Georges Ifrah

[KALKI]

Georges Ifrah ( ? ) French historian of Mathematics and author of the book, The Universal History of Numbers

"The Indian mind has always had for calculations and the handling of numbers an extraordinary inclination, ease and power, such as no other civilization in history ever possessed to the same degree. So much so that Indian culture regarded the science of numbers as the noblest of its arts...A thousand years ahead of Europeans, Indian savants knew that the zero and infinity were mutually inverse notions."

(source: Histoire Universelle des Chiffres - By Georges Ifrah Paris - Robert Laffont, 1994, volume 2. p. 3 ).

Claiming India to be the true birthplace of our numerals, Ifrah salutes the Indian researchers saying that the "...real inventors of this fundamental discovery, which is no less important than such feats as the mastery of fire, the development of agriculture, or the invention of the wheel, writing or the steam engine, were the mathematicians and astronomers of the Indian civilization: scholars who, unlike the Greeks, were concerned with practical applications and who were motivated by a kind of passion for both numbers and numerical calculations."

He refers to 24 evidences from scriptures from India, whose dates range from 1150 BC until 458 BC. Of particular interest is the work by Indian mathematician Bhaskaracharya known as Bhaskara (1150 BC) where he makes a reference to zero and the place-value system were invented by the god Brahma. In other words, these notions were so well established in Indian thought and tradition that at this time they were considered to have always been used by humans, and thus to have constituted a "revelation" of the divinities.

"It was only after the eighth century BC, and doubtless due to the influence of the Indian Buddhist missionaries, that Chinese mathematicians introduced the use of zero in the form of a little circle or dot (signs that originated in India),...".

The early passion which Indian civilization had for high numbers was a significant factor contributing to the discovery of the place-value system, and not only offered the Indians the incentive to go beyond the "calculable" physical world, but also led to an understanding (much earlier than in our civilization) of the notion of mathematical infinity itself.

“The real inventors of [the numeral system], which is no less important than such feats as the mastery of fire, the development of agriculture, or the invention of the wheel, writing or the steam engine, were the mathematicians and astronomers of Indian civilization: scholars who, unlike the Greeks, were concerned with practical applications and who were motivated by a kind of passion for both numbers and numerical calculations.”

Sanskrit notation had an excellent conceptual quality. It was easy to use and moreover it facilitated the conception of the highest imaginable numbers. This is why it was so well suited to the most exuberant numerical or arithmetical-cosmogonic speculations of Indian culture."

"The Indian people were the only civilization to take the decisive step towards the perfection of numerical notation. We owe the discovery of modern numeration and the elaboration of the very foundations of written calculations to India alone."

"It is clear how much we owe to this brilliant civilization, and not only in the field of arithmetic; by opening the way to the generalization of the concept of the number, the Indian scholars enabled the rapid development of mathematics and exact sciences. The discoveries of these men doubtless required much time and imagination, and above all a great ability for abstract thinking. These major discoveries took place within an environment which was at once mystical, philosophical, religious, cosmological, mythological and metaphysical."

"In India, an aptitude for the study of numbers and arithmetical research was often combined with a surprising tendency towards metaphysical abstractions; in fact, the latter is so deeply ingrained in Indian thought and tradition that one meets it in all fields of study, from the most advanced mathematical ideas to disciplines completely unrelated to 'exact sciences.

In short, Indian science was born out of a mystical and religious culture and the etymology of the Sanskrit words used to describe numbers and the science of numbers bears witness to this fact. "

"Sanskrit means “complete”, “perfect” and “definitive”. In fact, this language is extremely elaborate, almost artificial, and is capable of describing multiple levels of meditation, states of consciousness and psychic, spiritual and even intellectual processes. As for vocabulary, its richness is considerable and highly diversified. Sanskrit has for centuries lent itself admirably to the diverse rules of prosody and versification. Thus we can see why poetry has played such a preponderant role in all of Indian culture and Sanskrit literature. "

(source: The Universal History of Numbers - By Georges Ifrah p 365 - 441). For more refer to chapter on GlimpsesIX and Hindu Culture1).