Aryabhata (Mathematician): History & Biography

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  • 0:01 A Shrouded Figure
  • 0:21 Aryabhata's World
  • 0:49 Contributions - Time
  • 1:47 Contributions - Math
  • 2:48 Contributions - Astronomy
  • 4:01 Lesson Summary
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Lesson Transcript
Instructor: Flint Johnson

Flint has tutored mathematics through precalculus, science, and English and has taught college history. He has a Ph.D. from the University of Glasgow

This is a short biography on one of the great Indian mathematicians, Aryabhata, accompanied by an explanation and historical context for his accomplishments. Following the lesson is a brief quiz.

A Shrouded Figure

Aryabhata was born in India around 476 CE, the same year as Odoacer conquered Italy and effectively ended the Roman Empire. In India, his life would see the decline and fall of the Gupta Empire. The time that he lived in, as well as his choice of vocations, are probably why we know almost nothing about his personal life or his appearance.

Aryabhata's World

Though it's difficult to say exactly where the state of mathematics in India were before Aryabhata, it is safe to assume that India had been affected by the Hellenistic World that had followed Alexander the Great in the fourth century. India was also influenced by trade with the Roman Empire that followed it up through the fifth century. Through them both, Aryabhata was probably familiar with the famous Western mathematicians and astronomers of Greece and Rome: Pythagoras and Euclid, among many others.

Aryabhata's Contributions

Aryabhata enhanced our understanding of the Earth and its place in the galaxy
The World of Aryabhata

Aryabhata published his first book, Aryabhatiya, when he was 23. In it, he not only wrote about advanced ideas in mathematics and astronomy, but he wrote in the tight poetry meters of the Hindu philosophical texts.


Aryabhata's work, from his first book on, was groundbreaking for many reasons. For one, there was his notion of time, which he divided into eons, half-eons, and ages, which varied in length and extended from a few thousand years up to millions of years. He determined some of this through his work with the rising of zodiacal signs on the horizon and other astronomical work. His divisions were heavily influenced by his religion, but they were remarkably accurate.

He suggested other, and smaller, measurements of time, along with explorations into the seven-day week and the intercalary month, a month inserted into a year to make the calendar align with the seasons. He also wrote analyses on sundial measurements so that time could be measured more accurately.


However, Aryabhata focused on mathematics. He went into great detail about arithmetic and geometric progressions like 2, 4, 6, and 8 or 2, 10, 50, and 250.

In algebra, Aryabhata wrote important observations on four types of equations.

  1. Equations with one variable or simple equations
  2. Quadratic equations or equations with a variable that has a polynomial
  3. Several equations with interrelated variables that have a common solution or simultaneous equations
  4. Indeterminate equations, equations with more than one possible solution

His studies into pi led to the closest approximation then known, 60,832/20,000 or 3.1416. In trigonometry, he discussed the concept of sine and was the first to calculate sine, cosine, versine, and inverse sine to four decimal places.


Another field Aryabhata studied was astronomy. He explored several geometric and trigonometric aspects of the celestial sphere and these are still used to study stars.

Astronomy in the time of Aryabhata
Celestial Sphere

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