Hindsa

The Arabs borrowed so much from India in the field of mathematics that even the subject of mathematics in Arabic came to known as Hindsa which means 'from India' and a mathematician or engineer in Arabic is called Muhandis which means 'an expert in Mathematics'.

Ganit (Mathematics) has been considered a very important subject since ancient times. We find very elaborate proof of this in Veda(which were compiled around 6000 BC). The concept of division, addition et-cetera was used even that time. Concepts of zero and infinite were there. We also find roots of algebra in Vedah. When Indian Beez Ganit reached Arab, they called it Algebra. Algebra was name of the Arabic book that described Indian concepts. This knowledge reached to Europe from there. And thus ancient Indian Beez Ganit is currently referred to as Algebra.

This fact was well known to intellectuals of India that is why they gave special importance to the development of Mathematics, right from the beginning. When this knowledge was negligible in Arab and Europe, India had acquired great achievements.

People from Arab and other countries used to travel to India for commerce. While doing commerce, side by side, they also learnt easy to use calculation methods of India. Through them this knowledge reached to Europe. From time to time many inquisitive foreigners visited India and they delivered this matchless knowledge to their countries. This will not be exaggeration to say that till 12th century India was the World Guru in the area of Mathematics.

"10th place value method" dispersed from India to Arab. From there it got transferred to Western countries. This is the reason that digits from 1-9 are called "hindsa" by the people of Arab. In western countries 0,1,2,3,4,5,6,7,8,9 are called Hindu-Arabic Numerals. 

Roots of the Modern Trignometry lie in the book titled Surya Siddhanta . It mentions Zya(Sine), Otkram Zya(Versesine), and Kotizya(Cosine). Please remember that the same word (Zia) changed to "Jaib" in Arab. The translation of Jaib in Latin was done as "Sinus". And this "Sinus" became "Sine" later on.

It is without doubt that like Aank Ganit (Numerical Mathematics) Beez Ganit (Later the name Algebra became more popular) reached Arab from India. Arab mathematician Al-Khowarizmi (780-850 AD) has described topics based on Indian Beez Ganit in his book titled "Algebr". And when it reached Europe it was called Algebra.

Shridharacharya (850 AD) book titled "Pati Ganit" has been translated into Arabic by the name "Hisabul Tarapt".

The Hindu-Arabic numeral system is a decimal place-value numeral system that uses a zero glyph.

Its glyphs are descended from the Indian Brahmi numerals. The full system emerged by the 8th to 9th centuries, and is first described in Al-Khwarizmi's On the Calculation with Hindu Numerals (ca. 825), and Al-Kindi's four volume work On the Use of the Indian Numerals (ca. 830). Today the name Hindu-Arabic numerals is usually used.

Singaporean historian of mathematics Lam Lay Yong (National University of Singapore) claims that the computation in Kitab al-Fusul fi al-Hisab al Hindi (925) by al-Uqlidisi, and another Latin translation of the Arab manuscript written by the Persian mathematician Khwarizmi (825), are almost identical to algorithms for square root extraction, multiplication and division of Indian Mathematics.

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 Nestorian scholar Severus Sebokht who wrote the following:

"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."

According to al-Qifti's chronology of the scholars:

"... a person from India presented himself before the Caliph al-Mansur in the year [776 AD] who was well versed in the siddhanta method of calculation related to the movement of the heavenly bodies, and having ways of calculating equations based on the half-chord [essentially the sine] calculated in half-degrees ... This is all contained in a work ... from which he claimed to have taken the half-chord calculated for one minute. Al-Mansur ordered this book to be translated into Arabic, and a work to be written, based on the translation, to give the Arabs a solid base for calculating the movements of the planets ..."

The work was most likely to have been Brahmagupta's Brahmasphutasiddhanta (Ifrah)  (The Opening of the Universe) which was written in 628. Irrespective of whether Ifrah is right, since all Indian texts after Aryabhata's Aryabhatiya used the Indian number system, certainly from this time the Arabs had a translation of a text written in the Indian number system. 

In his text The Arithmetic of Al-Uqlîdisî (Dordrecht: D. Reidel, 1978), A.S. Saidan's studies were unable to answer in full how the numerals reached the Arab world:

"It seems plausible that it drifted gradually, probably before the 7th century, through two channels, one starting from Sind, undergoing Persian filtration and spreading in what is now known as the Middle East, and the other starting from the coasts of the Indian Ocean and extending to the southern coasts of the Mediterranean."

Al-Uqlidisi developed a notation to represent decimal fractions. The numerals came to fame due to their use in the pivotal work of the Persian mathematician Al-Khwarizmi, whose book On the Calculation with Hindu Numerals was written about 825, and the Arab mathematician Al-Kindi, who wrote four volumes "On the Use of the Indian Numerals" (Ketab fi Isti'mal al-'Adad al-Hindi) about 830. They, amongst other works, contributed to the diffusion of the Indian system of numeration in the Middle-East and the West.

The significance of the development of the positional number system is 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."