[bridgeyman]

I read this a couple weeks ago and decided to try and find a math book that incorporates some history in it. I found Journey through Genius: The Great Theorems of Mathematics with some great reviews.

I am working on an iPad app that pairs up people to mentor each other through books like this. It has video chat and a shared whiteboard, so it is ideally suited for discussing math. If anyone is interested in reading the book with someone, email me at [e-mail]. I could really use some beta testers for the app!

If you have already read it, you could still mentor someone in it to review the material again.

[codyb]

To add to the suggestions here, "Number" by Tobias Dantzig is absolutely a wonderful history of mathematics. I mean, shoot, it's actually got a quote from Einstein:

"This is beyond doubt the most interesting book on the evolution of mathematics which has ever fallen into my hands. If people know how to treasure the truly good, this book will attain a lasting place in the literature of the world. The evolution of mathematical thought from the earliest times to the latest constructions is presented here with admirable consistency and originality and in a wonderfully lively style."

—Albert Einstein

http://www.amazon.com/Number-Language-Science-Tobias-Dantzig...

[auggierose]

if you are in a hurry:

http://www.engineering108.com/Data/Engineering/Maths/Number_...

[westoncb]

I've spent a lot of time looking for books that'd teach some mathematical ideas while keeping the original progression of motivations/concepts in tact.

I'd first recommend "Men of Mathematics" by E.T. Bell. It's a collection of short biographies on 20 or so Mathematicians, also discussing a few of the most salient points of each's work. It's an enjoyable introduction, useful for getting a broad view of what math is made of and how mathematicians think. Bell was a serious mathematician himself (not of the rank of anyone he's writing about, of course), as well as a sci-fi author apparently :)

edit: could also try "Mathematics and the Imagination" as an alternate introduction.

After that would be "What is Mathematics?," by Richard Courant and Herbert Robbins. This one's a bit tougher, and I have to admit I had the experience of being perplexed at the selection of topics, and that it didn't tell me immediately what mathematics is -- but! Without too much time passing, I now appreciate the selection and think it could be read profitably by trusting that the selection is good and trying to answer the question why that's the case while reading.

At the moment I'm trying my second book from E.T. Bell, The Development of Mathematics, and like it quite a lot so far, though it assumes a little more math knowledge. This one's probably great if you did a mathematics undergrad, or similar, but would like to see the various topics related and given context.

Another I believe worth checking out, if none of the others fits exactly, is William Kingdon Clifford's "Common Sense of the Exact Sciences." I've only skimmed sections in this one, but it looks extremely promising; and from what I've read about it and about Clifford, I think it could be an important piece of pedagogy along the lines of what Lockhart's into. Not too long and pretty accessible I think.

[nsphere]

Check out this book as well.

http://amzn.com/039306204X

[bridgeyman]

Thanks! It is next on my list now.

[Someone]

Another suggestion: http://archive.org/details/TheWorldOfMathematicsVolume1 (and volumes 2, 3, and 4).

Lots of interesting stories, many of applied mathematics. And, to my surprise, available for free from archive.org.

[Nate75Sanders]

Journey through Genius is an absolutely fantastic book. I took History of Math from a professor in undergrad who had a conjecture named after him and this was his choice of textbook (along with a few other materials) for the course.

[prestonbriggs]

You might enjoy Lockhart's book, Measurement. http://www.amazon.com/Measurement-Paul-Lockhart/dp/067405755...

[thetwiceler]

Yes, a million times! Journey through Genius is an excellent book (I, too, had this book for a History of Math class). It's really appropriate for people of all different levels of mathematical maturity. It's aimed to be read by a pretty much lay audience. But it covers some interesting t material that you're likely not to have seen in an undergraduate curriculum (Heron's formula, cubic/quartic equations, Euler's windmill proof).

[aet]

Sounds like an interesting idea. Learning is much easier if you can find someone equally interested and at your same level.