Number by Tobias Dantzig

[PS_Mouse]

I just bought this book; I'm yet to read it and I'm curious to see what the fora think of it.

[EDIT] I've reached the fifth chapter and thus far, I'm enjoying it.

[skeptical scientist]

Haven't read it - what are your thoughts, besides finding it enjoyable?

[PS_Mouse]

The portion of the book that I've read so far has covered the evolution and growth of numbers and mathematics. All the while touching on topics such as why we settled on a decimal number system, the limitations of not having zero and others. While I'm no mathematician myself (my formal education on the subject ended soon after high school) I'm yet to be lost by the terminology or examples.
I'm finding it to be a very well written book, it isn't too obtuse or unnecessarily wordy (at the very least it's a lot more readable than The Universal History of Numbers).

I'm definitely going to be reading this a second (and perhaps third) time just to make sure I haven't missed anything.

In short, I suggest you try and get your hands on a copy of it.

[skeptical scientist]

My main worry is that as someone with a lot of math education, I'll be annoyed at the very same things you find appealing, i.e. the fact it is written for a non-mathematician and the lack of mathematical details which lay behind some of the things he is describing. Do you think this worry is justified, or will I still find it interesting even with a stronger math background than the target audience? Does he include appendices where some of the details he is glossing over in the interest of readability may be found?

[PS_Mouse]

I don't think you have reason to worry; it's less that it's written for a non-mathematician and more that he assumes the reader has at least a highschool education in the subject. It's worth mentioning at this point that Number isn't a new book, it was first published in 1930. I mention this because the dust jacket has an enthusiastic endorsement from Einstein, who apparently found it "[...] beyond doubt the most interesting book on the evolution of mathematics that has ever fallen into my hands". So yeah, I imagine you'll find it interesting.

Oh, and on the subject of appendices; there are 81 pages of them. There are also 21 pages of Notes and 11 of Further Reading (this is for a book that weighs in at just below 400 pages).

[skeptical scientist]

Well, all copies are checked out of the Seattle Public Library at the moment, but my university has 8 copies in 6 versions, only one of which is out, so I'll take a look in a couple of weeks when I'm back in Chicago.

[Nosforit]

I've read most of the book and did indeed find it very good. Dantzig explains the logical evolution of number rather than the historic chronology, and really paints a red line through it all which is somewhat easy to follow. Something which stuck to mind is how he justifies the placing of numbers 'in between' the natural numbers, and the following implication of how each time the total set of numbers is multiplied by infinity.

The book is truly enlightening and recommendable to all. It is so densely packed with information, either explicit or implicit, that I doubt no one having read the book could put it down having gained nothing.

[the keeper]

My favorite class I have had in all of my education was an undergraduate math class titled "This history of math."

We basically traced the evolution of math from Sumerian cuneiform up to Newton. It was very fascinating seeing how different civilizations and cultures studied math, and being able to study it in the same way.

I imagine the book is quite interesting, and I'll look at picking it up.

[Wilibus]

I took a class on the history of mathematics as well as an undergraduate.

I really didn't enjoy it. Kind of what skeptical scientist was talking about. Education students at my university are required to have 3 critical thinking credit hours for their degree numbered above 300. History of mathematics was the dumbed down course for them to take to fill this requirement, and was more memorization than math.

Real shame, I was looking forward to it quite a bit.

[Yakk]

I read "the World of Mathematics" Edited by James R. Newman, published 1956.

Imagine reading Descartes on Cartesian coordinates, Whitehead on mathematical logic, Weyl on symmetry, Dedekind on irrational numbers, Russell on number theory, Heisenberg on the uncertainty principle, Turing on computer intelligence, Boole on set theory, and Eddington on group theory. Biographical and historical articles are scattered throughout. I especially liked Bell's article Invariant Twins: Cayley and Sylvester, and The Great Mathematicians by Turnball.

Complete contents:
http://amapedia.amazon.com/view/THE+WOR ... 29/id=3613

Volume I has a rather nice walk through pre-historical mathematics, and why it was much harder to do math back then.