History of Calculus: Newton & Leibnitz Discoveries & Controversies

In summary, the conversation is about a person looking for books to help them understand the development of calculus by Newton and Leibniz, as well as the controversies and differences between their theories. The person is recommended to do a Google search for more information and is also suggested to look for a companion book to complement "The Origins of the Infinitesimal Calculus" by Margaret Baron. They also discuss the difference in ideas between Newton's and Leibniz's approaches to differentiation and the concept of "limit" in mathematics. The person is grateful for the recommendation and mentions a chapter in Baron's book that specifically covers the mathematics of Newton and Leibniz, but is still looking for another book to aid in their understanding.
  • #1
ynuo
18
0
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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  • #2
Try a "google" on "Leibniz + Newton". I found a number of sites.
 
  • #3
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.
 
  • #4
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).
 
  • #5
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.
 

1. What is the history of calculus?

The history of calculus dates back to ancient civilizations such as Greece and Egypt, where basic principles of geometry and algebra were used to solve problems related to motion and area. However, the modern development of calculus is credited to two mathematicians, Sir Isaac Newton and Gottfried Wilhelm Leibniz.

2. Who discovered calculus?

Sir Isaac Newton and Gottfried Wilhelm Leibniz are credited with independently developing the foundations of calculus in the 17th century. Newton published his work, "The Method of Fluxions," in 1687, while Leibniz published his work, "Nova Methodus Pro Maximis et Minimis," in 1684.

3. What were the key discoveries of Newton and Leibniz in calculus?

Newton and Leibniz both developed the fundamental principles of calculus, including the concept of limits, differentiation, and integration. Newton's work focused on the physical applications of calculus, such as understanding motion and forces, while Leibniz's work focused on the mathematical applications of calculus, such as solving equations and calculating areas under curves.

4. What was the controversy surrounding the discovery of calculus?

There has been a long-standing debate over who should be credited as the true discoverer of calculus. Newton and Leibniz both claimed to have developed calculus independently, leading to a bitter dispute between them. The controversy was finally settled in the 18th century when it was accepted that both mathematicians had made significant contributions to the development of calculus.

5. How did calculus revolutionize mathematics and science?

The discovery of calculus revolutionized mathematics and science by providing a powerful tool for solving complex problems related to motion, geometry, and optimization. It allowed for the development of new theories and formulas in physics, engineering, and other fields, leading to significant advancements in technology and our understanding of the natural world.

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