Subject: Re: [HM] History of negative numbers
From: Ralph A. Raimi (rarm@math.rochester.edu)
Date: Thu Jan 20 2000 - 23:18:16 EST
On Thu, 20 Jan 2000, Douglas Jimenez wrote:
>
> I want to know if somebody in the list knows a good book about the
> evolution of the concept of negative number. It could not even be
> dedicated exclusively to the topic, but it is important a rigorously
> treatment.
I don't know when rigor got into the act, but an interesting book
that shows the attitude prevalent at least in England in 1831 is Augustus
DeMorgan's *Study and Difficulties of Mathematics*, which I have read in
an 1898 reprint by Open Court Publishers (Chicago). It is a sort of
textbook for high school age children or for their teachers, I'm not sure
which, and treats negatives very tenderly, beginning by showing how they
are needed, or can be evaded, in "story problems" of this sort:
"A father is 56 and his son 29 years old. When will the father be
twice the age of the son?" He arrives at the equation
2(29 + x) = 56 + x
where x is the time (from now) that this will happen, but the answer
turning out to be negative, DeMorgan explains that we should rephrase the
problem, "... when *was* the father twice the age of the son?" to avoid
imaginary or impossible answers for x. But in succeeding chapters he
shows how one can make sense of the apparent nonsense without changing the
wording of the problem.
Ralph A. Raimi Tel. 716 275 4429 or (home) 716 244 9368
Dept. of Mathematics FAX 716 244 6631
University of Rochester Webpage http://www.math.rochester.edu/u/rarm
Rochester, NY 14627 (Webpage contains links to papers)
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