Wednesday, February 19, 2014

History: Brahmagupta

As we learn about history’s great mathematicians, I am frequently struck by how often their pursuits are intertwined with other disciplines. We now have concrete job titles for what a person does—they are a mathematician, an astronomer, an engineer, a poet, a physicist—and it is implied that one will chose a profession and stick to it. I wonder if “mathematician” once encompassed all of these titles, and that to be a mathematician would have implied the various applications, or if we have now forced titles onto the work that people do, thereby corralling their ambitions to one topic.

One individual that was heavily involved in two disciplines—astronomy and mathematics—was Brahmagupta. It has been estimated that Brahmagupta was born in 598 in Ujjain, India, and that he passed in 670. During his lifetime he wrote (at least) two influential books, as well as held the position as the head of the astronomical observatory at Ujjain, “which was the foremost mathematical centre (sic) of ancient India at this time.” (O’Connor and Roberts). A portion of his work has been preserved in his book Brahmasphutasiddhanta, which displayed his insights in both astronomy and mathematics. The first ten chapters of the book described astronomical phenomena. The final fifteen further explored astronomical phenomena, but it also delved into algebra and geometry (O’Connor and Roberts).

Brahmagupta uncovered great mathematical truths in both algebra and geometry, but perhaps even more impressively, he is attributed to defining zero as a number and negative numbers. As early as 200 A.D., a closed circle-symbol or the word “kha” would be used by those who wanted to indicate an absence of a number or an empty place (“Zero as a Number”). Brahmagupta defined zero as a number and dug deeper, thereby unearthing negative numbers. In his book Brahmasphutasiddhanta he outlines rules for math using zero and negative numbers, where he calls an arbitrary negative number a “debt”, an arbitrary positive number a “fortune”, and zero as zero (Mastin).

Not only did Brahmagupta provide us with some of the building blocks of our modern number system, he concluded that quadratic equations could have two possible solutions (and one could be negative), he solved quadratic equations with two unknowns (which wasn’t considered in the West for another 1000 years), and gave a formula for the area of a cyclic quadrilateral as well as a formula for its length in relation to its sides (Mastin; Hayashi). In exploring these concepts, Brahmagupta even began to dabble in how we now view algebra by using the initials of the names of colors to represent the unknowns in his equations (Mastin).

Brahmagupta’s work explored the concretes of our solar system as well as the abstract concepts of mathematics. In describing zero and negative numbers, Brahmagupta unequivocally changed mathematics, and his other contributions further confirm the genius he possessed.


Works Cited
Hayashi, Takao. “Brahmagupta.” Encyclopedia Britannica, n.d. Web. 19 Feb. 2014.
Mastin, Luke. “Indian Mathemtatics-Brahmagupta.” The Story of Mathematics, n.d. Web. 19 Feb. 2014.
O’Connor, JJ, and E. F. Roberts. “Brahmagupta.” School of Mathematics and Statistics, University of
        St. Andrews, Scotland, n.d. Web. 19 Feb. 2014.
“Zero as a Number—Brahmagupta Period.” Wayne State University, n.d. Web. 19 Feb. 2014.

1 comment:

  1. Very nice! Good overview of Brahmagupta, and your intro paragraph is a good theme that bears further exploration. 5C's: +