Aryabhata

By Laura Whitfield

In the year 499, a twenty-three-year-old in Pataliputra wrote a book of 118 verses that quietly overturned the heavens. Aryabhata — the first great name in Indian mathematics and astronomy — declared that the Earth rotates on its axis, explained eclipses without demons, and gave the world the place-value number system in its working form. He did it all in Sanskrit verse, because in his world, science was poetry that had to be memorized.

The Aryabhatiya, composed in 499 CE during the Gupta golden age, is divided into four sections: astronomical constants, mathematics, time-reckoning, and the sphere. Its most famous claim is stated with disarming simplicity: just as a man in a boat moving forward sees stationary objects moving backward, so the fixed stars appear to move westward because the Earth rotates eastward. This was a full thousand years before Copernicus. Aryabhata went further: he explained solar and lunar eclipses as the shadows of the Earth and Moon — explicitly rejecting the mythological demon Rahu that popular belief blamed — and gave the length of the sidereal year as 365.25868 days, astonishingly close to the modern value.

His mathematics was revolutionary in a quieter way. The Aryabhatiya uses a place-value system with zero — the decimal notation that would, via the Islamic world, become the arithmetic of the entire planet. He gave pi as 3.1416, correctly noting it was approximate; he solved linear and quadratic equations, summed arithmetic series, and computed sine tables — the word "sine" itself descends from his jyā, the Sanskrit term for the bowstring, mistranslated through Arabic into Latin. His sine table, calculated at intervals of 3.75 degrees, was accurate to several decimal places.

Aryabhata worked in Kusumapura, near modern Patna, possibly heading an astronomical school or university institution. Later Indian astronomers — Brahmagupta, Bhaskara — argued with him, corrected him, and built on him, which is exactly what a founder is for. The Islamic astronomers who inherited his work through translations called his tradition the Sindhind. Every time a student multiplies in the decimal system, or a navigator trusts that the Earth turns beneath the stars, the twenty-three-year-old of Pataliputra is in the room.

Impact on civilization

Aryabhata gave the world two of its most consequential ideas: the rotating Earth, stated a millennium before Copernicus, and the place-value decimal system with zero, the notation in which all modern science computes. His sine tables founded trigonometry's Indian tradition; his eclipse theory replaced mythology with geometry; his year-length stood among the most accurate of antiquity. The Gupta-era synthesis he authored traveled via Baghdad to become, quite literally, the arithmetic of the entire planet — the twenty-three-year-old who gave the world its numbers.