He was twenty-three when he wrote that the ground under our feet is what moves
In the year we call 499 a young man at Kusumapura, near modern Patna, finished a book of a hundred and twenty-one verses. He put his own age into it, in the way the text reckons years, and that is the only reason we know he was born in 476.
In the last section of the book he deals with the sphere of the sky, and he says something that nobody around him was saying. The stars do not travel westward across the night. The earth turns eastward, and the sky only appears to move.
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He explains it with a boat. A man going downstream sees the trees on the bank slide past him in the opposite direction, and knows perfectly well that the bank is not moving.
He was twenty-three. He had no telescope, no instrument beyond sightlines and arithmetic, and he was right.
A hundred and twenty-one verses
The Aryabhatiya is very short, because it was built to be memorised. Thirteen verses of astronomical constants and his own alphabetic system for writing large numbers. Thirty-three verses of mathematics: arithmetic, algebra, plane and solid geometry, series, and a table of sines. Twenty-five on the reckoning of time. Fifty on the sphere.
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Into that space he fits a method for solving linear equations in integers, the kuttaka or pulveriser, which is still the standard way such problems are approached. The compression is so severe that the text cannot be read without a commentary, and the commentaries began within a century.
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The numbers
He gives the ratio of a circle’s circumference to its diameter as 62832 to 20000, which is 3.1416, correct to four places.
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The interesting part is the word attached to it. He calls the value approximate. A man who thought he had found the exact ratio would have had no reason to say so, and the remark has been read ever since as a sign that he suspected the number could not be written down exactly at all.
He gives the length of the sidereal year as 365 days, 6 hours, 12 minutes and 30 seconds. He is out by about three minutes and twenty seconds. His word for the half-chord in his sine table, jya, travelled into Arabic as jiba, was misread as jaib, was translated into Latin as sinus, and is the reason the function is called sine.
Eclipses
The standard account of an eclipse in his world was Rahu, the severed head that swallows the sun and the moon and lets them go again.
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He wrote instead that the moon and the earth cast shadows, that a lunar eclipse is the moon entering the earth’s shadow and a solar eclipse the moon’s shadow falling on us, and he gave the arithmetic for calculating when it would happen and how long it would last.
He was not arguing with the story. He was quietly making it unnecessary by predicting the thing it was there to explain.
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What his successors did
Here the story stops being triumphant. Bhaskara I wrote the first great commentary in 629 and handled the rotating earth cautiously. Varahamihira dismissed it. Brahmagupta, in 628, rejected it outright and argued for an earth that stands still, and he refers to Aryabhata by name more than a hundred times, frequently to disagree.
Later commentators went further and reread the verse as a figure of speech, or as a description of how things look rather than how they are. The idea did not survive in the tradition that produced it.
Indian astronomy kept his mathematics, used his sine table for centuries, refined his constants, and put his best physical insight in a drawer. Europe arrived at the same conclusion with Copernicus in 1543, independently, a thousand years later.
His own successors did not suppress him. They read him, respected him, and decided he was wrong about the one thing he was most right about.
The name
He is often written as Aryabhatta in India, with the double t. Every astronomical text spells it Aryabhata, including all those hundred references by Brahmagupta, and the doubled form will not scan in the metre the verses are written in. It is a small thing and worth getting right.
India’s first satellite, launched in 1975, was named after him. It was a reasonable choice. He had, after all, been the first person in the country to say out loud what the thing would see from up there.
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If you think you have remembered everything about this topic take this QUIZ
Results
#1. At what age did Aryabhatta complete his famous work, the Aryabhatiya?
#2. What revolutionary theory did Aryabhatta propose regarding the Earth’s physical nature?
#3. Aryabhatta calculated the value of Pi ($pi$) to be approximately:
#4. The phrase “Sthanam sthanam dasha gunam” refers to which mathematical concept established by Aryabhatta?
#5. How did Aryabhatta explain the true cause of solar and lunar eclipses?
#6. Aryabhatta correctly identified that the Moon and planets shine due to:
#7. Which modern trigonometric function is derived from Aryabhatta’s concept of ‘Jya’?
#8. In 1975, India honored Aryabhatta’s legacy by naming what after him?
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Did Aryabhatta actually invent the number zero?
While he may not have been the first to use a symbol for zero, Aryabhatta was instrumental in defining the place-value system and the mathematical concept of zero that allowed it to be used in complex calculations.
Why is the Aryabhatiya so important?
It is one of the oldest surviving Indian mathematical texts that combines both astronomy and mathematics, providing formulas for areas, volumes, and planetary positions that were ahead of their time.
How did Aryabhatta calculate the Earth’s rotation?
Through meticulous observation of the stars and the application of spherical trigonometry, he deduced that the apparent motion of celestial bodies was caused by the Earth spinning on its axis.
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Sources & References
Encyclopaedia Britannica (“Aryabhata”) — his life, the structure of the Aryabhatiya and his principal results.
MacTutor History of Mathematics Archive, University of St Andrews — the evidence for his date and birthplace and the uncertainty over Kusumapura and Ashmaka.
The Aryabhatiya of Aryabhata, translated by Walter Eugene Clark (University of Chicago Press, 1930) — the verses on the rotation of the earth, the value of pi and the eclipse calculations.
Indian Space Research Organisation — the 1975 satellite named after him.
