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Aryabhata: A great figure in ancient Indian mathematics and astronomy

Around 476 AD, Gupta rule was going on in ancient India. At that time, there came to the world a wise man, whose light of knowledge blossomed the special branches of mathematics and astronomy at that time. His name is Aryabhata. Aryabhata's name is bound to appear directly or indirectly in ancient scriptures when discussing astronomy or mathematics. Various mathematical rules and formulas discovered by Aryabhata are being used since ancient times even today.

The Birth

Not much information is available about Aryabhata's personal life. There are many disagreements about his birth place. Some claim Aryabhata's birthplace as Patliputra, others Kusumpur. According to one of Aryabhata's commentators Pratham Bhaskar, Aryabhata was born in a place called Ashmaka. Today it is identified as a place around South Gujarat and North Maharashtra. However, many researchers agree that he was born somewhere in present-day Kerala. The time of birth is fixed from one of his writings. He wrote that he was 23 years old during the three Yugapadas and Shatayugas. According to astrology, he was born in 476 AD.

Education life

Aryabhata had a great thirst for knowledge from childhood. From where he used to get learning materials, he used to learn with interest. Aryabhata's inquisitive mind was constantly searching for answers to various questions. At that time the fame of Nalanda University was spread all over the world. He left Kerala at a young age and set foot in Nalanda. For this he had to cross many uphills and downhills including forests, hills and mountains. In the fifth and sixth centuries of Christ, the system of practical teaching was in operation in this university, where science met theology and philosophy.

Astronomy was given special importance here. An astronomy laboratory was set up at Khagola village near the university. Basically, it is from this center that Aryabhata's complete astronomical education is at hand. Aryabhata's fame spread far and wide after his admission to Nalanda University, he became more popular among students and teachers. Gradually his talent began to blossom. He was hardworking and diligent. Therefore, he never hesitated to reveal the truth that he used to uncover in his research.

working life

Gupta era was going on in India. Religion had a great influence in the society then. Emperor Buddhagupta was seated on the throne as the ruler. Aryabhata's revolutionary ideas reached the emperor's ears. If someone comes up with something new by breaking the shell of the traditional way of thinking, he has to face the cannon and endure criticism. As we have seen with the medieval church. But going against the grain, the emperor embraced Aryabhatta's brilliant wisdom. Aryabhatta will publish his research results in public. All royal arrangements were completed. March 21, 499 AD. Aryabhata said,

The earth revolves around the sun, the earth is spherical in shape. Because this spherical earth rotates in its own axis, the day approaches the night, and the night ends and the day appears. The fact that Rahu has eclipsed the Moon and the Sun is a fabrication. These stories of mythology are baseless. An eclipse occurs when the shadow of the earth and the moon fall on the sun.

He declared his revolutionary decision to the public by showing the courage to deny the ancient Brahminical doctrine prevalent at that time. He declared in an unequivocal voice, that the moon has no light of its own, the light of the sun is reflected on the moon, and the moon appears illuminated from the earth.

Despite going against the scriptures, Aryabhatta was not humiliated in any way. Thumbing up the reverse trend, he added an entirely new concept to astronomy. Emperor Buddhagupta was immediately impressed by his research. As a gift, the emperor appointed him as Sarvamaykarta of Nalanda University, one of the best schools of ancient times. Aryabhatta's appointment to Nalanda heralded a revolutionary transformation in the education system of ancient India.


Around 499 AD, Aryabhatta composed his famous book 'Aryabhatia'. He composed the book in verse form. No idea is available about the exact number of years spent on the entire book. But according to some researchers, the book was composed in the first decade of the sixth century. Aryabhata used to record mathematical results and conclusions very briefly. Its detailed explanation, discussion of research methods are not mentioned in his works. It is believed that he used to describe it orally to his disciples in detail, so it was not written down. However, the other known work of Aryabhatta in ancient literature is the 'Arya-siddhanta'. No manuscripts of the Arya-siddhanta have been found. It is mentioned in the works of Varahamihira, Brahmagupta, and Bhaskara I. 'Aryabhatia' was divided into four padas or sections with a total of 118 hymns.

1. The first verse was called 'Das Gitika'. This section shows how to express large mathematical numbers using the Sanskrit alphabet in verse.

2. The second part or pada is called 'Ganet Pada'. The thirty-three verses of this verse describe numbers and formulas of numbers. Also Arithmetic, Algebra, Plane Trigonometry, Quadratic Equations, Sum of various exponential terms of first natural number n are discussed in this section. In this chapter, Aryabhatta gives the ratio of the circumference to the diameter of a circle as 3.1416 as the value of pi. He wrote,

In the deep depths of the ocean of knowledge lies a great store of jewels. Some of them are genuine, some are fake. With the help of his judgment he tried to collect only the authentic ones.

3. The third part is Kalakriya. The calculation of time is shown in verse 25 of this verse.

4. And the last part is 'Gola pada'. Its 50 verses contain Gola Tattva or Golak Tattva. It mainly deals with astronomy and spherical trigonometry.

Aryabhatta always wanted to break the shell of antiquity and give new pure ideas to Indians. Therefore, he felt free to express his own thoughts in line with the opinions of ancient astronomers and enumerators. His revolutionary mathematical and scientific theories overturned many old decisions.

Aryabhata in Arabic

Aryabhata's knowledge reached Arabia before the 8th century. Aryabhatta was looked upon with great respect by the sages and ascetics of Arabia. His works ushered in a new tide in Arabian mathematics and astronomy. Aryabhata was known as Arjavar in Arabia. The famous historian al-Biruni came to India in the 11th century. He also mentions Aryabhatta in the travelogue. He did not find any original works of Aryabhata. Got some quotes, which were compiled by Brahmagupta, another famous sage of ancient India. In the modern era, they were bound to two malts by the initiative of the scientist Kern. He published 'Aryabhatia' in 1874, collecting Aryabhata's quotations from the city of Leiden. It was translated into French in 1879.

Contribution of Aryabhata

Mathematics was an essential part of the daily life of ancient Indians. Since pen and paper were not invented then, the practice of mathematics was practiced by word of mouth. Aryabhata was the first to organize the oral mathematics and astronomy into written form.

Decimal number system and zero

The most common and popular in the present world is the decimal number system. This method is based on counting the ten fingers of two hands.

The first evidence of full use of the decimal number system is found in Aryabhata's work. Since the Aryabhatia texts were written verbatim, he also invented his own method of representing numbers. Numbers were expressed in words. Consonants were used as different numbers, and vowels were used to mark the position of numbers.

Although it initially differs from the present-day decimal number system, many similarities can be observed in methodological aspects. However, he was the first to describe the mathematical process of determining the square root and cube root of numbers using the decimal system. Aryabhatta is regarded as the originator of the full decimal number system as he ensured systematic generalization using the decimal system at that time. The key to the decimal system is the use of zero. Although the concept of zero was prevalent in the ancient Mesopotamian, Maya civilizations, they considered zero as absence, lack, and evil.

Aryabhatta is credited with inventing and documenting the effective use of zero and the ten-based number system in light of this. In 498 he mentions in a Sanskrit poem, "sthanam sthanam dasa gunam" meaning space to space tenfold, indicating the current spatial decimal numbering system.


He was the first to introduce algebra to the ancient Indians. He discovered the formula ax – by=c for solving indeterminate algebraic equations. Aryabhata also determined the value of pi almost exactly. He calculated the value of pi as {(4+100) × 8 + 6200} ÷ 20000 = 62832÷20000 = 3.1416, about one and a half thousand years ago. Aryabhatta also has a special contribution to the Diophantine equation of today's era. He found a way to solve equations containing multiple unknowns. It is named 'Kuttak'.


Mathematical branches like trigonometry, parametric, square root, cube root have been touched by his knowledge. Modern trigonometry was started by Aryabhata. Supposedly, he knew the formulas for compound and half angles for sine functions. He gave some ideas about sine, cosine, versine (1-Cosx), and inverse sine, which later advanced the branch of trigonometry.

Also, he was the first to list specific values ​​of sine and versine (1 − cos x) at 3.75° intervals from 0° to 90°. Interestingly, the value obtained is accurate to 4 decimal places. Aryabhata used RsinX instead of sinX directly in his sine table. Here 'R' is the radius of a given circle. Aryabhata set this 'R' value at 3438. Mathematicians believe that Aryabhata calculated this by taking the length of the arc in a circle of unit radius as one unit for a minute amount of angle. The circumference of a circle subtends an angle of (360 × 60) = 21600 minutes at its center. Therefore, the circumference of the circle is O 21600 units and the radius of the circle will be 21600÷2π. Aryabhatta found the value of π (pi) = 3.1416, which when placed gives the value of the radius as 3438.


Aryabhata was the first to discover this thing which is the sphere which is our cold and familiar earth. The full scientific explanation of how the earth always rotates on its axis, how day and night happen, the moon does not have its own light, or eclipses came from Aryabhata. Every six months, the sun crosses the two extremes as it moves north-south around the equator every year. Aryabhatta called these two points 'Ayanast' and 'Haripadi Bindu'. These two points have a specific period of oscillation of the Sun's motion - this is also information from the astronomer Aryabhata.

He also observed that at these two points the length of night and day are essentially equal. As of today, 21st March and 23rd September. The term 'epicycle' has its origins in astronomy. The Greek astronomer Ptolemy tried to master the motion of the planets using this epicycle theory. Aryabhata also discussed the epicycle. He provided a clearer and more logical scientific theory of epicycles than Ptolemy in observing planetary motion. He invented many new theories of geometry and mathematics to calculate the size and position of the planets.

A thousand years before Copernicus, he discovered the heliocentric theory of the solar system. He mentions the shadow of the moon and the earth as the reason for the eclipse. In traditional astrology, Aryabhata introduced two alternative counting systems called 'Udayika' and 'Ardharatrika'. The astrological doctrines propounded by Aryabhata were able to make a deep impression on contemporary astronomers. He calculated the Earth's speed. According to his calculations, the circumference of the earth was 39,968 km. It was the most accurate of any measurement of that time, but the difference with today's calculation is only 0.2%.

In 455 AD, this great man of ancient astronomy passed away from Dharani. The world lost the footsteps of a genius. India's first artificial satellite launched on April 19, 1975 was named 'Aryabhatta' to pay tribute to this great astronomer of ancient India.

Among Aryabhatta's disciples Latdeva, Bhaskara, and Lagna became world famous. Post-Vedo India has rightly valued scholars and scientists. If someone countered the superstition with new arguments and research findings instead of conventional thinking, it was welcomed. Therefore, this world got pioneers like Aryabhatta, Brahmagupta, Bhaskaracharya, Kanada, or Susruta. Those who in ancient times have advanced the world in the glory of their knowledge yojan yojan krosh agare.

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