Aryabhata(476 — 550)
Āryabhata
6 min read
Āryabhata was an Indian mathematician and astronomer born in 476, the first of the great scholars of India's classical age. Author of the Āryabhaṭīya, he set down major advances in arithmetic, algebra, and astronomy.
Frequently asked questions
Key Facts
- Born in 476, in India during the classical age (Gupta Empire)
- Wrote the Āryabhaṭīya in 499, at the age of 23
- Gave a remarkable approximation of the number π (3.1416)
- Described methods for calculating square and cube roots
- Put forward the idea of the Earth's rotation on its axis to explain the apparent motion of the stars
Works & Achievements
Major treatise in Sanskrit verse covering arithmetic, algebra, trigonometry and astronomy; a cornerstone of classical Indian mathematics.
Calculation of a remarkably precise value of π, described as “approximate”, which reveals great mathematical sophistication.
One of the earliest trigonometric tables in history, the origin of the word “sine” by way of Arabic and then Latin.
The claim that the Earth spins on its axis, explaining the apparent motion of the stars — a remarkably bold idea for its time.
Demonstration that eclipses result from the shadows of the Earth and the Moon, rejecting mythological explanations.
An algorithm for solving indeterminate equations (Diophantine analysis), used in astronomy for calculating periods.
A poetic notation allowing very large astronomical numbers to be encoded in a memorable form.
Anecdotes
In his Āryabhaṭīya, Āryabhata calculates the value of π with remarkable precision: 3.1416. He even specifies that this number is “approximate” (āsanna), which suggests he may have had an intuition that π cannot be written exactly — an idea that mathematicians would not prove until the 18th century.
Āryabhata claims that the Earth spins on its own axis and that it is this rotation which gives the illusion of a sky turning above our heads. He compares this to a traveler on a boat who sees the trees on the riverbank “go by” when in fact it is he and his vessel that are moving. This bold idea ran counter to the beliefs of his time.
To write very large numbers in his verses, Āryabhata invents a system in which syllables represent digits, allowing him to encode enormous astronomical values in a few words that are easy to memorize. Scholars thus used poetry as a way to remember complex calculations.
Āryabhata offers a scientific explanation of eclipses: the Moon darkens because it enters the Earth's shadow, and the Sun is hidden by the Moon. He thereby rejects the popular belief that a demon named Rāhu “swallowed” the celestial bodies during eclipses.
He completes his treatise at just 23 years old, as he himself indicates in the text by specifying his age. This astonishing youthfulness shows just how thoroughly he had already mastered the mathematics and astronomy of his era.
Primary Sources
Add 4 to 100, multiply by 8, then add 62,000: the result is approximately the circumference of a circle of diameter 20,000. (i.e. π ≈ 3.1416)
Just as a man in a moving boat sees the stationary objects move backwards, so the fixed stars appear to an observer at Laṅkā to move westward.
The Moon eclipses the Sun, and the great shadow of the Earth eclipses the Moon.
When sixty times sixty years and three quarters of a yuga had elapsed, twenty-three years had passed since my birth.
Key Places
Great city of Magadha where Āryabhata lived, studied and composed the Āryabhaṭīya; a major intellectual center of the Gupta Empire.
Historical region where he was probably born and which formed the heart of the Gupta Empire.
Famous center of learning in Magadha; some historians believe that Āryabhata headed a scholarly institution there.
A major astronomical center of ancient India, located on the Indian reference meridian, whose observations were in dialogue with Āryabhata's work.
