Ancient Indian mathematics was infused with religion, mainly with Hinduism and in some cases Jainism. It is said that the early Indian mathematicians derived their mathematical concepts from the ideas found in the Vedas. Evidence suggests that the Pythagoras formula was found (although not in the explicit form that we use now) in Baudhayana Sulba Sutra written by the Hindu mathematician, Baudhayana. Although the applications of the formula seem unclear to me, I remember reading somewhere that it was used for measurements in temple constructions. However, the works of later mathematicians showed a move towards secular mathematics in the sense that the connections with the scriptures weakened, and applications were increasingly for secular purposes.
One famous example is the Bakhshali Manuscript. According to Dick Teresi, it was the first document in “Indian mathematics that is devoid of religious association.”[1] It was found in the village of Bakhshali in present day Peshawar, Pakistan. Scholars date it to around A.D. 200 to 400. This work may have been the origin of algebra, as its notations for equations are found to contain a large dot which represents the “unknown”[2]. Other topics contained in the manuscript are arithmetic, geometry and the calculation of square root. I came across a rather interesting example of the problems contained in the Bakshali Manuscript. I will not explain or provide the solution in this post; however for the sake of your interest, it goes: “Before you are a group of 20 people comprising men, women and children. They earn 20 coins between them. Each man earns 3 coins, each woman 1.5 coins, and each child 0.5 coins. How many men, women and children are there?”[3] This may seem trivial, even unimportant; however we have to remember that this was presented in a period when there was no calculator, nor algebra. Nonetheless, in my opinion it will be a good IQ question to be posed to a bunch of secondary school kids.
Another example of an early secular treatise on Mathematics is the Ganita Sara Samgraha dated A.D. 850. It is written by Mahaviracharya, a Jaina scholar who resided in South India. It has been said to contain all the Indian mathematical ideas in the ninth century. Perhaps the most important ideas of the work are the explanation of the concept of zero, and methods for solving linear and quadratic equations. These ideas most probably laid out the foundations for the further expansion of mathematics by the Arabian/Muslim scholars.
One of the most significant products of revision and expansion of Indian mathematics in the Arab world is the Kitab al-fusul fi al-hisab al-Hindi (Chapters in Indian Mathematics) by Al-Uqlidisi. Most important contribution from this work was the use of Hindu-Arabic numerals[4]. Coupled with the use of decimal systems and pen-paper for calculations, it led to the possibility of performing multiplications and long divisions. Apart from this, the Islamic civilization also made other important contributions to mathematics during the Dark Ages.
Further expansion of mathematics involved the participation of the Western scholars during the Renaissance. The scientific revolution also happened around that time, accelerating the pace of growth. Subsequently, this resulted in the form of modern mathematics that we now have. We can see here that the early Indian mathematicians, drawing inspiration from the scriptures, played a part in the development of modern mathematics.
[1] (2009). Bakshali Manuscript. In C. A. Pickover, The Math Book : From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (p. 76). New York: Sterling Publishing.
[2] The idea of using a symbol to represent an unknown quantity in mathematics is the central idea in algebra. The most commonly used symbols are letters “x”, “y”, and “z”
[3] (2009). Bakshali Manuscript. In C. A. Pickover, The Math Book : From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (p. 76). New York: Sterling Publishing.
[4] Hindu-Arabic numerals system is the precursor to the modern numerals system we use.
February 1, 2010 at 5:24 am |
we should have learned Vedic from young, it’s so much simpler man..
February 4, 2010 at 11:30 am |
yes.. but this can’t be considered as formal mathematics.
this is more like mnemonics.. helpful in calculation and computations, but some of the methods are hard to be formalized, and some claim that certain methods will only work for limited cases. Nevertheless, it’s very interesting.. Think there are classes teaching Vedic methods for kids in singapore.