Newton versus Leibniz: Who Invented Calculus? - Tony Weathers - April 30, 2015

The speaker begins by expressing gratitude and introducing the topic of calculus, referencing the book 'The Calculus Wars' as a starting point. They delve into the historical background, mentioning other books like 'Philosophers at War' and a book on the history of calculus itself. The speaker outlines the structure of the talk: defining calculus, its historical emergence, contributions by key figures like Newton and Leibniz, and the controversy surrounding its invention. The explanation of calculus's definition varies according to different sources but centers around the concept of change. The speaker also touches on the ancient problems that led to the development of calculus, such as calculating areas of known geometric shapes and finding equations for tangent lines.

This paragraph delves into the evolution of algebra and geometry that set the stage for calculus. It highlights the contributions of Francois Vieta, who introduced modern algebraic notation, and Rene Descartes, who combined algebra with geometry, leading to the Cartesian coordinate system. The speaker explains how these developments allowed mathematicians to analyze arbitrary curves beyond classical shapes like conic sections. The paragraph also introduces the problems that drove the development of calculus: finding the area of a region bounded by an arbitrary curve and determining the slope of a tangent to a curve. The speaker mentions early contributors like Bonaventura Cavalieri, who worked with curves of the form y = x^n and derived an integration formula using the method of indivisibles.

The speaker discusses the contributions of various mathematicians to the development of calculus. Pierre de Fermat is recognized for his work on the difference quotient and integration power rule for rational values. Isaac Barrow, Newton's predecessor at Cambridge, is noted for his work on tangents and partial development of the fundamental theorem of calculus. The speaker then focuses on Isaac Newton, mentioning his development of the method of fluxions by 1669. Newton's work on the concept of limits and his dismissal of the idea of infinitesimals are also highlighted. The paragraph touches on the priority dispute between Newton and Leibniz, noting that while Newton had developed his methods earlier, he did not publish them until later.

The speaker shifts focus to Gottfried Wilhelm Leibniz, who was not a mathematician by training but made significant contributions to calculus. Leibniz developed a comprehensive notation for derivatives and integrals, publishing his work in 1684 and 1686. The paragraph details the priority dispute between Newton and Leibniz, emphasizing that while Leibniz published his work first, Newton had developed his methods earlier but chose not to publish due to a negative experience with the scientific community. The speaker also mentions the role of John Collins and Henry Oldenburg in the exchange of ideas between Newton and Leibniz.

This paragraph discusses the escalation of the controversy surrounding the invention of calculus. It begins with the publication of a paper by Johann Bernoulli, which insinuates that Leibniz may have borrowed from Newton's work. Leibniz responds by demanding action from the Royal Society, leading to a series of exchanges between the two camps. The speaker describes how Leibniz anonymously reviewed Newton's work, drawing parallels to previous instances of plagiarism, which further fueled the dispute. The paragraph highlights the personal nature of the conflict and the involvement of other mathematicians in the debate.

The speaker recounts the formation of a committee by the Royal Society to investigate the priority of calculus' invention, prompted by accusations of plagiarism against Leibniz. The committee, handpicked by Newton, concluded that Newton had developed his calculus before Leibniz, a finding that was later revealed to be authored by Newton himself. The evidence considered by the committee was primarily based on Leibniz's visits to London and his access to Newton's correspondence. The speaker questions the fairness of the committee's verdict, given the lack of direct evidence and the fact that the committee did not interview Leibniz or request any documentation from him.

The speaker describes the aftermath of the controversy, noting the impact on the careers and reputations of both Newton and Leibniz. Newton went on to become a national hero, serving as president of the Royal Society, master of the Royal Mint, and being knighted by Queen Anne. In contrast, Leibniz faced a decline in his reputation and struggled with his career as a diplomat and philosopher. The speaker reflects on the broader implications of the controversy, suggesting that the focus on Newton and Leibniz overshadows the contributions of other mathematicians who laid the groundwork for calculus.

In conclusion, the speaker emphasizes the importance of recognizing the collective contributions to the development of calculus, rather than focusing solely on Newton and Leibniz. They recommend further reading, including the Newton Project, which aims to digitize Newton's letters and papers, and several books that provide a comprehensive account of the history of calculus and the personalities involved. The speaker also mentions the MacTutor History of Mathematics as a valuable resource and acknowledges the role of Wikipedia for biographical information on historical figures.