But now by the calculus of Leibniz the whole of geometry is subjected to analytical computation..." (1)"The Early Mathematical Manuscripts of Leibniz" https://archive.org/details/earlymathematic01gerhgoog
This most notorious controversy that tarnished noble mathematics for over three centuries has not yet entirely been laid to rest. Who was the inventor of Calculus? Did Isaac Newton and Wilhelm Leibniz invent the system in isolation of each other, or did Leibniz somehow have access to some of Newton's unpublished documents, which he then used to infer the direction of Newton's thinking, and "invent" the calculus to then claim as his own?
What is clear is that the invention of the calculus was an enormous feat of human accomplishment and ingenuity, and here, in the limited scope of this small website, we can just take the perspective that it was an enormous leap forward, and that both thinkers made enormous contributions, and that Newton ultimately won the PR war.
What is clear is that the invention of the calculus was an enormous feat of human accomplishment and ingenuity, and here, in the limited scope of this small website, we can just take the perspective that it was an enormous leap forward, and that both thinkers made enormous contributions, and that Newton ultimately won the PR war.
And I have come to realize that when Newton won the PR war against Leibniz over the invention of calculus, it was not just credit that was at stake; it was a way of thinking about science. Newton was in a sense quintessentially practical: he invented tools then showed how these could be used to compute practical results about the physical world. But Leibniz had a broader and more philosophical view, and saw calculus not just as a specific tool in itself, but as an example that should inspire efforts at other kinds of formalization and other kinds of universal tools. -Stephen Wolfram. http://blog.stephenwolfram.com/2013/05/dropping-in-on-gottfried-leibniz/
Even more remarkable about Leibniz's contributions to this new field was the story behind his acquisition of mathematical knowledge. He began studying mathematics in earnest much later than did Newton, and only at the age of twenty four did he begin to study mathematics seriously with significant time devoted to it. Correspondences between esteemed mathematicians and Leibniz somewhat later in his life make explicit references to his being quite unschooled in mathematics, at least initially, when compared to many of his contemporaries.
In a letter written to his close friend James Bernoulli in 1703, Leibniz wrote "When I arrived in Paris in the year 1672, I was self-taught as regards geometry, and indeed had little knowledge of the subject, for which I had not the patience to read through the long series of proofs. As a youth I consulted th e beginner's Algebra of a certain Lanzius, and afterward that of Clavius; that of Descartes seemed to be more intricate..." [3, p. 12]
The mathematical notation of Leibniz is one of his most enduring contributions to modern mathematics. His notations for many of the core concepts of calculus, including for the derivate and the "elongated S" meaning summa that he introduced to represent integration, are still in use to this day and form the standard notations of calculus.