Indian Mathematicians and their Contributions

Introduction

This document provides a glimpse into the rich and continuous tradition of Indian mathematics by highlighting some of the prominent mathematicians and their significant contributions to various branches of mathematics.

Vedic Texts and Early Works (3000 BCE - 600 CE)

• Vedic Texts (3000 BCE or earlier): These texts contain early mathematical concepts like number systems, Pythagorean triplets, and the decimal system.
• Lagadha's Vedanga Jyotisa (1300 BCE): This astronomical text includes mathematical models for the movement of the sun and equinoxes.
• Sulba Sutras (Earliest Texts of Geometry): These texts discuss the approximation of √2 and π, and the construction and transformation of squares.
• Panini's Ashtadhyayi (500 BCE): This work on grammar introduces concepts like algorithms, arrays, and contact-sensitive rules, which are relevant to modern programming languages.
• Pingala's Chandah-shastra (300 BCE): This treatise on prosody contains early ideas on binary sequences, binary to decimal conversion, and Pascal's Triangle.
• Baudha Mathematical Works (500 BCE - 500 CE): These works explore indeterminate and infinite numbers.
• Jaina Mathematical Works (200 BCE - 300 CE): These works cover concepts like logarithms, large numbers, algorithms for powers, the decimal system, and approximations of π.
• Aryabhata's Aryabhatiya (475 - 550 CE): This significant work covers a wide range of topics including square roots, cube roots, the place value system, sine tables, geometry, quadratic equations, and sums of squares and cubes.
• Varahamihira's Brihat Samhita and Pancha Siddhantika (6th Century CE): These works summarize five ancient astronomical treatises and discuss sine tables, trigonometric identities, combinatorics, and magic squares.
• Bhaskara I's Commentary on Aryabhatiya (600 - 680 CE): This commentary expands on Aryabhata's work on indeterminate equations and planetary astronomy.
• Brahmagupta's Brahmasphuta Siddhanta and Khandakhadyaka (598 - 668 CE): These works introduce the concept of zero, negative numbers, Pythagorean triplets, cyclic quadrilaterals, and arithmetic mean.
• Virahanka's Vrttajatisamuccaya (600 CE): This work discusses the Fibonacci sequence.

Later Works (800 CE - 1700 CE)

• Sridharacharya's Trisatika and Patiganita (875 - 930 CE): These texts cover arithmetic, algebra, commercial mathematics, and quadratic equations.
• Mahaviracharya's Ganita-Sara-Sangraha (800 - 870 CE): This comprehensive work covers arithmetic, geometry, algebra, permutation combination, and sums of squares and cubes.
• Jayadeva's Cakravala method (10th Century CE): This work presents a method for solving second-order indeterminate equations.
• Sripati's Ganita Tilaka, Siddhanta Sekhara, and Dhikotidakarana: These works focus on planetary astronomy.
• Bhaskaracharya II's Lilavati, Bijaganita, and Siddhanta Shiromani (12th Century CE): These works cover arithmetic, geometry, algebra, and astronomy, including concepts like surds, permutation combination, calculus, and the mean value theorem.
• Narayana Pandita's Ganita Kaumudi and Bijaganita Vatamsa (1395 - 1400 CE): These treatises on arithmetic and algebra advance the works of Bhaskaracharya and discuss cyclical quadrilaterals, magic squares, and combinatorics.

Kerala School of Mathematics (1340 CE - 1700 CE)

• Madhava of Sangama Grama (1340 - 1425 CE): Considered the founder of the Kerala School of Mathematics, Madhava pioneered the development of calculus, infinite series approximations for π, cosine, and sine functions.
• Paramesvara's Commentaries (1360 CE): Paramesvara wrote commentaries on earlier works, including Aryabhatiya, Mahabhaskariya, Laghubhaskariya, Lilavati, and Surya Siddhanta, further developing ideas on cyclical quadrilaterals and iterative techniques.
• Nilakantha Somayaji's Planetary Model (1500 CE): Nilakantha developed a planetary model that closely approximated Kepler's model, and made contributions to the understanding of the irrationality of π, calculus, and spherical astronomy.
• Jyesthadeva's Yukti-Bhasa (1500 - 1575 CE): This work is considered the first textbook of calculus, providing detailed explanations and proofs of infinite series given by Madhava.
• Shankara Variyar's Kriyakramakari (1500 - 1569 CE): This commentary on Lilavati and Tantrasangraha provided proofs for the results and procedures in Lilavati.
• Ganesha Daivajna's Buddhi Vilasini: This commentary on Lilavati provided further explanations and proofs.
• Krisna Daivajna's Bijapallva: This commentary on Bhaskaracharya's Bijaganita provided explanations and proofs.
• Munishvara's Siddhanta-Sarvabhauma (17th Century CE): This commentary on Lilavati and Patisara provided explanations and proofs, and discussed trigonometric identities.

Conclusion

The contributions of Indian mathematicians span various branches of mathematics, including arithmetic, algebra, geometry, trigonometry, calculus, and astronomy. The continuous tradition of mathematical inquiry, the practice of building upon earlier works, and the geographical spread of mathematical activity across India highlight the rich and influential legacy of Indian mathematics.