There's plenty of Isaac Newton biographies out there to read up on, but I'm just going to give my thoughts on this, I'll also add a very funny, but very informative video which better describes my point.
Background
The Calculus War was a dispute between Isaac Newton and Gottfried Leibniz, both fully accomplished Philosophers who had both invented a method of Calculus. Their individual variations on the subject are surprisingly different, yet, the history between both men caused an outbreak which ended up in one of them losing their reputation. The separate versions of Calculus meant that although they were in fact different in the ways they were used, they both carried out the same way of thinking and, of course, through both you achieved the same answer. Calculus today is the German version invented by Leibniz, but there is (still) and on-going battle between who actually came up with it first.
Apparently, neither of them did.
It was in fact the Ancient Greeks who invented the first methods of Calculus. But for the purposes of argument, the 'modern' Calculus is what this is about.
Isaac Newton had in fact written draft notes explaining a method of Calculus some time before Leibniz, and the papers had circled the continent between other Philosophers. However, it's debated that Leibniz himself saw these papers, and (the point used against him) took the ideas from Newton to start his own version. Of course, this all kicked off when our dear friend and bff Nicolas Fatio de Duillier labelled Leibniz as a plagiarist. It is to be noted that Fatio and Leibniz were on good terms throughout his time before coming into contact with Newton, so his sympathies for Leibniz were all but gone when it came to choosing a side. His reasons for starting up the conflict? My guess is it had something to do with gaining favour in the Royal Society circle again, after his stint with the Camisards...
Anyway, my thoughts are that although I believe Newton invented the foundations for modern Calculus, which reached eyes on the continent, I feel that Leibniz dis-regarded Newton's version (supposing that he had seen it) and reshaped it into the Calculus we use today. Yet because Newton did in fact write down his methods onto paper prior to Leibniz publishing his work, as well as plenty of Newton supporters from the continent ready to back him up, Leibniz didn't stand much of a chance.
Plus, as Newton had an army of support, he was able to wing his way through having his version published and causing Leibniz to be labelled a plagiarist. As a Newtonian, while his actions are deemed inexcusable, I must admit I'd feel the same if someone had read my papers which had my version of Calculus on, and then went ahead to create their own version based on mine. From Newton's perspective, combined with his superiority complex, any means (including lying) to have your name on the final print, isn't that much of a surprise.
However, I feel for Leibniz, despite my patriotism, as I'm sure he meant nothing of it, feeling he had come up with a completely independent form of Calculus. However, from this I conclude that both Isaac Newton and Gottfriend Leibniz invented Calculus independently.
Enjoy!
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