Aryabhata the Elder

476-550

Indian Mathematician and Astronomer

His Aryabhatiya assumed a level of significance among Indian mathematicians comparable to that of Euclid's Elements in the West, but as was typical of many Hindu thinkers, Aryabhata considered mathematics of secondary importance to astronomy. Indeed, most of his achievements in math were in service to his study of the planets, yet it was as a mathematician that he had his greatest impact on the thinking of scholars in India, and later in Arabia. Thanks largely to Aryabhata, Indian mathematics passed out of the "S'ulvastra period," when math fell primarily under the control of priests, and into the more scientifically oriented "astronomical period" that lasted until about 1200.

During the sixth century, at a time when Europe was descending into darkness and Arabia had not yet awakened, India had the beginnings of a thriving scientific community at the city of Ujjain in the central part of the subcontinent. Yet Aryabhata, one of India's greatest mathematicians, came from Patna or Pataliputra in eastern India. Already a millennium old, the city, capital of the Mauryan Empire centuries before, had long since fallen into ruins. Symbolic of its state of disrepair was the fact that Pataliputra was a center of superstition where priests taught that Earth was flat and that space was filled with invisible and demonic planet-like forms. The persistence of these ideas made the achievements of Aryabhata all the more impressive.

The form of the Aryabhatiya (499), written in the same sort of verse used for social amusements, further reflected the climate of Indian learning in his time: in one famous passage from his great work, Aryabhata used the poetic conceit of commanding a "beautiful maiden" to answer an inversion problem. In fact inversion—which involves starting with a solution and working backward, developing the steps whereby one reached that solution—would be one of many new concepts introduced in the Aryabhatiya.

Bringing together teachings from ancient Greek and Indian astronomers, as well as new ideas from Aryabhata himself, the Aryabhatiya developed various rules for arithmetic and trigonometric calculations. It also contained a number of important "firsts" or near-firsts, including one of the first recorded uses of algebra. Furthermore, it was one of the first texts to include the idea of number position or place value (i.e., tens, hundreds, thousands, etc.). These concepts would have enormous impact as they moved westward, as would another idea implemented by Aryabhata in his text: the Hindu numeral system.

In addition, Aryabhata calculated the most accurate number for π up to that point in history, and in his Ganita—a poem in 33 couplets—he correctly stated the formula for finding the areas of a triangle and circle. He developed a solution to the indeterminate quadratic xy = ax + by + c, a solution that would be rediscovered by Leonhard Euler (1707-1783) some 1,200 years later.

As an astronomer, Aryabhata proved highly prescient in his suggestion that the reason the stars and planets seem to move around Earth is that Earth is in fact rotating on its axis as it moves around the Sun. It would be nearly a thousand years before a Western astronomer, Nicolaus Copernicus (1473-1543), recognized the same fact.

JUDSON KNIGHT