Infinitesimal Battle - Clash of the Titans
The battle for the credit of the discovery of calculus was a long and bitter one
Isaac Newton was born prematurely on Christmas day in 1642. His father had passed away three months before his birth. His mother married a wealthy Reverend and left baby Isaac in the care of his maternal grandmother.
By the time he finished his schooling, his mother widowed again, wanted to send him into the profession of a farmer. She was instead persuaded to send him to Trinity College. His uncle had studied at the University of Cambridge and wrote him a letter of recommendation.
He joined Trinity College at the University of Cambridge in 1661 and was provided a full-time scholarship to study at the college in 1664
In 1665 he returned to Trinity and discovered the generalised binomial theorem.
Aryabhata discovered the binomial theorem two millennia (in 500 BC) earlier, but the English wrote history, so it is called the Binomial Theorem and not Aryabhata’s Theorem BUT you have Newton’s Identities rather than Symmetric Polynomial Theorem.
In August 1665, the COVID of its times, “the great plague” swept across Europe. The college was closed to avoid the contagion from spreading. (and we thought we invented lockdowns)
A year after he finished his MA, in 1669, he was appointed the second Lucasian Professor of Mathematics
At this time he started his work on calculus which was known at the time as the infinitesimal calculus and today as differential calculus. This would eventually lead to a controversy that would rock the mathematical world in Europe.
Being a polymath, he worked in several areas at the same time. He worked on Optics, studying the refraction of light and the nature of light itself. Most people know him for his work in the area of gravity. He went on to explain the universal laws of motion and distill them into equations which are taught in schools even today. He also worked in the area of heat and energy flow.
Gottfried Leibniz was born in Leipzig, Saxony (now Germany) on 1 July 1646. His father passed away when he was 6. His father was the dean of philosophy at the University of Leipzig and he got access to all of his books at the age of 7.
He enrolled at the very same university, studied philosophy and presented his thesis in 1664. His attention was drawn to the area of combinatorial maths thereafter and he wrote a book on the subject in 1666.
In 1672 he moved to Paris and started studying under the tutelage of Christiaan Huygens. It was at this time that he started work in the area of calculus.
In 1684 he published his first paper on the new method of calculating maxima and minima. This text was further published by L’Hôpital in 1696.
In the meantime, Newton published his derivation in Section 1 of Book 1 of the Principia in 1687.
Newton claimed to have been working on Calculus since 1666 but he did not have any proof apart from his word. Various mathematicians from England attacked Leibniz over his claim that he was the first to discover calculus.
The truth of the matter is that the work on calculus lies on a long continuum of various mathematicians building on the works of others.
The Dutchman Simon Stevin (1548–1620), the Italian Luca Valerio(1553–1618), the German Johannes Kepler (1571–1630) were engaged in the development of the ancient "method of exhaustion" for calculating areas and volumes. The latter's ideas, apparently, influenced – directly or through Galileo Galilei – on the "method of indivisibles" developed by Bonaventura Cavalieri (1598–1647).
Source: Wikipedia
To be fair both were standing on the shoulders of giants.
At the time, the British establishment went into overdrive to discredit Leibniz and he spent the last decade of his life embittered in this controversy.
Not only did Leibniz have a jump on publishing the claims by about 3 years. He also showed private papers where he had started work in the area in a manner independent of Newton. As opposed to that Newton only had his word to offer. For the 17th-century English establishments, this was sufficient.
Today, they are jointly credited for the discovery.
I vividly remember my Mathematics tuition teacher talking to my class about Newton vs Leibniz. I admired his pedagogy because it was rare for mathematics teachers back home to even know about the narrative surrounding these concepts.