The History of Numbers and Numerals

Date: 12/08/98 at 22:42:09
From: Julianne
Subject: History of Numbers

I tried to find the History of Numbers on the Net but I still couldn't 
find why and how numbers have been invented, and who invented them. I 
could only find information on prime numbers. All I want to know about 
is numbers. Without numbers we can't use the phone, count cash, and so 
on.

Date: 12/09/98 at 10:33:51
From: Doctor Rick
Subject: Re: History of Numbers

Hi, Julianne. This is certainly a big topic. First, we need to 
distinguish between NUMBERS and NUMERALS. A number is an abstract 
concept. A numeral is a way of writing down (or talking about) a 
number. We couldn't do much of anything in today's world without either 
of these! I don't know which of these you are interested in - maybe 
both!

Numbers were "invented" (or discovered, depending on one's 
philosophical viewpoint) long before history. This happened when people 
realized that they could think about "how many" without needing to know 
"how many WHAT?" - that there is an idea of number that is separate 
from the world of things that can be counted.

Mathematics has developed in part through the extension of the idea of
number to new types of number. Mathematicians added negative numbers 
to the counting numbers, inventing the INTEGERS. Then they added 
fractions to get RATIONAL NUMBERS; then they discovered that they 
needed numbers that were not rational (IRRATIONAL), thereby extending 
numbers to the REAL NUMBERS. Later they added IMAGINARY NUMBERS to the 
reals, making the COMPLEX NUMBERS. There are still other things that 
can be called numbers, such as the TRANSFINITE NUMBERS. Many of these 
types of numbers were used long before they were named and carefully 
studied. 

You can search for any of these types of number on our Math Search 
page:

   http://mathforum.org/grepform.html   

You can also look at these sites on the history of math:

   http://www-history.mcs.st-and.ac.uk/history/   
   http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html   

Turning to NUMERALS, there have been many types of numerals used in 
various cultures. You are most familiar with Hindu-Arabic numerals (the 
ones we use every day), and Roman numerals. Here are some interesting 
sites I have found about numerals.

You can find information about Roman numerals here:

   http://www.deadline.demon.co.uk/roman/front.htm   

This page shows how the Babylonians wrote numerals.

   http://www.phys.virginia.edu/classes/109N/lectures/babylon.html   

This page shows Egyptian hieroglyphics.

   http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/en.htm   

You can find an entirely different Egyptian way of writing numerals in
Encyclopedia Britannica (I've got an old 1970 edition) under "Numerals 
and Numeral Systems." It's called the hieratic system. I haven't found 
it on the Web, you'll have to look it up.

Here is a page about the Mayan numeral system.

   http://www.astro.uva.nl/michielb/maya/math.html   

The Greeks used letters to represent digits; see Encyclopedia 
Britannica again. In Hebrew the same method was used. You can find the 
Hebrew letters and the numbers they stood for here:

   http://www.amerisoftinc.com/hebletr1.htm   

Our symbols came from India by way of the Arabs. Here is a page that 
shows the early Indian numerals and the present-day Arabic numerals, 
along with other versions in between.

   http://www.islamicity.org/mosque/ihame/Ref6.htm   

I would like very much to find a good site on Chinese numerals or other 
East Asian or African numeral systems.

For more information on the difference between numbers and numerals, 
please see:

   http://mathforum.org/dr.math/problems/crall11.20.98.html   

I hope you find the information you are looking for, whether it is 
about numbers or numerals.

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

Date: 12/10/98 at 20:26:17
From: Julianne
Subject: History of Numbers

Thanks for your help earlier! But I still couldn't find the answer to 
my assignment. My assignment topic is 'History of Numbers.' 

My Outline is :

* Who invented Numbers?
* Where did they discover Numbers?
* When did they invented Numbers?
* How useful is Numbers to us?
* Where did inventors get the idea to invent Numbers?

I have to find the specific answers to the question above. Thanks for 
your time.

Date: 12/11/98 at 08:28:26
From: Doctor Rick
Subject: Re: History of Numbers

Hi again, Julianne. I'm afraid none of these questions (except the 
usefulness of numbers, which is a very broad question) has a solid 
answer. Numbers were invented/discovered well before recorded history. 
I gave you pointers to the kinds of solid information we have: when 
particular kinds of numbers were invented, and where particular kinds 
of numerals were used. 

The latter information indicates that numbers were in use several 
thousand years BC in Babylon and Egypt; and the Maya, who had no 
contact with the old world, had numbers too. I believe numbers go back 
to the very beginning of the human race. The Bible says that Adam 
noticed that there were two of each kind of animal and only one of 
him; that's numbers!

Look up "Numerals" in an encyclopedia, such as Britannica. You will 
probably find some suppositions about how numbers began in the form of 
pebbles or sticks, knots in a cord, etc., used to keep track of the 
number of animals in a herd and things like that. So counting of 
property was a very early use of numbers. The invention of money 
increased the usefulness of numbers. Then measuring of lengths for 
building introduced a new kind of number - not just a counting number; 
a length can include fractions. 

Now, with computers, all kinds of information are converted into 
numbers (binary numbers, specifically) in a computer's memory. Numbers 
are used by scientists to describe how the world works - expressing 
the laws of nature in equations. They are used by engineers, 
architects, musicians, ... name any profession and you can think of 
how they use numbers. As I said, it's a big topic!

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