier to incorporate historical info into our teaching'."
With Pascal listening on the right to confirm, my reply was: "Not an easy question to form a response to...as I am not a believer in Readers's Digest version of mathematical history. First, the history is too long for a short form. Second, what happens in shorted versions is that the mathematics gets left out and all it focuses on are interesting stories about people. Third, the mathematics in 'old' history becomes quite difficult very fast, as the modern form of mathematics has made things much easier to do and comprehend. And fourth, a level of commitment on the part of the reader is needed to even partially understand the history of mathematics (people, concepts, context, etc.)...and most people are not willing to make this commitment.
My suggestions, in order of priority....
Finally, with this reply, I also mentioned the implementing of a new "history of mathematics" web site (extension of MathNEXUS) in the spring of 2011. It will include a 300+ page text on problem-solving involving the history of mathematics (written a year ago but not published and will be made available free on the web), plus a collection of historical mathematics problem keyed to the standard matrix of topics taught in 6-12 mathematics AND plus...resources for getting young students to investigate/write about the history of mathematics. The website, suported by Tony Jongejan's computer magic, is being designed for 6-14 mathematics teachers. Consider it announced....
- First, buy a standard history of mathematics (e.g. Suzuki, Eves, Katz, ), but that does not fit your criteria.
- Second, one can Google almost any math topic and find its history on-line...e.g. 'division' with 'history' and 'mathematics.' Overall, the best mathematics history web site is The MacTutor History of Mathematics Archive (reviewed at this link). In the Archive section of my web site, one can find reviews of special history-based web sites focusing on women in mathematics, symbols in mathematics, and the history of mathematical words.
- Third, a few years ago, someone tried to write a 'short-form' text on mathematics history (see Math Through the Ages). An attractive feature is that it provides a brief 50+ overview of mathematics history, then has 25 short discussions on the history of mathematical notions (e.g. negative numbers). I tried to use the text as part of my mathematics history course, but ended up disliking the book because of some errors, felt-fabrications, and tendency to gloss over big ideas.
- And fourth, other books have been written as 'quickies' for teachers, providing short bios and worksheet examples of the mathematics involved. Be aware that often the examples are artificial and have nothing to do with the person involved. Three examples are Sanderson Smith's Agnesi to Zeno: Over 100 Vignettes from the History of Math), Luetta Reimer's two-volume set Mathematicians Are People, Too), and John Tiner's Exploring the World of Mathematics). Of the three, the first is the best in my opinion."