# Indian mathematics

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**Indian mathematics** emerged in the Indian subcontinent until the end of the 18th century. In the classical period of Indian mathematics (400 AD to 1200 AD), important contributions were made by scholars like Aryabhata, Brahmagupta, and Bhaskara II.

## Quotes[edit]

**The Indian system of counting is probably the most successful intellectual innovation ever devised by human beings. It has been universally adopted. ...It is the nearest thing we have to a universal language.**- John D. Barrow,
*The Book of Nothing*(2009) chapter one "Zero—The Whole Story"

- John D. Barrow,

- In the whole history of Mathematics, there has been no more revolutionary step than the one which the Indian made when they invented the sign ‘0’ for the empty column of the counting frame.
- Lancelot Thomas Hogben. source: Mathematics for the Million, Lancelot Thomas Hogben. Quoted from Gewali, Salil (2013). Great Minds on India. New Delhi: Penguin Random House.

- I shall not now speak of the knowledge of the Hindus … of their suitable discoveries in the science of astronomy—discoveries even more ingenious than those of the Greeks and Babylonians, of their rational system of mathematics, or of their method of calculation which no words can praise strongly enough; I mean the system using nine symbols.
- Severus Sebokht, quoted in The Wonder That Was India, A.L. Basham. Quoted from Gewali, Salil (2013). Great Minds on India. New Delhi: Penguin Random House.

- It is India that gave us the ingenious method of expressing all numbers by ten symbols, each 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.
- Will Durant, Our Oriental heritage

- We owe a lot to the Indians who taught us how to count, without which no worthwhile scientific discovery could have been made.
- Albert Einstein, source: Ignited Minds: Unleashing the Power Within India, A.P.J. Abdul Kalam. Quoted from Gewali, Salil (2013). Great Minds on India. New Delhi: Penguin Random House.

- In order to instill a proper and well-founded pride in Hindus, it is (once more) most important to restore the truth about Hindu history, especially about Hindu society's glorious achievements. In technology, it cannot match China, which was the world leader until a mere three, four centuries ago. But in abstract sciences like linguistics, logic, mathematics, Hindu culture has been the chief pioneer.
- Elst, Koenraad (1991). Ayodhya and after: Issues before Hindu society.

- In the Vedic Age, India was very religious, but it was also ahead of the rest in mathematics and astronomy. Thus, the geometry of the Shulba Sutras, geometrical appendices to the manuals of ritual (Shrauta Sutras), include the oldest known formulation of the theorem named after Pythagoras, developed in the context of Vedic altar-building. Modern Hindus are fond of recalling this scientific element in their tradition, e.g. by quoting Carl Sagan: “Hindu cosmology gives a time-scale for the earth and the universe which is consonant with that of modern scientific cosmology”, as opposed to the limited Biblical-Quranic cosmology, which was protected against more far-sighted alternatives by a vigilant religious orthodoxy.
- Decolonizing the Hindu Mind, 2001, p. 29-30, by Koenraad Elst

- 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.
- Georges Ifrah. source: The Universal History of Numbers, Georges Ifrah. Quoted from Gewali, Salil (2013). Great Minds on India. New Delhi: Penguin Random House.

- Ancient Indian culture has regarded the science of numbers as the noblest of its arts … A thousand years ahead of Europeans, Indian savants knew that zero and infinity were mutually inverse notions. In short, Indian science was born out of a mystical and religious culture and the etymology of the Sanskrit word used to describe numbers and the science of numbers bears witn 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.
- Georges Ifrah. source: The Universal History of Numbers, Georges Ifrah. Quoted from Gewali, Salil (2013). Great Minds on India. New Delhi: Penguin Random House.

- Nesselmann observes that we can, as regards the form of exposition of algebraic operations and equations, distinguish three historical stages of development... 1. ...
*Rhetoric Algebra*, or "reckoning by complete words." ...the absolute want of all symbols, the whole of the calculation being carried on by means of complete words, and forming... continuous prose. ...2. ...*Syncopated Algebra*... is essentially*rhetorical*and therein like the first in its treatment of questions, but we now find for often-recurring operations and quantities certain abbreviational symbols. ...3. ...*Symbolic Algebra*...uses a complete system of notation by signs having no visible connection with the words or things which they represent, a complete language of symbols, which supplants entirely the*rhetorical*system, it being possible to work out a solution without using a single word of the ordinary written language, with the exception (for clearness' sake) of a conjunction here and there, and so on.**Neither is it the Europeans posterior to the middle of the seventeenth century who were the first to use***Symbolic*forms of Algebra. In this they were anticipated many centuries by the Indians.- Sir Thomas Little Heath,
*Diophantos of Alexandria: A Study in the History of Greek Algebra*(1885) pp. 78-79.

- Sir Thomas Little Heath,

*C'est de l'Inde que nous vient l'ingénieuse méthode d'exprimer tous les nombres avec dix caractères, en leur donnant à la fois, une valeur absolue et une valeur de position; idée fine et importante, qui nous paraît maîntenant si simple, que nous en sentons à peine, le mérite. Mais cette simplicité même, et l'extrême facilité qui en résulte pour tous les calculs, placent notre système d'arithmétique au premier rang des inventions utiles; et l'on appréciera la difficulté d'y parvenir, si l'on considère qu'il a échappé au génie d'Archimède et d'Apollonius, deux des plus grands hommes dont l'antiquité s'honore.*- It is India that gave us the ingenious method of expressing all numbers using ten characters, giving these numbers simultaneously a value absolute and a value of position; a fine and important idea, which seems so simple now, that we hardly appreciate its merit. But this very simplicity, the extreme ease resulting in all calculations, place our system of arithmetic in the first rank of useful inventions; and we appreciate the difficulty of achieving this, considering that it escaped the genius of Archimedes and Apollonius, two of the greatest and most honored men of antiquity.
- Pierre-Simon Laplace,
*Exposition du Système du Monde*, Vol. 2 (1798) also quoted in Tobias Dantzig,*Number: The Language of Science*(1930).

- My confidence in our shared future is grounded in my respect for India’s treasured past—a civilization that has been shaping the world for thousands of years. Indians unlocked the intricacies of the human body and the vastness of our universe. And it is no exaggeration to say that our information age is rooted in Indian innovations—including the number zero.
- Barack Obama. Quoted from Gewali, Salil (2013). Great Minds on India. New Delhi: Penguin Random House.