History of the Hindu–Arabic numeral system
The full system emerged by the 8th to 9th centuries, and is first described outside India in Al-Khwarizmi's On the Calculation with Hindu Numerals (ca.
The Brahmi numerals have been found in inscriptions in caves and on coins in regions near Pune, Maharashtra[2] and Uttar Pradesh in India.
During the Vedic period (1500–500 BCE), motivated by geometric construction of the fire altars and astronomy, the use of a numerical system and of basic mathematical operations developed in northern India.
[4][5] Hindu cosmology required the mastery of very large numbers such as the kalpa (the lifetime of the universe) said to be 4,320,000,000 years and the "orbit of the heaven" said to be 18,712,069,200,000,000 yojanas.
[9][10] The form of numerals in Ashoka's inscriptions in the Brahmi script (middle of the third century BCE) involved separate signs for the numbers 1 to 9, 10 to 90, 100 and 1000.
Karl Menninger believes that, in such computations, they must have dispensed with the enciphered numerals and written down just sequences of digits to represent the numbers.
The Jain text entitled the Lokavibhaga, dated 458 CE,[18] mentions the objectified numeral "panchabhyah khalu shunyebhyah param dve sapta chambaram ekam trini cha rupam cha"meaning 'five voids, then two and seven, the sky, one and three and the form', i.e., the number 13107200000.
[22] In 628 CE, astronomer-mathematician Brahmagupta wrote his text Brahma Sphuta Siddhanta which contained the first mathematical treatment of zero.
By the end of the 7th century, decimal numbers begin to appear in inscriptions in Southeast Asia as well as in India.
[22] Before the rise of the Caliphate, the Hindu–Arabic numeral system was already moving West and was mentioned in Syria in 662 AD by the Syriac Nestorian scholar Severus Sebokht who wrote the following: According to Al-Qifti's History of Learned Men:[29] The work was most likely to have been Brahmagupta's Brāhmasphuṭasiddhānta (The Opening of the Universe) which was written in 628.
[29] 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: Al-Uqlidisi developed a notation to represent decimal fractions.
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 ingenious 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.
