Download pdf
A historical analysis of the independent development of calculus by Newton and Leibniz
- 1 Shijiazhuang Jingying Middle School
* Author to whom correspondence should be addressed.
Abstract
This paper undertakes a historical investigation of the separate and independent development of calculus by Isaac Newton and Gottfried Leibniz in the late 17th century. Through analysis of primary sources and historiographical perspectives, it explores the differences in notation, methods, and applications used by each mathematician to formulate foundational concepts of calculus. The research demonstrates that Newton relied more on geometric intuition, developing calculus concepts like fluxions and fluents rooted in kinematic problems. His 1687 Philosophiae Naturalis Principia Mathematica synthesized many calculus innovations. Meanwhile, Leibniz approached calculus from an algebraic mindset, utilizing infinitesimal differentials and comprehensively explaining integral and differential calculus in publications like Nova Methodus pro Maximis et Minimis. Evaluation of letters and documents from the 1670s and 1680s shows no direct collaboration or communication about calculus between Newton and Leibniz. This lack of transmission, coupled with the disparities in their notation and calculus techniques, provides evidence for independent creation. However, Newton and Leibniz shared key insights regarding rates of change, derivatives and integrals, hinting at a broader zeitgeist in early modern mathematics and science. Thus, this dual achievement illustrates how the Scientific Revolution facilitated conceptual convergence despite geographic separation between great thinkers. Investigating this case study offers perspective on the interplay between individual genius and wider social contexts in driving scientific progress. This paper concludes by assessing the legacy of the Newton-Leibniz debate over priority and analyzing work that paved the way for modern unified calculus notation and applications.
Keywords
Mathematics, Contrasting Perspectives, Geometric, Algebraic 1. Introduction
[1]. Yanfang L,Shuyan M,Xiaoye J, et al. Independent development and validation of a novel six-color fluorescence multiplex panel including 61 diallelic DIPs and 2 miniSTRs for forensic degradation sample.[J]. Electrophoresis,2022,43(13-14).
[2]. Jessica E,Chavez C,Amie R, et al. ITK independent development of Th17 responses during hypersensitivity pneumonitis driven lung inflammation[J]. Communications Biology,2022,5(1).
[3]. Islombek N M,N. J,K. N, et al. The way of independent development - A key factor of national revival and progress of Uzbekistan[J]. ACADEMICIA: An International Multidisciplinary Research Journal,2022,12(2).
[4]. Enxing Z,Zenghui Y,Guotian L, et al. Research on quality evaluation of lubricating oil based on China’s independent development[J]. E3S Web of Conferences,2022,360.
[5]. Dongju C,Minghui S,Pei M, et al. GSA: an independent development algorithm for calling copy number and detecting homologous recombination deficiency (HRD) from target capture sequencing[J]. BMC Bioinformatics,2021,22(1).
Cite this article
Li,J. (2024). A historical analysis of the independent development of calculus by Newton and Leibniz. Theoretical and Natural Science,30,1-5.
Data availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
Disclaimer/Publisher's Note
The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of EWA Publishing and/or the editor(s). EWA Publishing and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
About volume
Volume title: Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
© 2024 by the author(s). Licensee EWA Publishing, Oxford, UK. This article is an open access article distributed under the terms and
conditions of the Creative Commons Attribution (CC BY) license. Authors who
publish this series agree to the following terms:
1. Authors retain copyright and grant the series right of first publication with the work simultaneously licensed under a Creative Commons
Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this
series.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the series's published
version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial
publication in this series.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and
during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See
Open access policy for details).