Negative Number History

Date: 11/25/2001 at 08:53:01
From: Jam
Subject: When was the negative number understood?

What happened in the 16th century that caused people to need to use 
negative numbers, and what was their image of a negative number before 
that?

Date: 11/28/2001 at 22:54:18
From: Doctor Peterson
Subject: Re: Negative number history

Hi, Jam.

Good question!

There was actually a very gradual development in attitudes toward 
negative numbers; people didn't just suddenly start to use them at 
that time. You can read some of this history here:

   Millennium and the Year 0
   http://mathforum.org/library/drmath/view/52565.html   

This refers to the Kevin Brown's Negative Numbers page:

   http://www.mathpages.com/home/kmath298.htm   

Another page I have found with more details is

   Some elements of history of the negative numbers - Anne Boye
   http://nti.educa.rcanaria.es/penelope/uk_confboye.htm   

which, unfortunately, seems to be a poor translation into English, but 
shows negative attitudes toward negative numbers persisting almost to 
the present.

Negative solutions to problems were for centuries called "false" 
because they can't be found in the real world. The basic ideas of 
negative numbers were recognized in some form as early as Diophantus 
(third century A.D.), and were explicitly discussed by Brahmagupta 
(seventh century); Fibonacci, about 1200, allowed negative solutions 
in financial problems where they could be interpreted as a loss rather 
than a gain. D. E. Smith's _History of Mathematics_, from which I am 
getting some of these facts, mentions a problem by Chuquet (1484) 
whose solutions are -7 3/11 and 27 3/11, written using his notation 
with an "m" for the minus sign. Cardan in 1545 more clearly discussed 
negative solutions, and others such as Descartes and Fermat 
contributed to giving full recognition to negative numbers. By 1659, 
Hudde was willing to allow a variable to represent either a positive 
or negative number, rather than having to write -x for a negative 
quantity.

As you can see, it was just a gradual recognition of the value of 
negative numbers that led them from grudging acceptance to full 
equality with positive numbers. A more detailed study would be 
interesting.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/