Invention of calculus is generally considered as beginning of scientific revolution.
Newton and Leibniz faught each other for credit of calculus which actually belongs to kerala school of mathematics and astronomy
India has always been known for advancements in science and mathematics, rightly so.
India's wealth derived mainly from trade and agriculture which required good astronomy, navigation and trigonometry which led to advancements in maths.
This should not surprise you that CALCULUS and infinite series have their origin in India.
Today calculus and many other indian works are wrongly credited to European scholars.
These indian works reached to europeans through Jesuits who had a centre for mass translation of indian manuscripts in cochin college. Be it sine series [credited to Newton] or alleged "Leibniz" series [credited to Leibniz] both were indian works. In 1581 letters, Ricci explicitly aknowledged that he was trying to understand local methods of timekeeping (jyotisa), from "an intelligent Brahmin or an honest Moor"
Wikipedia claims indian mathematics only gave "non- rigorous method", "resembling" differentiation and credits indian mathematics for stating "components of calculus". Wikipedia denies credit to indian mathematicians for their work by saying they were not able to "combine many differing ideas under the two unifying themes of the derivative and the integral, show the connection between the two, and turn calculus into the great problem-solving tool we have today".
Actually, Europe didn't had philosophical foundation to discover calculus independently, it was mass palgarism and appropriation of indian work, not a surprise for many. Also we should not forget that there have been several instances before Newton where european scholars were found hiding there pagan/indian sources. Concept of Differentials and infinitesimals were also 17th century eurpean palgarism from Bhaskara II
"Indian mathematicians really had no use of generalizing the concepts of calculus for non-trigonometric functions. Perhaps this is why the Indian invention of calculus is rarely recognized even though it predates European calculus by nearly 200-300 years." says
Phoebe Webb
Legacy of Narayaṇa Paṇḍita
Narayana Pandita stated the result Varasankalita of terms in AP.
He derived Varasankalita formula for the sum of kth power of a series. Later this formula was also palgarised by Bernoulli and is still credited to him in "indian school textbooks."
Meaning: The numbers beginning with the number of terms in the series increasing by one and equal in number to one more
than the number representing the order of summation separately from the numerators. The corresponding denominators
are the natural numbers beginning with one. Product of these (fractions) is the Varasankalita.
According to modern text Varasankalita is the integration of integration.
The idea of Sama-ghata-sankalita in Yukti-bhasa and Vrasankalita in Ganita Kaumudi create the basic development of Integration and infinite series India.This work leads to evaluate integration
as the summation of series.
Intrestingly, this formula, a critical input for development of calculus, appears in europe AFTER Newton and Leibniz!
Mādhava of sangamagrāma
Founder of Kerela school of mathematics who later invented calculus.
Iriññāttappiḷḷi Mādhavan Nampūtiri laid the foundations of calculus.
He used early form of differentiation, integration, and developed integration for simple functions.
(Madhava of sangamagrama)
Madhava used his invention to find the value of Pi, correct to 11 decimal places. Then he derived the alleged 'Taylor series' and Trigonometric series which was also palgarised by Gregory.
one of the first application of infinite series ever by mādhava:
Yuktibhāṣā by jyeshthadeva
Yuktibhāṣā also known as Gaṇitanyāyasaṅgraha is first text on calculus.
For the first time in history, an integral equation is stated by Jyestadeva.
The sankalita(integral/summation) of a pada(variable) is half its varga(square).
∫xdx=x²/2 +C
From the basic to the very advanced, Yuktibhasa is the founding text of calculus.
Jyestadeva or one of his predecessors had also arrived on the concept of double integration.Multiple integration appeared and developed in Europe in 18th and 19th centuries.
Parameshwara discovered the mean value theorem of calculus which was later falsely credited to Cauchy.
Newton's dark secrets
Newton who had a dispute with Leibniz regarding priority in the invention of calculus also had works,to our modern eyes, is so thoroughly silly so as to be beyond ridicule.
Newton personally thought that alchemy and occult studies were far more important than his mathematics.he “was not the first of the age of reason, he was the last of the magicians.” ~ john maynard
He believed he found a recipe for the philosophers’ stone, a substance that could turn base metals like iron and lead into gold and also help humans achieve immortality. He thought the philosophers’ stone was located at the center of the Earth.
End of world and biblical chronology.
Newton wrote: “So then the time times & half a time are 42 months or 1260 days or three years & an half, reckoning twelve months to a year & 30 days to a month as was done in the Calendar of the primitive year. And the days of short lived Beasts being put for the years of [long-] lived kingdoms the period of 1260 days, if dated from the complete conquest of the three kings A.C. 800, will end 2060. It may end later, but I see no reason for its ending sooner."
He later revised the date for the end of the world to 2016.
His works clearly shows how ideas of Newton resonated with church. Newton was not just a simple palagarizer, he also was a deep thinker and while appropriating calculus Newton also added his dogmas of metaphysics into it.
Let's see how Newton affected the calculus we study today and how history of calculus is relevant today
As professor Raju says,"Europeans did not understand Indian methods of summing infinite series using “non-Archimedean” arithmetic, and a different philosophy, now called zeroism. They tried to fit it into their religious beliefs about mathematics as “perfect” and error-free.
Newton thought, as in his theory of fluxions, that this could be done by making time metaphysical (“mathematical time which flows equably”).The error about time was the reason why his physics failed. This history has contemporary value."
Prof. Raju In his book Euclid and jesus " Newton, however, was undoubtedly a great scholar. His fifty years of Biblical scholarship, uncovering a systematic process of fraud and misinterpretation, could easily have sparked a real revolution had it not been suppressed, as it remains to this day."
Newton and leibniz can be appreciated for their works in developing the functional notation we use today but much of what we know today as calculus from basic to very advanced are works of madhava and KSOMA.
Didn't Newton himself said that he was standing on the shoulders of giants to see the distant lands.
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Mathematics is not universal, it has cultural foundations to it. Calculus we teach in schools today is polluted with Newton's dogmas of metaphysics, unfortunately mainstreamed during colonial era.Eliminating redundant dogmas and teaching calculus without limits will make it easy and fun!
References and further reading
Sanjay madhukarrao deshpande,Basics of Development of Integration and Series in India, http://ijmaa.in/v5n4-b/265-270.pdf
Joseph T Noony, tweets on yuktibhasa by jyestadeva, https://twitter.com/JoeAgneya/status/1197855877119660034?s=20 https://twitter.com/JoeAgneya/status/1303008998505902082?s=20
Hithes pathiyil, sangam grama madhvan, https://www.scribd.com/doc/134342802/Sangama-Grama-Madhavan
CK Raju, calculus:the real story, http://ckraju.net/papers/Calculus-story-abstract.html
Subhash kak,Newton's many dark secrets, https://subhashkak.medium.com/newtons-many-dark-secrets-503bb0f7c365
Calculus is indian !?
ReplyDelete"This should not surprise you that CALCULUS and infinite series have their origin in India."
Thanks.