The Concept Calculus is the branch of mathematics that studies how objects change over time. The ‘Infinite Series’ is an important part of it. It entails adding up an infinite series of smaller and smaller integers until you reach a finite sum. This helps us understand how curves and motion function.
The Story The invention of Calculus is usually told as a bitter rivalry between Newton and Leibniz in the late 1600s. But the ‘Kerala School of Mathematics’ had already won the race 300 years earlier. Led by Madhava of Sangamagrama, these scholars were trying to do something ‘impossible’: track the exact, instantaneous motion of the Moon. To do it, they developed the ‘Infinite Series,’ adding up smaller and smaller pieces of time until they reached a finite sum. Legend has it that Jesuit missionaries in Kerala were so stunned by these texts that they carried them back to Europe, where they likely planted the seeds for the ‘Newtonian’ revolution.
The Timeline
| Milestone | Details |
| Western Ref. |
1660s CE (Newton & Leibniz)
|
| Indian Source |
1350 CE (Madhava of Sangamagrama)
|
| Chron. Gap |
Over 300 Years
|
The Evidence
Sanskrit Shloka: निहत्य चापवर्गेण रूपं तत्फलहारके । हरेत् समूलायुग्वर्गैस्तैस्तैरेषोऽल्पशः क्रमान् ॥ Transliteration: Nihatya cāpavargeṇa rūpaṃ tatphalahārake | Haret samūlāyugvargaistaistaireṣo’lpaśaḥ kramān || (Tantrasamgraha 2.437, 2.440 in some editions) Meaning: This verse describes the algorithm: ‘Multiply the arc by its square, and divide the result by the square of the even numbers…’ leading to the infinite series.
Related Innovations Madhava’s sine and cosine formulas are identical to the later Taylor series. Bhaskara II also proposed Tatkalika Gati (instantaneous velocity), a fundamental concept in differential calculus.
The Modern Legacy Calculus is the language of physics and the foundation of modern science. It enables us to predict planetary motion, economic shifts, and population growth.
