I take it you're not interested in books like Underwood Dudley's "Elementary
Number Theory," San Francisco: W.H. Freeman and Company, 1969, and others in
that vein.
Whitehead's quoted often enough in HM, it seems. Selections from Newman's
four-volume set, The World of Mathematics, might be too obvious.
Martin Heidegger's little 1957 essay, "Identity and Difference" might
qualify, though it's probably one already on your list.
Has Denis Guedj's 1996 "Numbers: the universal language [Empires des
Nombres]," NY: Harry N. Abrams, Inc., [1997] been mentioned yet? It's may be
along the lines of what you're really looking for -- simple, comparative,
historical, well illustrated. Hardly "serious," though.
The first quarter or third of Lancelot Hogben's "Mathematics for the
Million," may have something of what you're looking for as well.
In the meantime, here are the couple that prompted my reply:
Gelman, R. and Gallistel, C.R. The Child's Understanding of Number.
Cambridge, MA: Harvard University Press, 1978.
Piaget, Jean and Szeminska, Alina. The Child's Conception of Number. NY:
Humanities Press, Inc., 1952. [Translated by C. Gattengno and F.M. Hodgson;
Original French edition, 1941.]
I especially recommend the former. There are few others like it.
Well, that's my contribution. Would you mind sharing your bibliography once
you have it all together?
David Coia
Arlington, VA
In a message dated 5/28/99 11:19:43 PM Eastern Daylight Time,
owner-historia-matematica-digest@chasque.apc.org writes:
<< Date: Thu, 27 May 1999 22:09:24 -0400
From: Ed Wall <ewall@umich.edu>
Subject: [HM] Number
Folks
I was asked the following question by a colleague:
******
Do you know of any very good essays or other treatments of domain of number
(e.g., the major objects , operations, etc, of the whole, integer,
rational, and real number systems) that would be serious and yet accessible?
I'd like help in assembling a small number of very good pieces that
would serve as a resource for a group of mathematicians with whom I am
working to write an essay on number. In part, I want them to see some
other people's takes on this domain, and in part, I also want them to see
what examples of serious writing that is accessible to an educated, but not
mathematically trained, reader might look like.
******
What is perhaps being asked for is something that lies in the intersection
of philosophy and mathematics. I have some ideas, but I would be interested
to hear the ideas of others.
Ed Wall
>>