In the year 650 A.D. the Indian mathematician Brahmagupta was about 52 years old  He wrote two books entitled Brahma- sphuta- siddhanta (The Opening of the Universe) and Khandakhadyaka in 628 and 665 respectively.  Brahmagupta studied many different areas of math including, arithmetic progressions, right triangles, volumes, and surfaces.  He also produced a formulas for the area of a cyclic quadrilateral and the length of its diagonals in terms of its sides.  Brahmagupta  invented rules for solving quadratic equations and second degree intermediate equations such as ax^2 + b = y^2.  Brahmagupta is also accredited to inventing the concept of zero. Brahmagupta also the first mathematician to use algebra to solve astronomical problems, his other main interest.  Brahmagupta computed the length of the year to be 365 days, 6 hours,5 minutes, and 19 seconds, but then later changed that number to 365 days, 6 hours, 12 minutes, and 36 seconds.  Interestingly enough the first value that he gave was the more accurate, since the true length of the year is a little less than 365 days and 6 hours. Brahmagupta died somewhere between 668 and 670 A.D.

Author: Tim Lucas

References:
Mac Tutor History of Mathematics Archive, http://www-history.mcs.st-and.ac.uk:/history/Mathematicians/Brahmagupta.html

Brahmagupta (598-668)
 http://mathserv.math.sfu.ca/History_of_Math/India/7thCenturyAD/brahmagupta.html