Madhava and the Kerala School develop infinite series
- Date
- c. 1400
- Category
- Science, technology & invention
- Region
- Kerala, South India
- Era
- Post-Classical / Medieval
- Significance
Around the turn of the fifteenth century in present-day Kerala, southern India, the mathematician and astronomer Madhava of Sangamagrama (c. 1340-1425) pioneered the use of infinite series, founding what became known as the Kerala school of astronomy and mathematics.
Madhava derived power-series expansions for the sine, cosine, and arctangent functions, along with the alternating series for pi now called the Madhava-Leibniz series (pi/4 = 1 - 1/3 + 1/5 - 1/7 + ...), and devised correction terms that yielded the value of pi accurate to eleven decimal places. In treating the passage to a limit and summing infinitely many terms to obtain finite results, his work anticipated key ideas of differential and integral calculus by roughly two to three centuries. His methods and proofs were preserved and extended by successors such as Parameshvara, Nilakantha Somayaji (Tantrasangraha, c. 1500), and Jyeshthadeva, whose Yuktibhasa (c. 1530) gave rigorous demonstrations. The Kerala school flourished into the seventeenth century, though its achievements remained largely unknown in Europe until the nineteenth century.
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Empires active in c. 1400
- Malacca Sultanate1400 CE – 1511 CE
- Kanem-Bornu Empire700 CE – 1900 CE
- Ming Dynasty1368 CE – 1644 CE
- Ottoman Empire1299 CE – 1922 CE
- Solomonic dynasty1270 CE – 1974 CE
- Byzantine Empire330 CE – 1453 CE
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Further reading
The wider story
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