History of Numbers

Date: 09/04/97 at 20:54:16
From: Lesa
Subject: History Of Numbers

My Algebra 2 teacher asked us to do a report on the history of 
numbers. What was the first number? Who discovered it/invented it? 
When and where? 

Please help.

Date: 09/15/97 at 10:52:41
From: Doctor Guy
Subject: Re: History Of Numbers

This is actually a fascinating question, which recently has been 
answered. 

Most older books on the history of math and numbers say that at some 
point (they are vague on when) somebody made a connection between the 
number of fingers on a hand and the number of cows or sheep, and 
figured out the concept of "number." See Boyer & Merzbach, "A 
History of Mathematics" (Wiley & Sons, 1968, 1989, 1989) for 
example, or O. Neugebauer, "The Exact Sciences in Antiquity."

But in the past ten years or so, truly marvelous results have been 
obtained by one Denise Schmandt-Bessarat, doing research into 
interesting "tokens" found all over the Middle East. Her book, which 
is not too hard to understand, is called "Before Writing." She also 
published at least one article in Scientific American magazine. 

The gist of what she said is that mathematics (or numbers and the 
writing thereof) came before writing itself. In the Fertile Crescent 
of southwest Asia, where farming may have developed first, people had 
surpluses of wheat, or barley, or beans, or wine, or oil, or beer, or 
various other things like that. Containers of them would be stored in 
central locations (whether voluntarily or not, I cannot tell), or else 
someone would owe someone else some of these (or live cows, chickens, 
goats, sheep, etc.), and records were made. 

The form that these records took is most curious: people would make 
little "tokens" out of clay and then fire the tokens in hot fires so 
that they would not fall apart, exactly as people today make pottery 
and "fire" it in kilns. In fact, Schmandt-Bessarat claims these tokens 
were the very first clay objects to be intentionally fired! If I gave 
you two baskets of wheat to keep for me, then you would give me two 
tokens that stood for the two baskets.
 
Remember, though, numbers per se hadn't been invented yet. Each style 
and shape of token stood for a different type of item. 

In order that these tokens would not disappear, various things were 
tried; sometimes they were tied to strings, but that didn't work well. 
Eventually they were put into clay "envelopes" and stored; some of 
these envelopes were found. The only problem was, once you put 
something in a clay envelope, you couldn't see what was inside unless 
you broke the "envelopes," which would have people's "seals" 
embedded in them to prevent fraud. 

After a few thousand years, someone got the bright idea that before 
you put the tokens inside the clay envelope, you should press each one 
into the wet clay of the envelope. Then people could tell exactly what 
the contents were inside. 

Then someone else got another bright idea: instead of pressing 9 
tokens for "sheep" and 8 tokens for "bottles of oil" on the outside, 
and so on, which could get pretty crowded, they invented a shorthand: 
press "sheep" one time, then 9 little marks; one "oil" and 8 little 
marks. This was a big step! Later, they invented some shortcuts for 
the numbers. 

Then a few thousand years later, someone else got an even brighter 
idea: why put the tokens inside the envelope at all? We have 
everything we need on the outside of the envelope! Thus, the 
Mesopotamians invented cuneiform writing on slabs of wet clay, meaning 
that they took reeds (like from bamboo) and pushed the ends of the 
bamboo sticks carefully into the clay to mean different things, 
including numbers.

According to this same author, Egyptian writing and numerals were 
invented a bit later, all at once, as a conscious decision of some 
committee, rather than "growing" naturally as cuneiform did.

Clearly the Maya developed mathematics and writing completely on their 
own; nobody from Europe or Asia influenced them in the slightest.

I highly recommend her book. It has lots of pictures.

-Doctor Guy,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/