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/
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