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### The History of Numbers and Numerals

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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.
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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.phys.virginia.edu/classes/109N/lectures/babylon.html

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.

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

I hope you find the information you are looking for, whether it is

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
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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
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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/
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Associated Topics:
High School History/Biography
Middle School History/Biography