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### 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/
```
Associated Topics:
High School History/Biography
High School Negative Numbers
Middle School History/Biography
Middle School Negative Numbers

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