The Kerala School of Astronomy and Mathematics, founded by Madhava of Sangamagrama in the 14th century, was a pioneering mathematical tradition in India. It was based in present-day Kerala and made significant advancements in infinite series, trigonometry, geometry, algebra, and calculus—many of which predated similar discoveries in Europe by several centuries.
- Infinite Series and Calculus
Madhava derived the infinite series for sine, cosine, and tangent functions, centuries before the formal development of calculus in Europe.
He formulated a version of the Taylor-Maclaurin series for trigonometric functions.
His work anticipated concepts later developed by Newton and Leibniz.
- Madhava’s Pi Series
He derived an infinite series for π (pi), now known as the Madhava-Leibniz series:
π=4(1−13+15−17+… )\pi = 4 \left(1 – \frac{1}{3} + \frac{1}{5} – \frac{1}{7} + \dots \right)
He also provided more accurate approximations of π than those available in Europe at the time.
- Contributions to Trigonometry
The Kerala school developed precise approximations for sine and cosine functions using infinite series expansions.
They formulated an early form of the sine and cosine power series expansions that were later rediscovered in Europe.
- Algebra and Geometry
Kerala mathematicians worked on polynomial equations and their solutions.
They developed geometric methods to study celestial motions and planetary positions.
Madhava of Sangamagrama (c. 1340–1425): Founder of the school, discovered infinite series for π and trigonometric functions.
Parameshvara (c. 1370–1460): Made extensive astronomical observations and corrected earlier planetary models.
Nilakantha Somayaji (1444–1544): Author of the Tantrasamgraha, which detailed the heliocentric planetary model.
Jyeshthadeva (c. 1500–1610): Wrote the Yuktibhāṣā, one of the earliest texts explaining calculus concepts in detail.
Achyuta Pisharati (1550–1621): Contributed to mathematical astronomy.
Though the Kerala School’s findings were not widely known in Europe at the time, there is speculation that Jesuit missionaries and traders may have transmitted some of these ideas, influencing later European developments in calculus. However, the independent development of calculus by Newton and Leibniz remains the widely accepted historical narrative.
The Kerala School’s contributions to mathematical analysis and infinite series demonstrate the advanced nature of Indian mathematics long before similar ideas emerged in Europe. Today, their work is recognized as an important part of the global history of mathematics.
