Aryabhatta : Discovery of Zero

Aryabhata was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.

Aryabhatta was an acclaimed mathematician-astronomer. He was born in Kusumapura (present day Patna) in Bihar, India. His contribution to mathematics, science and astronomy is immense, and yet he has not been accorded the recognition in the world history of science. At the age of 24, he wrote his famed “Aryabhatiya”. He was aware of the concept of zero, as well as the use of large numbers up to 1018. He was the first to calculate the value for ‘pi’ accurately to the fourth decimal point. He devised the formula for calculating areas of triangles and circles. He calculated the circumference of the earth as 62,832 miles, which is an excellent approximation, and suggested that the apparent rotation of the heavens was due to the axial rotation of the earth on its axis. He was the first known astronomer to devise a continuous counting of solar days, designating each day with a number.

He asserted that the planets shine due to the reflection of sunlight, and that the eclipses occur due to the shadows of moon and earth. His observations discount the “flat earth” concept, and lay the foundation for the belief that earth and other planets orbit the sun.

Quick facts

FULL NAME :  Aryabhatta

FAMOUS AS : Mathematician, Astronomer


BORN ON : 476 CE


PLACE OF BIRTH : Kusumapura (Pataliputra),Now Patna

DIED ON : 550 CE

NOTABLE WORKS: Aryabhatiya, Arya-siddhanta

Major Works

Aryabhata’s major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature, and has survived to modern times. The Aryabhatiya covers arithmetic, algebra, and trigonometry.


Early Life and Carrier

  • Aryabhata’s birthplace is uncertain, but it may have been in the area known in ancient texts as Ashmaka, which may have been Maharashtra or Dhaka or in Kusumapura in present day Patna.

  • Some archaeological evidence suggests that he came from the present day Kodungallur, the historical capital city of Thiruvanchikkulam of ancient Kerala – this theory is strengthened by the several commentaries on him having come from Kerala.

  • He went to Kusumapura for advanced studies and lived there for some time. Both Hindu and Buddhist traditions, as well as Bhāskara I, the 7th Century mathematician, identify Kusumapura as modern Patna.
  • His contribution to the study of Algebra is immense. In Aryabhatiya, Aryabhata provided elegant results for the summation of series of squares and cubes through well tried formulae.

  • His system of astronomy was called the audayaka system, in which days are reckoned from uday, dawn at lanka or “equator”. His later writings, which apparently proposed the ardha-rAtrikA, or midnight model, are lost.

  • He correctly believed that the earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the earth, challenging the prevailing view.

  • In Aryabhatiya, he writes that ‘setting and rising of planets’ is a perception similar to that of someone in a boat going forward sees an unmoving (object) going backward.

  • He correctly asserted that the planets shine due to the reflection of sunlight, and that the eclipses occur due to the shadows of moon and earth, and not caused by a demon called “Rahu”!

  • He correctly deduced that the orbits of the planets are ellipses; this is another great discovery not credited to him but to Johannes Kepler (a German astronomer, born AD 1571).

Mathematical Work

Aryabhata wrote many mathematical and astronomical treatises. His chief work was the ‘Ayrabhatiya’ which was a compilation of mathematics and astronomy. The name of this treatise was not given to it by Aryabhata but by later commentators. A disciple by him called the ‘Bhaskara’ names it ‘Ashmakatanra’ meaning ‘treatise from the Ashmaka’. This treatise is also referred to as ‘Ayra-shatas-ashta’ which translates to ‘Aryabhata’s 108’. This is a very literal name because the treatise did in fact consist of 108 verses. It covers several branches of mathematics such as algebra, arithmetic, plane and spherical trigonometry. Also included in it are theories on continued fractions, sum of power series, sine tables and quadratic equations.

Aryabhata worked on the place value system using letters to signify numbers and stating qualities. He also came up with an approximation of pi (π) and area of a triangle. He introduced the concept of sine in his work called ‘Ardha-jya’ which is translated as ‘half-chord’.

Astronomical Work

Aryabhata also did a considerable amount of work in astronomy. He knew that the earth is rotating on an axis around the sun and the moon rotated around it. He also discovered the position of nine planets and stated that these also revolved around the sun. He pointed out the eclipses; both lunar and solar. Aryabhata stated the correct number of days in a year that is 365. He was the first person to mention that the earth was not flat but in fact a spherical shape. He also gave the circumference and diameter of the earth and the radius of the orbits of 9 planets.


Aryabhata died in 550 AD. He was 74 years old when he died.

Notable Ideas 

Explanation of lunar eclipse and solar eclipse, rotation of Earth on its axis, reflection of light by moon, sinusoidal functions, solution of single variable quadratic equation, value of π correct to 4 decimal places, circumference of Earth to 99.8% accuracy, calculation of the length of sidereal year

Some Unknown Facts About Aryabhata

  1. Aryabhata is credited to have set up an observatory at the Sun temple in Taregana, Bihar.

2. He wrote his book ‘Aryabhatiya’, when he was only 23.

3. He formulated a brilliant technique for finding the lengths of chords of circles with half chords as opposed to the full chord strategy utilized by Greeks.

4. Aryabhata did not use the Brahmi numerals; he used letters of the alphabet to denote numbers.

5. He also came up with an approximation of pi and determined that pi(π) is irrational.

6. He was the first mathematician to give what later came to be known as the tables of sine, cosine, versine, and converse sine to four decimal spots, which brought forth trigonometry.

7. Aryabhatta worked on the place value system and discovered zero for the first time, making use of letters to indicate numbers and pointing out qualities.

8. He discovered the position of nine planets and expressed that these likewise rotated around the sun.

9. He also gave a theory on eclipse; he said it wasn’t because of Rahu, as preached by many priests, but because of shadows cast by the earth and moon.

10. In his old age, Aryabhatta composed another treatise, ‘Aryabhatta-siddhanta’.

11. India’s first satellite Aryabhatta was named after him. There is also an Indian research center is called ‘Aryabhata Research Institute of Observational Sciences’.

Books by Aryabhatta


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