Madhava and the Kerala school of astronomy
Madhava of Sangamagrama, a fourteenth-century astronomer of the Kerala school, developed infinite series for trigonometric functions, centuries before they appeared in Europe.
What it is
The Kerala school worked on accurate planetary models and corrections for the Moon's motion. Their methods were more precise than earlier Indian models in several respects.
How it is worked out or read
The site's calculations use the modern library and do not apply the Kerala models. The history is included for context on Indian mathematical astronomy.
Where it appears on this site
See history of Jyotish and why the Moon's speed varies.
Madhava of Sangamagrama
Madhava of Sangamagrama, who lived roughly from 1340 to 1425 CE, is regarded as the founder of what historians call the Kerala school of astronomy and mathematics. Few of his own writings survive, and much of what is known about his work comes from later members of the school who quoted and explained his results. He is credited with infinite series for the sine, cosine and arctangent, and with a series for pi, results that in Europe were found only centuries later.
For a reader of Jyotish, the point is that these series made it possible to compute the trigonometric values used in planetary calculation far more precisely than before.
The scholars who followed
The Kerala school was a line of teachers and students over roughly two centuries. Parameshvara, active in the early fifteenth century, is known for the Drigganita system of 1431, a revision of planetary parameters based on his own observations over many decades. Nilakantha Somayaji wrote the Tantrasangraha around 1500, which revised the model of the inner planets. Jyeshthadeva wrote the Yuktibhasha, around 1530, in Malayalam, giving proofs and explanations of the school's results in a way that is unusual for Sanskrit technical literature.
Together these works show a tradition that valued observation, revision and demonstration, not only the repetition of older rules.
Drik: checking against the sky
The word drik means what is seen. The Kerala astronomers stressed that computed positions should agree with what is actually observed, and that when they do not, the parameters should be corrected. This drik principle is the root of the modern distinction between drik panchangs, which use positions that agree with observation, and older almanacs that keep traditional siddhanta parameters even when they have drifted from the sky.
The panchang on this site is a drik panchang in this sense: its positions come from a modern astronomical model, which is the present-day form of the same principle.
Why the history matters
The Kerala school is sometimes presented only as a chapter in the history of mathematics, but its work was driven by astronomy, and its astronomy served the calendar and the chart. Knowing this history helps a reader answer a common question: whether Jyotish calculation was ever open to correction. The answer from Kerala is clearly yes. The tradition at its best expected its numbers to match the sky.