# Talk:Gottfried Leibniz

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## Misleading reasoning

*Both deserve credit, but modern calculus descends more from Leibniz because Newton largely kept his early work secret.*

The main reason for the use of Leibniz's version is the notation: he introduced not only the integral sign, but the differentials which can be used more flexible then Newton's flux - notation . Today, both notations are used, often simultaneously . --BRichtigen 15:47, 5 November 2008 (EST)

- what happened I think is that European mathematicians like Bernoulli built primarily upon Leibniz's work. Ball says, "The development of that calculus was the main work of the mathematicians of the first half of the eighteenth century. The differential form [of Leibniz] was adopted by continental mathematicians. The application of it by Euler, Lagrange, and Laplace to the principles of mechanics laid down in the Principia was the great achievement of the last half of that century, and finally demonstrated the superiority of the differential to the fluxional calculus. The translation of the Principia into the language of modern analysis, and the filling in of the details of the Newtonian theory by the aid of that analysis, were effected by Laplace." (Ball 1904) RJJensen 15:52, 5 November 2008 (EST)
- Ball's view seems to be a little bit outdated. I just looked into John Stillwell's book "Mathematics and Its History" (4th ed, 1997):
There is no doubt that Leibniz discovered calculus independently, that he had a better notation, and that his followers contributed more to the spread of calculus than did Newton's. Leibniz' wok lacked the depth and virtuosity of Newton's, but the Leibniz was a librarian , a philosopher, and a diplomat with only a part-time interest in mathematics. His

*Nova methodis*[1684] is a relatively slight paper, though it does lay down some important fundamentals - the sum, product, and quotient rules for differentiation - and it introduces the dx/dy notation we now use. He also introduced the integral sign , in his*De Geometria*[1686] and proved the fundamental theorem of calculus, that integration is the inverse of differentiation. This result was known to Newton and even, in a geometric form, to Newton's teacher Barrow, but it became more transparent in Leibniz's formalism.- Nowadays, the consensus is that British mathematics suffered for quite a while for not using Leibniz's notations out of ideological reasoning.
- --BRichtigen 16:10, 5 November 2008 (EST)

- what happened I think is that European mathematicians like Bernoulli built primarily upon Leibniz's work. Ball says, "The development of that calculus was the main work of the mathematicians of the first half of the eighteenth century. The differential form [of Leibniz] was adopted by continental mathematicians. The application of it by Euler, Lagrange, and Laplace to the principles of mechanics laid down in the Principia was the great achievement of the last half of that century, and finally demonstrated the superiority of the differential to the fluxional calculus. The translation of the Principia into the language of modern analysis, and the filling in of the details of the Newtonian theory by the aid of that analysis, were effected by Laplace." (Ball 1904) RJJensen 15:52, 5 November 2008 (EST)