History of Calculus: Newton & Leibnitz Discoveries & Controversies

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The discussion revolves around the historical development of calculus, focusing on the independent contributions of Newton and Leibniz, the controversies that arose from their discoveries, and the evolution of their theories over time.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants inquire about resources and books that can provide insights into the contributions of Newton and Leibniz, as well as the controversies surrounding their work. There are discussions about the differences in their approaches to calculus, particularly regarding the concept of limits and the use of infinitesimals.

Discussion Status

Some participants have provided suggestions for further reading and resources, while others express a need for additional materials to clarify complex ideas presented in existing literature. The conversation appears to be ongoing, with multiple perspectives being explored.

Contextual Notes

Participants mention specific texts and chapters that address the mathematics of Newton and Leibniz, indicating a focus on understanding historical context and theoretical differences. There is an acknowledgment of the challenges in interpreting the original concepts and definitions used by both mathematicians.

ynuo
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I am looking for books that can help me to answer the following questions.

1. How Newton and Leibnitz independently invent calculus.
2. What were the controversies that followed.
3. How did the two theories continue to evolve? Did one theory win over the other?

Can you please recommend any.
 
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Try a "google" on "Leibniz + Newton". I found a number of sites.
 
Is there a companion that I can use to complement "The origins of the infinitesimal Calculus" by Margaret Baron. I am having trouble following the ideas in Baron on the development of Calculus by Newton and Leibnitz.

Thanks a lot.
 
If you want a good rough idea of the difference in ideas,
Newton was EXPLICIT in stating that in differentiation, we were finding the limiting expression of a fraction, and not that the derivative should be regarded as a fraction between infinitesemal quantities (he regarded that as meaningless)

Leibniz, however, used infinitesemals freely.

Neither were particularly clear with what they meant by "limit"; the precise definition of this belongs to mathematicians from Cauchy, Bolzano and onwards 8in particular Weierstrass).
 
Thank you very much for your reply and your help. Actually, there is a chapter devoted to the Mathematics of Newton and Leibniz in M. Baron's book the first edition. It is chapter 7. I was wondering if I can find another book to help me understand this chapter.
 

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