Indian Mathematicians and Their Contributions

Indian Mathematicians and their Contributions in Ancient India ranges from Arithmetic to Algebra to Geometry to Astronomy. In this article, you will learn about great ancient Indian mathematicians and their contribution, their list, their biography or history, providing key insights for GS Paper- I Art and Culture section of UPSC IAS Exam.

Table of Content

• Mathematics in Ancient India
• Aryabhata            
• Brahmagupta
• Mahaviracharya
• Bhaskara
• Bhaskaracharya (Bhaskara-II)
• Other important mathematicians
• Other Book on mathematics
• Mathematicians in India in Medieval period
• Conclusion
• Frequently Asked Questions

Indian Mathematics in Ancient India:

• Between 1000 BC and 1000 AD, Indian mathematicians authored several books on mathematics that includes- Arithmetic, Algebra, Geometry and Astronomy.
• Ancient names of different sections of Mathematics or Ganita:
  • Arithmetic– Pattin Ganita or Anka Ganita
  • Algebra– Bija Ganita
  • Geometry– Rekha Ganita
  • Astronomy– Khagolshastra
• India had played a significant role in the development of algebra and the concept of zero.
• The town planning of Harappa reflects that the people were proficient in measurement and geometry during that era.
• Geometric patterns can also be observed in ancient temple architecture.
• The term “Bijaganita” means “the other mathematics“.
  • The adoption of this name for the computational system indicates its recognition as a parallel system of computation.
• One of the earliest mathematical books, “Shulbasutra,” was written by Baudhayana around the 6th century BC.
• Shulbasutra mentions the formula for the square root of 2, introduces concepts similar to the Pythagorean theorem and incorporates geometry principles relevant to the construction of fire altars.
• In the 2nd century BC, Apastamba introduced concepts of practical geometry involving acute, obtuse, and right angles.
  • This knowledge of angles was used in the construction of fire altars during that time.

Aryabhata:

• Around 499 AD, Aryabhata penned the Aryabhatiya.
• He is counted as one of the most famous Indian mathematicians and amongst the first mathematician of India.
• He is known as the father of Indian mathematics.
• Aryabhatiya is a Sanskrit book containing information on mathematics and astronomy.
• Divided into four sections, Aryabhatiya covered various topics:
  • Calculation of large units of time
  • Number theory, geometry, trigonometry,
  • Bijaganita or Algebra
  • Astronomy (Jyotisa)
• Aryabhata had studied at the astronomical laboratory called Khagol in Nalanda.
  • During that era, astronomy was also known as “khagol shastra“.
• In Aryabhata’s book, the objectives of studying astronomy were to get:
  • Accurate calendars
  • Understand climate and rainfall patterns
  • Navigation
  • Horoscope analysis
  • Knowledge of tides and stars for night time guidance in crossing deserts and seas
• Aryabhata proposed that the Earth is spherical and rotates on its axis.
• Aryabhata formulated the area of a triangle and made discoveries in algebra.
  • Thus, he was the first well known exponent of algebra among Indian mathematicians.
• Aryabhata’s approximation of Pi was more precise than the Greek estimation.
• The Jyotisa section of Aryabhatiya dealt with astronomical definitions, methods for determining the true positions of planets, the movement of the Sun and Moon, and calculations of eclipses.
• Aryabhata explained that a lunar eclipse occurs when the Earth’s shadow falls on the Moon during its rotation, while a solar eclipse happens when the Moon’s shadow falls on the Earth.
  • These scientific explanations diverged from the orthodox theories that attributed eclipses to a celestial entity swallowing the planets.
• The first Indian satellite was named after him.

Brahmagupta:

• In the 7th century AD, Brahmagupta had mentioned the concept of Zero as a number in his work Brahmasputa Siddhanta.
• The Brahmasputa Siddhanta contained the concept of negative numbers by referring to them as debts, and by referring positive numbers as fortunes.
• The Brahmasputa Siddhanta also included the explanation of the Quadratic formula.

Mahaviracharya:

• In the 9th century AD, Mahaviracharya wrote Ganit Sara Sangraha.
• The Ganit Sara Sangraha is the earliest Indian mathematical text that was dedicated entirely to the subject.
• In Ganit Sara Sangraha, Mahaviracharya had provided detailed explanations of algebra and geometric concepts, such as equilateral and isosceles triangles, rhombuses, and circles.
• Mahaviracharya was patronised by the Rashtrakuta King- Amoghavarsha.

Bhaskara

• In the 7th century, Bhaskara wrote Aryabhatiyabhasya related to Mathematics and astronomy.
• ISRO had launched Bhaskara I rocket in 1979 in order to honour the mathematician Bhaskara.

Bhaskaracharya (Bhaskara-II):

• In the 12th century AD, Bhaskaracharya wrote Siddhanta Shiromani.
• SiddhantaShiromani is organized into four distinct sections:
  • Lilavati– for Arithmetic
  • Bijganita – for Algebra
  • Goladhyaya – for Spheres
  • Grahaganita– for Planetary mathematics
• In his book Lilavati, Bhaskaracharya had introduced the concept of chakrawat method or the cyclic method which aims to solve algebraic equations.
• In the 19th century, James Taylor had translated Lilavati, making it accessible to a global audience.

Other important mathematicians:

• The Vedic scholar Pingala in his book Chandashastra had introduced the concept of binarynumbersystem.
  • Chandashastra is the earliest Sanskrit book on poetic metres and verse.
• The Pingala had also mentioned about the matrameru, which is associated with the Fibonacci numbers and their sequence.
• Mathematicians Virahanka, Gopala, and Hemacandra had provided methods for generating Fibonacci numbers before the Italian mathematician Fibonacci introduced this concept.
• Baudhayana had explained the concept of the Pythagorean theorem.

Other Books on mathematics:

Indian Mathematicians in Medieval period:

• Narayan Pandit had contributed to the field of mathematics with works like Ganitakaumudi and Bijaganitavatamsa.
• Nilakantha Somayaji had written Tantrasamgraha, an astronomical text that included rules on Trigonometric Functions.
• Faizi was a mathematician in the court of Akbar who had translated Lilavati into Persian.
• Mahendra Suri was the court astronomer of Feroz Shah Bahamani, who had invented the Yantaraja, an astronomical instrument.

Conclusion

Great Indian mathematicians have significantly contributed to the development of mathematics and have led towards the advancement of the subject. From Aryabhata to Pingala, these mathematicians have developed numerous methods and formulas which are still used by modern mathematicians. Arabs also referred to mathematics as “Hindisat,” acknowledging their debt to India in this domain.

Ref: Source-1

FAQs (Frequently Asked Questions)