Brahmagupta's contribution to Mathematics

Against the popular perception, I would say that none including Aryabhat has invented ‘zero’ because the concept of ‘zero’ was always part of our life in different way academically or professionally since the origin of the universe.

Brahagupata’s major contribution to modern science and technology was - how to use zero in mathematical calculations that is used as base to calculate every field. He has formed the set of rules in the mathematics for positive and negative number in addition to forming the rules for using zeros in calculations and that has become the basis of mathematics and rest of the field including economics, finance, physics, chemistry, astronomy and so on…

Brahmagupta was born in 598 CE and died in c. 670. He lived in during king Vyagrahamukha in Bhillamala (modern Bhinmal) a capital of Gurjaradesa Chapa dynasty, one of the largesst kingdoms of Western India in parts of southern Rajasthan and Northern Gujarat.

He studied 5 traditional siddhantas in Brahmapaska in one of top schools for the astronomy during those days.

He also studied his predecessors’ (Aryabhata I, Latadeva, Pradyumna, Varahamihira, Simha, Srisena, Vijayanandin and Vishnuchandra) work to continue their research work. His rules of zero is in continuation of Aryabhata I ‘s work.

Brahmagupta gave the solution of the general linear in chapter eighteen of Brahmasphutasiddhanta,

bx + c = dx + e equivalent to x =< (e−c) / (b-d)


In chapter eighteen of Brahmasphutasiddhanta, Brahmagupta describes operations on negative numbers. He first describes addition and subtraction,

18.30 (Additions)

· 3 + 4 = 7 (a positive number)

· -3 + (-4) = -7 (a negative number)

· -3 + 4 = 1 (positive number)

· 3 + (-4) = -1 (negative number)

· -3 + 3 = 0 (zero when both positive and negative numbers are same)

· -3 + 0 = -3 (negative number)

· 3 + 0 = 3 (positive number)

· 0 + 0 = 0 (no difference)

18.32 (subtractions)

· -3 – 0 = -3 (negative number)

· 3 – 0 = 3 (positive number)

· 0 - 0 = 0 (no difference)

· 3 - (-4) = -1 (negative number is added)

· -3 – 4 = - 7 (negative number is added)

18.33(Multiplication)

· 3 * - 4 = - 12 (one negative and one positive product becomes negative number)

· 3 * - 4 = 12 (two negative becomes positive)

· 3 * 0 = 0 (any number multiplied with zero is zero)

18.34 (Division)

·     3
     ----  = 1 (positive number)
      3

·    - 3
       ----  = 1 (positive number)
      -3

·    0
    ---  = 0 (zero)
     0

·     3
     --- = -1
     -3

·      -3
      ---  = -1
       3

·    √0   =  0

·    0 square   = 0

·    0
    ----
     0

·    3
    ---- = undefined
     0

Except the last definition of zero, we use all his rules in the modern mathematics.

Watch out this space for part II on his other contributions in calculating complex mathematical formulas.

References:

Brahmagupta (598–668)," Department of Mathematics, Simon Fraser University (British Columbia, Canada), http;//www.math.sfu.ca/histmath/India/7thCenturyAD/Brahmagupta.html (February 17, 2006).

"Brahmagupta (ca. 598–ca. 665)," Wolfram Research, http://www.scienceworld.wolfram.com/biography/Brahmagupta.html (February 17, 2006).

"Brahmagupta," School of Mathematics and Statistics, St. Andrews University, http://www-groups.dcs.st-and.ac.uk/∼history/Mathematicians/Brahmagupta.html (February 17, 2006).

"Brahmagupta," Vidyapatha, http://www.vidyapatha.com/scientists/brahmagupta.php (February 17, 2006).

http://www.encyclopedia.com/topic/Brahmagupta.aspx