History of Numerals and Symbols

Date: 06/22/98 at 21:50:49
From: Melanie Edgar
Subject: Symbol history

We originally used the Roman system of nurmerals but the current 
symbols originated from the Hindo-Arabic system of numerals. Why and 
when did this change ocour?

The symbols + and - have been commonly used in arithmetic texts since 
the 15th century. Can you tell us the history of symbols like =, 
divided by, times, etc.?

Thank you.

Date: 06/23/98 at 12:58:13
From: Doctor Mateo
Subject: Re: Symbol history

Hello Melanie,

You ask some very interesting questions here.

Actually there were many numeral systems in existence even before the 
Roman system of numerals to which you refer. The Hindu-Arabic symbols 
have themselves changed over the centuries into what we use today.
The change on the European continent to the Hindu-Arabic system took a 
very long time.  The Spanish used Hindu-Arabic symbols in writing as 
early as the late 900s A.D.  

The spread of the Hindu-Arabic numerals into standard usage took a 
long time especially in Italy, where the Roman numeral system was 
dominant until the middle of the 16th century A.D. In some places in 
Italy it was forbidden to use anything but Roman numerals in the late 
1200s and early 1300s.

When did the big change or acceptance of the Hindu-Arabic numeral 
system take place? Probably during the mid-1500s. Why? Because the 
printing press came into existence in the mid-1400s and  the Hindu-
Arabic numerals were used in printing. By the middle of the 16th 
century (and even later in some of the conservative parts of Italy) 
most of Europe had accepted Hindu-Arabic numerals.

Why use Hindu-Arabic numerals instead of the Roman numerals? The 
transition happened after the printing press standardized the way the 
Hindu-Arabic numerals looked, but basically it was an issue of making 
good use of individuals' time. It took merchants and bookkeepers much 
longer to record data using Roman numerals. The Hindu-Arabic numerals 
made keeping records less time-consuming.

The + and the - sign were originally used to show surpluses and 
deficits in business dealings. Johann Widmann used them in his book 
Mercantile Arithmetic; the book was published in 1489. The Dutch 
mathematician Vander Hoecke was the first person known to use the 
+ and - symbols in writing algebraic expressions (early 1500s).

The = symbol was introduced by Robert Recorde in his book The 
Whetstone of Witte in 1557. The first = symbol was made with much 
longer lines. The = symbol was chosen by Recorde because he felt that 
there was nothing more equal than two straight parallel lines.

The multiplication symbol took a lot longer to develop. In the early 
1600s Thomas Harriot used the dot to indicate multiplication in his 
book _Artis Analyticae_ (1631), and William Oughtred used the x as a 
symbol for multiplication in his book _Clavis Mathematicae_ (1631).
The division symbol / was introduced into written form in 1659 by 
Johann Heinrich Rahn. He first used this symbol for division in his 
book _Teutsche Algebra_. (This division symbol was sometimes used for 
subtraction until symbols started becoming standardized.)

The symbols were introduced to make writing faster and easier, to take 
up less written space, and to help the printing process.

A good resource for learning more about the history of numbers and 
symbols is David M. Burton's _The History of Mathematics: An 
Introduction_. On the Web, consult "Earliest Uses of Mathematical 
Symbols" by Jeff Miller et al.:

  http://jeff560.tripod.com/mathsym.html   

Hope this helps you appreciate the development of mathematics as we 
know it today just a little more.

-Doctors Mateo and Sarah,  The Math Forum
 http://mathforum.org/dr.math/