## Hindu-Arabic Numerals in the West

### The Abacists and the Algorists

Spain played a central role in dissemination of Islamic intellectual tradition.

Since West Arabic gobar figures came into use early in Spain it was only a question of time before they appeared in Latin texts.

The oldest mathematical European manuscript is Codex Vigilanus contains 1 - 9 but no zero (AD 976).

So Hindu Arabic numerals came to the West helped by:

Introduction of the gobar numerals on the Abacus by GERBERT (980)
Translation of Algorithms from the Arabic and the writing of learned dissertations on arithmetic (C12, C13)

The final introduction "from below" by merchants (C15, C16).

### The Abacist

Gerbert had the numbers in the columns represented by special counters inscribed with numerals.
Over the centuries the numerals became like ours, with rotation from column to column.

In addition an unmarked round counter was placed in a column temporarily empty.

It didn't catch on - went back to unmarked counters. He had pinched his system from the Arabs but didn't see its advantages (only comes with calculation).

### The Algorists

The most important books for dissemination of Arabic - Hindu system appeared in C12.
"Arithmetic" by Al-Khouarizmi was translated - his name was used in its Latin form "Algorithms" to denote new Arithmetic.

All books used Hindu-Arabic numerals and showed elementary computing operations.

### The Zero

Essentially the confusion over the status of zero is that in one sense the zero was regarded as a figure whilst in another it was not.
The zero by itself meant nothing but when placed after another numeral the value of this numeral was enhanced 10 fold - difficult to understand!

### The final conquest

Region of highest population density and fullest urban development in medieval Europe was Italy - trade was good so they were interested in decimal place value system.
Italy had trade links with Arabs.

Leonardo of Pisa's "Liber Abaci" used the Hindu-Arabic figure and was a great success amongst the merchants.

General European use C15 (Florence banned them in 1299 because you could falsify them).

FIRST ASSESSMENT

Hindu-Arabic Numerals

Counting Systems and Notations

History of Mathematics Module

Links to other History of Mathematics sites

[ Comments ] [ Module Leader ]

These pages are maintained by M.I.Woodcock.