Thread by @gargiuvacha

The Rich Legacy of Indian Mathematics: A Comparative Thread

The term "algorithm" comes from al-Khwarizmi (c. 825), whose works introduced Indian arithmetic to the West. Indian mathematicians had been using algorithmic methods in texts like the Sulvasutras (prior to 800 BCE) and Aryabhatiya (c. 499 CE).

While the West struggled with Roman numerals, Indian numerals, praised by Pierre Simon de Laplace (18th century), revolutionized arithmetic with their simplicity and efficiency.

Euclid's Elements (c. 300 BCE) influenced Western math, but Panini’s Ashtadhyayi (prior to 500 BCE), a generative grammar for Sanskrit, had a similar profound impact on Indian mathematics and modern linguistics.

Pascal’s combinatorics (17th century) came much later than Pingala’s Chandahsastra (c. 300 BCE), which introduced algorithms for binary conversion and binomial coefficients.

Ptolemy’s geocentric model (2nd century CE) dominated Western astronomy. Meanwhile, Aryabhata (c. 499 CE) proposed a heliocentric model with Earth’s rotation, significantly advancing astronomical models.

Fermat posed the Pell’s equation (1657), solved by Euler and Lagrange (1770s). Yet, the Indian Chakravala method for this equation, found in Bhaskaracharya’s Bijaganita (c. 1114), was more efficient and predates the Western solution.

The Gregory-Leibniz series for Pi (1670s) was predated by Madhava of Sangamagrama (c. 1380-1460), who discovered the series and developed correction terms for better approximations.

Madhava of Sangamagrama (c. 1380-1460) pioneered the discovery of infinite series for trigonometric functions, notably the series for Pi, and developed correction terms for rapid convergence, significantly advancing mathematical analysis centuries before Western mathematicians.

Commentaries on Euclid’s Elements (5th century) provided insights in the West. Indian commentaries on Aryabhatiya by Bhaskara I (c. 629 CE) and Nilakantha Somayaji (1444-1544) offered detailed explanations and refinements.

Indian mathematicians like Srinivasa Ramanujan (1888-1920) continued the tradition of innovative mathematical thinking, influencing modern mathematics with their work on infinite series and number theory.
Source: brhat.in/openlibrary/it…