India’s contributions to mathematics span centuries, influencing global mathematical thought and practice. In the ancient period, the Sulba Sutras (~800 BCE) detailed geometric constructions, including the approximation of the square root of 2 and Pythagorean triples. Pingala (~200 BCE) introduced binary numbers and rules for permutations and combinations. The Jain texts (~500 BCE) explored concepts of infinity, while the place value system was fully developed between the 2nd century BCE and the 5th century CE.
During the classical period, Aryabhata (5th century CE) made pioneering contributions, including the approximation of π, advancements in trigonometry, and methods for solving quadratic equations. Brahmagupta (7th century CE) formalized the decimal system and introduced zero as a number, alongside rules for its operations. The Sulba Sutras and other texts also documented the rule of three, magic squares, and foundational mathematical astronomy. Mahavira (9th century CE) worked on algebraic solutions for cubic equations, while Halayudha (~10th century CE) expanded on Pascal’s triangle and binomial coefficients.
In the medieval period, Bhaskara II (12th century CE) advanced spherical trigonometry, logarithmic tables, and the Chakravala method for solving quadratic equations. The Kerala School of Mathematics, led by Madhava (14th century CE), developed infinite geometric series, approximations for π, and early concepts of calculus, including Taylor series-like expansions and tangent series. Nilakantha Somayaji (15th century CE) refined trigonometric calculations and planetary models. Jyesthadeva (16th century CE) documented these findings in Yuktibhasha, providing insights into the Newton-Gauss interpolation formula.
In modern times, Srinivasa Ramanujan (early 20th century CE) made groundbreaking discoveries in number theory, including infinite series, partitions, mock theta functions, and modular forms. Harish-Chandra contributed to Lie groups and representation theory, while Alladi Ramakrishnan, M.S. Narasimhan, and others advanced matrix analysis and topology. The AKS Primality Test by Manindra Agrawal, along with innovations in cryptography and coding theory, showcases India’s continued leadership in mathematics in the 21st century. This enduring legacy is a testament to India's rich mathematical heritage and its global influence across millennia.
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🪷 Ancient Period
Geometric Constructions and Proofs - Sulba Sutras - ~800 BCE
Pythagorean Triples - Sulba Sutras - ~800 BCE
Approximation of the Square Root of 2 - Sulba Sutras - ~800 BCE
Binary Numbers - Pingala (Chandaḥśāstra) -…