Bhaskaracharya – The Great Indian Astronomer and Mathematician

Bhaskaracharya Calculus

Bhaskaracharya – The Great Indian Astronomer and Mathematician. Since the childhood, we have been told that the period between 500 and 1200 A.D. is the Golden Age of Indian Astronomy. During this golden period, many Indian wizards were born who contributed greatly to the conception of Science and Mathematics. One such greatest mathematician of medieval India is Bhaskaracharya, whose contribution to Astronomy and Mathematics in the 12th century was unparalleled and significant.

Bhaskaracharya Biography

Bhaskaracharya India

                                                   Bhaskaracharya, the renowned Mathematician

Bhaskaracharya Early Life

Bhaskaracharya (1114–1185), otherwise known as Bhaskara II was born in Bijapur in Karnataka into the Brahmin family. His father, Mahesvara, was a well-known scholar. At his feet, Bhaskaracharya acquired the interest in Mathematics. After going through the works of the popular mathematician, Brahmagupta, Bhaskaracharya was very much inspired that he decided to dedicate his remaining life to mathematics. He achieved proficiency in 5 books of Bharat Shastras, 8 books of Grammar, 5 books of Mathematics, 6 texts of Medicine, 2 Mimansas, 4 Vedas and 6 books on Yoga. The innovations and researches made by him were not achieved in Europe, till the later period of time.

Works done by Bhaskaracharya

The textbooks written by Bhaskaracharya followed a simple and easy to understand methodology so as to stimulate student’s interests. These books gained a huge popularity that, even after four or five centuries of its inception, it was translated into Persian.

  1. The Siddhanta Shiromani scripted in two parts, (the first on mathematical astronomy), (the second part on the sphere);
  2. Lilavati, (on Mathematics);
  3. Bijaganita, (on Algebra);
  4. The Vasanabhasya of Mitaksha (commentary on the Siddhanta Shiromani);
  5. Karana-kutuhala (Calculations of Astronomical Wonders);
  6. Vivarana (commentary on the Shishyadhividdhidatantra).

However, among these six works, the first three lay more focus on mathematics. It’s translation in several languages of the world bear testimony to its eminence.

Siddhanta Shiromani Bhaskaracharya 

The “Crown of treatises,” (Siddhanta Shiromani) includes work in arithmetic, algebra, mathematics of the planets, and spheres. This work contains about 1450 verses. Bhaskara’s astronomical findings on positions of planets, instance of eclipses and cosmography, were composed in this treatise much before the world could even notice these findings. This book is considered as the pinnacle of all the astronomical works done for 700 years. It can be aptly called the “essence of ancient Indian Astronomy and Mathematics.

Siddhanta Shirmoani was split into four parts:  

  • Lilavati [Quadratic and Intermediate Equation] (278 Verses)
  • Bijaganita [Algebraic Calculation] (213 Verses)
  • Grahaganita [Astronomical Calculations] (451 Verses)
  • Goladhyaya [Trigonometry] (501 Verses)

Each part is so huge that they can be individually considered as a separate book. This book has literally surpassed all the ancient books present on astronomy and is enough to provide the complete knowledge of Ancient Indian Astronomy.

Bhaskaracharya Lilavati

Lilawati provides a clear example of Bhaskara’s expertise in putting a tough subject like mathematics into poetic language. This work has been translated into several languages throughout the world. Nearly for about 700 years, all the concepts of mathematics were taught from this textbook. It is the first and last book to enjoy such a long lifespan.

Bhaskaracharya Lilavati problem

                                                                Work of Lilavati by Bhaskaracharya

Bhaskaracharya Bijaganita

Bijaganita encompasses 12 chapters and covers topics like numbers, Zero, Surds, the kuttaka, Indeterminate quadratic equation with more than one unknown, Quadratic equation with more than one unknown, functions with products of several unknown.

Bhaskaracharya Karanakutuhala

“Karanakutuhala,” was the second book written by Bhaskara at the age of 69. This book puts key-focus on several astronomical calculations. This scripture remains as a reference book, even today in making the calendars.

Bhaskaracharya Contributions in the field of Mathematics

Bhaskaracharya’s innumerable contribution had earned him an outstanding position among the ancient Hindu mathematicians. His significant contributions towards the mathematical world continue to leave a tremendous impact in the numerical field even today.


Bhaskaracharya Pythagorean theorem

Some of several contributions to mathematics include:

  • A proof of the Pythagorean theorem just in two lines.
  • Arrived at the answers of quadratic and cubic indeterminate equations.
  • Primary concept of mathematical analysis, infinitesimal calculus, along with defined contributions within integral calculus.
  • Exhibited major work on differential calculus, after uncovering the derivative and differential coefficient.
  • Articulated Rolle’s theorem and the mean value theorem.
  • Developed spherical trigonometry and arrived at trigonometrical results.
  • Provided simple solutions to find the squares, cube, square roots, and cube roots of large numbers.
  • Suggested solutions for several problems on permutations and combinations.
  • Calculated an exact value of PI as 22/7 and more approximate value as 3.1416.

                                                         Sulbasutras of the Pythagorean Theorem

Bhaskaracharya Contributions in the field of Astronomy

Ganitadhyaya and Goladhyaya of Siddhanta Shiromani are completely devoted to astronomy phrasing about 1000 verses. Every little thing of astronomy has been prescribed within these two books. Some of worth mentioning highlights are:

  • Bhaskaracharya was the first to discover gravity, 500 years before Sir Isaac Newton.
  • He proposed the concept of Tatkalikagati, instantaneous motion which enables astronomers to approximately measure planetary movements.
  • Studied Astronomy based on the heliocentric solar system of gravitation.
  • One such contribution is made the appropriate calculation of the time taken by the Earth to orbit the Sun, as 365.2588 days which is fine representation to modern accepted measurement.
  • He also proved that when a planet is at the farthest, or at its closest to earth, the equation of the center vanishes.
  • The Earth is spherical and it exhibits a power of attraction.
  • The north and south poles of the Earth undergo 6 months of day and 6 months of night.
  • There is a vacuum beyond the Earth’s atmosphere.
  • Accurately calculated orbital periods of the Sun and that of Mercury, Venus, and Mars.

Bhaskaracharya Mathematician

Bhaskaracharya Calculation

Bhaskaracharya Legacy

Many scholars believe that Bhaskara’s work showed its impact in later developments of the Middle East and Europe. His work was already known to Islamic mathematicians who got inspired by his writing style. However, even though Europe got to know it by the end of the twelth century, it took a lot of time to introduce them into the texts. (1960).

Bhaskaracharya Final Days

Bhaskara was a natural born teacher and mathematician. He was married and blessed with two children. He handed over his complete knowledge on studies to his son, Loksamudra. Bhaskara was appointed as the head of the astronomical observatory at Ujjain, the leading Mathematical center in India at that time. Years later, in 1207, Loksamudra set up a school for the study of Bhaskara’s writings. It is believed that Bhaskara’s book ‘Lilavati’ was named after his daughter. Bhaskaracharya passed away at Ujjain in 1185 C.E.

Great Mathematician Bhaskaracharya

Statue of Bhaskaracharya at Patnadevi

Bhaskaracharya Works on Algebra Arithmetic And Geometry

Bhaskaracharya’s works on Algebra, Arithmetic, and Geometry propelled him to fame and immortality. In recognition of his invaluable contributions to mathematics and astronomy, he has been called the greatest mathematician of medieval India. He was bestowed an apt title by Ganesh Daivadnya for his genius work in Astronomy and Mathematics calling Bhaskaracharya “Ganakachakra chudamani” which means “a Gem among all the calculators of astronomical phenomena.”

His works inspired many of the Persian and European scholars, who through research on his works attained reputation. By now, everyone accepts the fact that after Bhaskaracharya, nobody could write excellent books on mathematics and astronomy in a lucid language in India.

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