1) Brahmagupta has certainly played a very important role in the development of arithmetic. Who is the "father of arithmetic" is not clear. Following mathematicians could also be called this: - "Nicomachus (Greek: ΝικÏŒμαχος) (c. 60 – c. 120) was an important mathematician in the ancient world and is best known for his works Introduction to Arithmetic (Arithmetike eisagoge) and The Manual of Harmonics in Greek. He was born in Gerasa, Roman Syria (now Jerash, Jordan), and was strongly influenced by Aristotle. He was a Pythagorean." Source and further information: http://en.wikipedia.org/wiki/Nicomachus - "Ä€ryabhaá¹­a (DevanāgarÄ«: आर्यभट) (b. 476 AD – 550) is the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Aryabhatiya (499) and Arya-Siddhanta." "The number place-value system, first seen in the 3rd century Bakhshali Manuscript was clearly in place in his work. ; he certainly did not use the symbol, but the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients. However, Aryabhata did not use the brahmi numerals; continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities (such as the table of sines) in a mnemonic form." Source and further information: http://en.wikipedia.org/wiki/Aryabhata 2) "Brahmagupta (bikhari) (598–668) was an Indian mathematician and astronomer." "Undoubtedly, the Brahmasphutasiddhanta (Corrected Treatise of Brahma) is his most famous work. The historian al-Biruni (c. 1050) in his book Tariq al-Hind states that the Abbasid caliph al-Ma'mun had an embassy in India and from India a book was brought to Baghdad which was translated into Arabic as Sindhind. It is generally presumed that Sindhind is none other than Brahmagupta's Brahmasphuta-siddhanta." "Brahmagupta made use of an important concept in mathematics, the number zero. The Brahmasphutasiddhanta is the earliest known text to treat zero as a number in its own right, rather than as simply a placeholder digit in representing another number as was done by the Babylonians or as a symbol for a lack of quantity as was done by Ptolemy and the Romans. In chapter eighteen of his Brahmasphutasiddhanta, Brahmagupta describes operations on negative numbers." "His rules for arithmetic on negative numbers and zero are quite close to the modern understanding, except that in modern mathematics division by zero is left undefined." Source and further information: http://en.wikipedia.org/wiki/Brahmagupta 3) Here some information about the history of arithmetic: "The prehistory of arithmetic is limited to a very small number of small artifacts indicating a clear conception of addition and subtraction, the best-known being the Ishango bone from central Africa, dating from somewhere between 18,000 and 20,000 BC. It is clear that the Babylonians had solid knowledge of almost all aspects of elementary arithmetic by 1800 BC, although historians can only guess at the methods utilized to generate the arithmetical results - as shown, for instance, in the clay tablet Plimpton 322, which appears to be a list of Pythagorean triples, but with no workings to show how the list was originally produced. Likewise, the Egyptian Rhind Mathematical Papyrus (dating from c. 1650 BC, though evidently a copy of an older text from c. 1850 BC) shows evidence of addition, subtraction, multiplication, and division being used within a unit fraction system. Nicomachus (c. AD60 - c. AD120) summarised the philosophical Pythagorean approach to numbers, and their relationships to each other, in his Introduction to Arithmetic. At this time, basic arithmetical operations were highly complicated affairs; it was the method known as the "Method of the Indians" (Latin "Modus Indorum") that became the arithmetic that we know today. Indian arithmetic was much simpler than Greek arithmetic due to the simplicity of the Indian number system, which had a zero and place-value notation. The 7th century Syriac bishop Severus Sebhokt mentioned this method with admiration, stating however that the Method of the Indians was beyond description. The Arabs learned this new method and called it "Hesab" or "Hindu Science". Fibonacci (also known as Leonardo of Pisa) introduced the "Method of the Indians" to Europe in 1202. In his book "Liber Abaci", Fibonacci says that, compared with this new method, all other methods had been mistakes. In the Middle Ages, arithmetic was one of the seven liberal arts taught in universities. Modern algorithms for arithmetic (both for hand and electronic computation) were made possible by the introduction of Hindu-Arabic numerals and decimal place notation for numbers. Hindu-Arabic numeral based arithmetic was developed by the great Indian mathematicians Aryabhatta, Brahmagupta and Bhāskara I. Aryabhatta tried different place value notations and Brahmagupta added zero to the Indian number system. Brahmagupta developed modern multiplication, division, addition and subtraction based on Hindu-Arabic numerals. Although it is now considered elementary, its simplicity is the culmination of thousands of years of mathematical development. By contrast, the ancient mathematician Archimedes devoted an entire work, The Sand Reckoner, to devising a notation for a certain large integer. The flourishing of algebra in the medieval Islamic world and in Renaissance Europe was an outgrowth of the enormous simplification of computation through decimal notation." Source and further information: http://en.wikipedia.org/wiki/Arithmetic#History 4) "Though the Arabs are given the credit of taking mathematics into broader frontiers, they had begun their work with the help of Indian manuscripts. The story goes something like this. It was in 773 that the Arabs were able to set their eyes on the astounding developments of numerical methods Indians used when one of the Indian palmist and fortune-teller happened to visit the Arabian lands. So impressed were the Arab mathematicians with Indian inventions that the Arab mathematician Muhammed-Ibna-Musa-Abu-Jafar-Al-Khwarizmi himself came to India to study Indian mathematics. After stating here for some time after learning the subjects to his satisfaction, he wrote his manuscript “Algebra ’–b-e-Mukabla? This is how ‘Algebra?was born. His works, which were nothing but a translation of his Indian studies, left the European mathematicians spell-bound, especially by the use of base 10 to represent numbers. The idea of representing numbers by base 10, is thus, originally Indian. The trend then caught on. From Arabs to Greeks, from Greece to Spain and from Spain to Europe. Europeans however, initially reluctant to use base 10 to represent numbers, inevitably began to use it in 1202 (during the time of Bhaskaracharya). Though the mathematical works went on improving as it changed hands, the world availed the first systematically documented use of base 10 only in Bhaskaracharya’s manuscript “Lilavati? 4th century mathematician Diophantus, who is also known as ‘Father of Arithmetic? has his works in his book ‘Arithmetica?coinciding closely with the Indian manuscripts of earlier age. These are but a few evidences that arithmetic and basic mathematics that has evolved today in various forms, is but the creation of those great olden Indian minds." Source and further information: http://www.cs.uml.edu/~asaxena/vedic-maths.html 5) "Diophantus of Alexandria (Greek: ΔιÏŒφαντος ὁ Ἀλεξανδρεύς b. between 200 and 214, d. between 284 and 298 AD), sometimes called "the father of algebra", was an Alexandrian mathematician. He is the author of a series of books called Arithmetica that deal with solving algebraic equations, many of which are now lost. Pierre de Fermat studied Arithmetica and made a fateful note in the margin of his copy of the book that a certain equation similar to the Pythagorean equation considered by Diophantus has no solutions and he found "a truly marvelous proof of this proposition", the celebrated Fermat's Last Theorem. This led to tremendous advances in number theory, and the study of diophantine equations ("diophantine geometry") and of diophantine approximations remain important areas of mathematical research. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought. Diophantus also made advances in mathematical notation." Source and further information: http://en.wikipedia.org/wiki/Diophantus

Nicomachus did computatio ns using Greek numbers which we are not using today. Brahmagupta was the first to develop rules for addition, subtraction, multiplication and division using Indian numbers that we use today. Hence it should be Brahmagupta who is the father of arithmetic since science, commerce, mathematics depends on these four fundamental processes.

Law of Liuhui Brahmagupta http://www.flickr.com/photos/trapassing http://coupdetat.net/Wushu_Sunya_Zero