Contribution of Aryabhatta in Mathematics (PDF Download)

Contribution of Aryabhatta in Mathematics: Aryabhata, a renowned Indian mathematician and astronomer, was born in 476 CE. Despite being commonly mispelled as ‘Aryabhatta’, his birth year is well-known as he mentioned in his book ‘Aryabhatia’ that he was only 23 years old when he wrote it. His birthplace is believed to be Kusmapura or Patliputra, which is present-day Patna, Bihar. Many scientists believe that he completed his studies in Kusumapura, as most of his important works were found there. Kusumapura and Ujjain were the two major mathematical centers during the time of Aryabhata. Some people also believe that he was the head of Nalanda university, but there is no solid proof to support these claims.

Aryabhata’s only surviving work is ‘Aryabhatia’, which is a small book consisting of 118 verses. The book is divided into four sections: 13 verses (Gitikapada) on cosmology, 33 verses (Ganitapada) giving 66 mathematical rules, 25 verses (Kalakriyapada) on planetary models, and 50 verses (Golapada) on spheres and eclipses. This book serves as a summary of Hindu mathematics up to that time.

Aryabhata made substantial contributions to both mathematics and astronomy. In astronomy, he presented the geocentric model of the universe and correctly predicted solar and lunar eclipses. He believed that the motion of stars appeared to move in a westward direction because of the Earth’s rotation on its axis. In 1975, India honored the great mathematician by naming its first satellite after him.

In the field of mathematics, Aryabhata is credited with inventing zero and the concept of place value. He made significant contributions to the topics of trigonometry, algebra, approximation of π, and indeterminate equations. Although the cause of his death is unknown, he passed away in 550 CE. Bhaskara I, who wrote a commentary on the Aryabhatiya about 100 years later, wrote about Aryabhata with admiration and respect.

Aryabhata was a trailblazer who reached the pinnacle of knowledge in mathematics, kinematics, and spherics. He delved deeply into these fields, unearthing their secrets and then, with generosity, shared his findings with the learned community. He truly mastered these subjects, becoming a renowned figure and leaving a lasting impact on the world of mathematics.

Bhaskara I

Contribution of Aryabhatta in Mathematics

Aryabhata contributions to mathematics are given below:-

Approximation of π

Aryabhata was one of the first mathematicians to approximate the value of π (pi), which is the ratio of the circumference of a circle to its diameter. He calculated it as 3.1416, which is close to the modern value of π.

Concept of Zero and Place Value System

Aryabhata is credited with inventing the concept of zero and the place value system. The introduction of zero as a number revolutionized the field of mathematics and made it easier to perform mathematical operations.

Indeterminate or Diophantine’s Equations

Aryabhata made significant contributions to the field of indeterminate or Diophantine equations, which are equations with more than one variable and no exact solution. He developed methods for solving these equations and provided the framework for future mathematicians to build upon.


Aryabhata was one of the first mathematicians to make major contributions to the field of trigonometry. He provided a systematic approach to the study of triangles and developed methods for calculating trigonometric ratios, such as sine and cosine.

Cube roots and Square roots

Aryabhata also made contributions to the study of square roots and cube roots. He provided methods for finding the square and cube roots of numbers, which were significant advances in the field of mathematics.

Aryabhata’s Identities

Aryabhata developed several mathematical identities that are now known as “Aryabhata’s Identities.” These identities are used in various mathematical applications and have been widely studied and used by mathematicians for centuries.

Area of Triangle

Aryabhata made significant contributions to the field of geometry, including the study of the area of triangles. He provided formulas for calculating the area of triangles based on the lengths of their sides, which have since become standard formulas used in geometry.

In Short : Aryabhatta Contributions in Mathematics

Aryabhatta was an Indian mathematician and astronomer who lived in the 5th century. He was born in Pataliputra (modern-day Patna, India) and is considered to be one of the greatest mathematicians of ancient India. His contributions to mathematics have had a lasting impact on the field and continue to be studied and used today.

One of the most significant contributions of Aryabhatta to mathematics is his work on the place value system. He was the first to use zero as a place holder in mathematical calculations and this helped to simplify arithmetic operations. This place value system is still used in the decimal system that is used in most countries today.

Another major contribution of Aryabhatta to mathematics was his solution to the problem of finding the square root of 2. He used an approximation method to find the value of the square root of 2, which was accurate to four decimal places. This approximation was later used by other mathematicians and is still used in modern times.

Aryabhatta was also known for his work in geometry. He wrote a book on mathematics called the “Aryabhatiya”, which contained a comprehensive treatment of geometry. In this book, he introduced the concept of sine and cosine, which are fundamental functions in trigonometry. He also developed a method for finding the area of a triangle, which is still used in geometry today.

In addition to his work in mathematics, Aryabhatta made important contributions to astronomy. He was the first to propose that the Earth rotates on its axis and that this rotation causes the apparent movement of the stars. This idea was later developed into the heliocentric model of the solar system.

Aryabhatta’s contributions to mathematics and astronomy have had a lasting impact on the field and continue to be studied and used today. His ideas and methods have paved the way for future generations of mathematicians and astronomers to make new discoveries and advancements.


Aryabhatta was a brilliant mathematician and astronomer who made numerous contributions to the fields of mathematics and astronomy. His ideas and methods have had a lasting impact and continue to be studied and used today.

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