The Arabs and the Indians

Aryabhata the Elder - 476 to 550 AD Kusumapura (now Patna), India
Brahmagupta - 598 to 670 AD, India
Al-Khwarizmi - About 780 to 850 AD in Baghdad (now in Iraq)

Notable Quotes: 

"Aryabhata is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world."

"A person who can, within a year, solve x2 - 92y2 = 1 is a mathematician."   Brahmagupta

"That fondness for science, ... that affability and condescension which God shows to the learned, that promptitude with which he protects and supports them in the elucidation of obscurities and in the removal of difficulties, has encouraged me to compose a short work on calculating by al-jabr and al-muqabala , confining it to what is easiest and most useful in arithmetic.  [al-jabr means "restoring", referring to the process of moving a subtracted quantity to the other side of an equation; al-muqabala is "comparing" and refers to subtracting equal quantities from both sides of an equation.]  Al Kwarizmi

BIOGRAPHICAL INFO

Aryabhata Bio Info  
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Aryabhata_I.html

Brahmagupta Bio Info  
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Brahmagupta.html

Al-Khwarizmi Biographical Info  
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Al-Khwarizmi.html

 

Mathematical Contributions

Our modern day concept of zero as a placeholder and our place value system was adopted from Indian and Arabic number systems. 

Aryabhata I 499 AD calculates p to be 3.1416. He produces his Aryabhatiya, a treatise on quadratic equations, the value of p, and other scientific problems.
 http://www-gap.dcs.st-and.ac.uk/~history/Chronology/1AD_500.html#499

Brahmagupta 628 AD Brahmagupta writes Brahmasphutasiddanta (The Opening of the Universe), a work on astronomy; on mathematics. He uses zero and negative numbers, gives methods to solve quadratic equations, sum series, and compute square roots.
  http://www-gap.dcs.st-and.ac.uk/~history/Chronology/500_900.html#628

Al-Khwarizmi -about 810 writes important works on arithmetic, algebra, geography, and astronomy. In particular Hisab al-jabr w'al-muqabala (Calculation by Completion and Balancing), gives us the word "algebra", from "al-jabr". From al-Khwarizmi's name, as a consequence of his arithmetic book, comes the word "algorithm"
http://www-gap.dcs.st-and.ac.uk/~history/Chronology/500_900.html#810