Favorite books about math, history of math, ancient Greece, philosophy...

[Laura Gibbs]

Please share your own favorite books as they touch on the topics at hand here! :-)

[Ian Carmichael]

Not so much a favourite book, but some interesting explorations in formal thinking, symbolic thinking and mathematics, taking some excurses through Greek mathematics.
(I'm just rummaging around while I wait for my copy of Klein! Skimmed a little Heath as well - History of Greek Mathematics)

[Laura Gibbs]

Wow, Ian, Luigi Borzacchini's pages look great; I have bookmarked them to come back to later this weekend. He starts out with observation by J.P. Vernant, who is the grand old man of the kind of training (such as it is, ha ha) that I've received in my study of the ancient world - not philosophy, but rather anthropology. Of course, many of the concerns that philosophers and anthropologists study do overlap, which is why I am so interested in reading Klein's book. For myself, I would prefer a study of the "anthropology" of math in ancient Greece... but finding out what the philosophers were doing with math is also very interesting and provides a wonderful springboard for thinking about the related but different questions that come up in a more anthropological inquiry.

About Heath: what a contrast to Klein! And I have to admit that I find Heath almost impossible to read. I don't have any strong personal devotion to ancient Greece at all, and Heath's opening pages about the "grandeur that was Greece" kind of thing is very off-putting to me. For all that Klein is very antiseptic by comparison, I much prefer Klein's straight-forward approach - I really appreciate the fact that Klein does not idealize the Greeks in some sweeping, vague, essentializing way as Heath seems to do, but instead focusing in on a particular body of thought evolved by a particular (a VERY particular) group of people in ancient Greece, and seeing what we can truly learn from their thoughts. :-)

[Ian Carmichael]

I don't mind Heath's style, personally, but he certainly is a booster for the Greek culture! Roll on Klein delivery!

[Ian Carmichael]

I can see I'm going to have to get modern! My new enthusiasm in Mathematics history (John Derbyshire) is telling me I should be suspicious of E T Bell's Men of Mathematics (romantic, but inaccurate is his take. Pity, perhaps I'm a sucker for romance?) And I quite liked Heath's roseate view of the Greeks - the picture of the noble pursuer of knowledge was quite uplifting, in an impressionistic way. However it does fall into the trap of attempting to characterise an age in an apothegm. A trap, by the way, which I love, and have willingly fallen into in characterising an age for its 'matching' ethic. But - of course - I digress.

[Ed Wall]

Two books people might find interesting are

Hoyrup's In Measure, Number, and Weight
Fowler's The Mathematics of Plato's Academy: A New Reconstruction

especially the latter as regards the Klein reading. There are some other possibilities that may provide some connections. However, these seem, at the moment, among some of the more relevant.