Aryabhata's mathematical contributions and algebraic innovations

ARAYBHATA'S CONTRIBUTIONS to MATHEMATICS & ALGEBRA

Aryabhata was born in 476 AD and was known as Aryabhata I or Aryabhata the elder. Aryabhata was a member of the Kusuma Pura School and a native of Kerala which is located in the most extreme South of India. Aryabhata is one of the greatest mathematicians of all times and is considered to be the father of the renaissance of mathematics in ancient India. (Hooda and Kapur, 2001, paraphrased) Indian mathematics historically claimed great achievements before Aryabhata's time and it was Aryabhata who first had the courage to break with tradition and to find knowledge gaps and to fill these gaps with his own research and knowledge. (Hooda and Kapur, 2001, paraphrased)

Important Contributions and Achievements in Mathematics and Algebra

Dutta (2005) in the work entitled: "Mathematics in Ancient India" states that in its earlier stages, mathematics "developed mainly along two broad overlapping traditions." (Dutta, 2005) According to Dutta (2005) these two traditions are those of:

(1) the arithmetical and algebraic; and (2) the geometric. (Dutta, 2005)

Included in Aryabhata's work on Mathematics are the following:

II. Most Notable Contribution in Algebra

It is stated in the work entitled: "Indian Mathematics" that of all the mathematics contained with in the work of Aryabhata entitled: "The Aryabhatiya" is

"...an approximation for ?, which is surprisingly accurate. The value given is: = 3.1416. With little doubt this is the most accurate approximation that had been given up to this point in the history of mathematics. Aryabhata found it from the circle with circumference 62832 and diameter 20000. Critics have tried to suggest that this approximation is of Greek origin. However with confidence it can be argued that the Greeks only used ? = 10 and ? = 22/7 and that no other values can be found in Greek texts." (Indian Mathematics, 2009)

There is stated by Selin (2001) in the work entitled: "Mathematics Across Cultures: The History of Non-Western Mathematics" to be "...no evidence of the method for extracting cube roots having been known earlier than Aryabhata I." (Selin, 2001)

Conclusion

Aryabhata made great contributions to mathematics and algebra and his greatest contribution to Algebra was that of his approximation for?

stated as equaling 3.1416 stated to be the most accurate approximation given at that time or previously in history. Aryabhata spent a great deal of time in examining previous mathematic and algebra study and filled in many knowledge gaps in these areas of study.