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Saturday 18 November, 2006

Hindu Arabic Nemeric system

Before the rise of the Arab empire, the Hindu-Arabic numeral system was already moving West and was mentioned in Syria in 662 AD
by the Syrian-Orthodox scholar Severus Sebokht who wrote:
"I will omit all discussion of the science of the Indians, ... , of their subtle discoveries in astronomy, discoveries that are more
ingenious than those of the Greeks and the Babylonians, and of their valuable methods of calculation which surpass description.
I wish only to say that this computation is done by means of nine signs. If those who believe, because they speak Greek, that they
have arrived at the limits of science, would read the Indian texts, they would be convinced, even if a little late in the day, that there are
others who know something of value."

Impact on Mathematics
The significance of the development of the positional number system is probably best described by the French mathematician
Pierre Simon Laplace (1749 - 1827) who wrote:
"It is India that gave us the ingenuous method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful
inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes
and Apollonius, two of the greatest minds produced by antiquity."

Tobias Dantzig, the father of George Dantzig had this to say in Number:

"This long period of nearly five thousand years saw the rise and fall of many a civilization, each leaving behind it a heritage of
literature, art, philosophy, and religion. But what was the net achievement in the field of reckoning, the earliest art practiced by man?
An inflexible numeration so crude as to make progress well nigh impossible, and a calculating device so limited in scope that even
elementary calculations called for the services of an expert [...]
Man used these devices for thousands of years without contributing a single important idea to the system [...] Even when compared
with the slow growth of ideas during the dark ages, the history of reckoning presents a peculiar picture of desolate stagnation.
When viewed in this light, the achievements of the unknown Hindu, who some time in the first centuries of our era discovered the
principle of position, assumes the importance of a world event."

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