Annotated Bibliography

Primary Sources

“A Leibniz Stepped Reckoner Calculator.” Computer History Museum. Retrieved February 14, 2021, from https://www.computerhistory.org/revolution/calculators/1/49/198.

This webpage from the Computer History Museum contains an image of Leibniz’s Stepped Reckoner Calculator from the 1670s.

"Commercium Epistolicum." Christie's. (2019). Retrieved February 2, 2021, from https://www.christies.com/en/lot/lot-6216659.

This auction listing contains a photograph of the front cover of the original Commercium Epistolicum. This photograph was included in the section regarding the omitted letters.

Duillier, Nicolas Fatio de. "Lineæ brevissimæ descensus investigatio geometrica duplex, cui addita est investigatio geometrica solidi rotundi in quo minima fiat resistentia." 1699, pp. 18.

This article by Nicolas Fatio de Duillier is historically significant because it is credited with sparking the dispute between Leibniz and Newton. Due to the importance of this publication, we included a quote from this article to show the inciting incident behind the calculus controversy.

Francke, Christoph Bernhard. "Gottfried Wilhelm Leibniz." Herzog Anton Ulrich Museum. 1695.

This is a portrait of Gottfried Wilhelm Leibniz. This work was used on the home page and the background page to introduce Leibniz for the first time.

Hecht, Hartmut. Der Junge Leibniz. Teubner-Archiv Zur Mathematik, 1992.

This is a German book that contains a detailed biography of Leibniz. We used an English translation of this book during our research, and it allowed us to learn more about Leibniz’s early life as well as his time during university. From the first chapter, we took a quote that gave Leibniz’s birthday and birth location. This quote was originally from the personal diary of Leibniz’s father, Friedrich Leibniz.

Kneller, Godfrey. "Sir Isaac Newton." National Portrait Gallery. 1702.

This is a portrait of Sir Isaac Newton. This work was used on the home page to introduce Newton for the first time.

Leibniz, Gottfried W. “Letter from M. Leibniz to M. Remond.” 1720. Retrieved February 12, 2021, from http://www.newtonproject.ox.ac.uk/view/texts/normalized/NATP00380.

This letter, in Latin, is sent by Leibniz in order to defend his claim to the creation of calculus. This primary source provided us a glimpse into Leibniz’s arguments against Newton, and it was very helpful in letting us understand his side of the dispute. We included a quote from this letter to better illustrate the argument between the two men.

Leibniz, Gottfried W. "Nova Methodus Pro Maximis Et Minimis." Acta Eruditorum, No. 10, 1684, pp. 467-473.

Nova Methodus Pro Maximis Et Minimis is the first published work that focused on calculus, and it compiled all of Leibniz’s work through the previous few years. This book is historically significant within our research, so we included the first two pages of this book on our project.

Newton, Isaac. "Draft Letter from Sir Isaac Newton to Pierre des Maizeaux." 1716. Retrieved February 2, 2021 from http://www.newtonproject.ox.ac.uk/catalogue/record/NATP00373.

This letter from Newton to writer Pierre des Maizeaux was crucial in letting us understand the way the omitted letters impacted the Royal Society inquiry into the controversy. This letter contained both Leibniz’s and Newton’s arguments regarding the missing letters, and various quotes from this section were used to support our claim regarding the significance of the omitted letters.

Newton, Isaac. Method of Fluxions. Henry Woodfall. 1736. pp. 1-2.

This book is Newton’s famous publication that established Newtonian notation for calculus. Published in 1736, this book was released after the death of Leibniz, but it was actually finished in 1671, according to Newton. This book is a very important aspect of the calculus controversy, so images of the first two pages of this article were included on the website.

Newton, Isaac. The Correspondence of Isaac Newton, Vol. 1: 1661-1675. H.W. Turnbull. Cambridge University Press. 1959.

This book contains a compilation of Newton’s letters to various other mathematicians and scientists, which are important primary sources. From one letter by Newton addressed to French writer Pierre des Maizeaux, he makes his position regarding the controversy clear when he states that “Second inventors have no rights.” We included this famous quote in our project to convey the depth of the polarization that was occurring as the controversy unfolded.

“Newton Papers : Newton's Waste Book.” Cambridge Digital Library. Retrieved February 2, 2021, from cudl.lib.cam.ac.uk/view/MS-ADD-04004/.

This section of the Cambridge digital library contains scans of the notebook that Newton used as a child. This primary source provides a glimpse into the mind of Isaac Newton at a younger age, and it helped show his mathematical curiosity and aptitude on the page regarding Newton’s early life.

Whiteside, D.T. "Newton's Marvellous Year: 1666 and All That." Notes and Records of the Royal Society of London. Vol. 21, No. 1, 1966, pp. 34.

This article focuses on the important events that occurred in Newton’s life within the year 1666. One such event was Newton’s claimed discovery of calculus. This article contained a transcript of a letter sent by Newton regarding these claims, and we used an excerpt from this transcript to better show Newton’s claimed early discovery of calculus.

Secondary Sources

Alfred, Randy. “Oct. 29, 1675: Leibniz Sums it All Up, Seriesly.” Wired. 2009. Retrieved February 2, 2021, from https://www.wired.com/2009/10/1029leibniz-integral-sign/.

This article by the Wired magazine was created on the anniversary of Leibniz’s creation of the integral notation. This article also focuses on a variety of Leibniz’s other mathematical achievements, and we used an excerpt to show Leibniz’s contribution to linear algebra.

Ball, W. W. Rouse. A Short Account of the History of Mathematics. Dover Publications Inc., New York, 1908. pp. 319.

This book contains a history of all major mathematical accomplishments throughout history. Within our research, we focused on chapter 16 of this book, which was entirely dedicated to the work of Newton. This chapter helped us understand the wide breadth of work that Newton completed during his lifetime, and we used a brief quote from this chapter to show this incredible intelligence during the section introducing Newton.

Bechler, Zev. Contemporary Newtonian Research. D. Reidel Publishing Company, 1982.

This book contains a technical analysis on Newton’s mathematical research as well as a brief biology of his life. This book was useful in letting us understand Newton’s mathematical interests as a young child, and we used a quote from the book to display his incredible curiosity.

Blank, Brian E. "The Calculus Wars, Reviewed by Brian E. Blank." Notices of the American Mathematical Society. 2009, pp. 602-610.

This article is a review of the book “The Calculus Wars” by Jason Bardi. In addition to being an analysis of the book, this review also provides a broad overview of the calculus controversy itself. Within this analysis, Blank makes an interesting comment regarding the disregard for truth that occurred during the dispute. We included this quote to introduce the section related to letters.

“Bonaventura Cavalieri.” Encyclopedia Britannica. 2021. Retrieved January 20, 2021 from https://www.britannica.com/biography/Bonaventura-Cavalieri.

This webpage provides a biography of Bonaventura Cavalieri, who was an Italian mathematician from the 17th century. Cavalieri made several papers that used indivisibles to calculate the area of various geometric shapes. These concepts are related to calculus, so we included a description of these articles in the background section to provide further information regarding mathematical development prior to the dispute.

Boyer, Carl B. The History of Calculus and Its Conceptual Development. Dover Publications. 1959.

This book provides a detailed chronology of the development of calculus starting from the ancient Greeks all the way to the 20th century. This book is a frequently cited source when analyzing the history of calculus. We were able to use specific chapters in this book to deepen our understanding of calculus during the era of Newton and Leibniz. We also included a quote from this book in our project to show the timeline of Newton’s work on calculus.

Broad, W. & Wade, N. Betrayers of the Truth, Fraud and Deceit in Science. Simon & Schuster. 1985, pp. 28.

This book analyzes the times in history where science was not driven by objective observations or inquiry. One chapter in this book is dedicated to the Newton-Leibniz controversy and how emotions became an important factor during the dispute. This chapter was crucial in helping us understand more about the Royal Society inquiry, and it provided valuable insight into the biased nature of the findings from this study.

Burnham, Douglas. "Gottfried Leibniz: Metaphysics." Internet Encyclopedia of Philosophy. Retrieved on February 2, 2021 from https://iep.utm.edu/leib-met/.

This web article provided a general overview of the life of Gottfried Leibniz. We used this article to discover other sources related to the man and his work. In addition, the section related to the historical effects of the controversy was especially helpful, and we included a quote from this portion within the page about the impacts of the dispute.

Casadevall, Arturo & Fang, Ferric C. "Reforming Science: Methodological and Cultural Reforms." American Society for Microbiology Journals, Vol. 80, No. 3, 2012, pp. 891-896.

This article provides an analysis into scientific priority within a modern context. This article did not directly relate to our project, but it did provide some interesting background information regarding scientific priority. A section of this paper was used to provide a definition for the idea of scientific priority.

Cirillo, Michelle. “Humanizing Calculus.” The Mathematics Teacher, vol. 101, no. 1, 2007, pp. 23–27.

This article provided a brief introduction to the calculus controversy, and it was intended to help calculus teachers to provide background regarding the development of calculus. Similar to the article by Dorothy Schrader, this article was helpful because it gave a broad overview of the important events that occurred during the controversy, and it provided other sources of information that we could use. A quote was used from this article to show Leibniz’s entry into the field of mathematics during the 1670s.

Dhombres, Jean G. “A Tentative Interpretation of the Epistemological Significance of the Encrypted Message Sent by Newton to Leibniz in October 1676.” Advances in Historical Studies, Vol. 3, No. 1, 2014, pp. 22-32.

This article focused on the encrypted message that Newton sent to Leibniz in 1716. This source, along with Louis More’s biography on Newton, was critical in giving us a better understanding of how the encrypted letter influenced the calculus controversy. This article also included a transcript of the message in its decoded form. The decoded message was clearly too vague to support Newton’s claims to developing calculus, so it perfectly shows how the encrypted letter merely worsened the argument between the two men.

"Discovering Methods to Cleverly Conceal." The Irish Times. 2000. Retrieved February 2, 2021, from https://www.irishtimes.com/news/discovering-methods-to-cleverly-conceal-1.1107143.

This newspaper article provides a general overview of times in history where encrypted letters were used to disclose important scientific discoveries before the creation of a publication. This news article also included a brief summary of Newton’s letter to Leibniz. We included an excerpt from this article to describe the way encrypted letters were used in general.

Gaab, Hans & Leich, Pierre. Simon Marius and His Research. Springer. 2019, pp. 197.

This book focuses on the work of German astronomer Simon Marius. Although the contents of this book did not directly relate to our research, the background section gave us a better understanding of scientific priority, and it was a very helpful tool when we were developing that section of our project.

Gobre, Tamas. “Fundamental Anagram of Calculus.” Tamas Gobre: A Blog about Math and Physics. 2015. Retrieved February 2, 2021, from https://tamasgorbe.wordpress.com/2015/11/25/fundamental-anagram-of-calculus/.

This article included a brief summary of the role the encrypted letter played within the calculus controversy. This article also included an image of the actual letter sent by Newton, and we included this image in the section about the encrypted message.

“Gottfried Leibniz and Mathematical Diagram.” Colnect.com. Retrieved on February 12, 2021, from https://colnect.com/en/stamps/stamp/39425-Gottfried_Leibniz_and_mathematical_diagra m-Germany_Federal_Republic.

This web page contains a photograph of a German stamp of Leibniz in celebration of the 350th anniversary of his birthday.

“Gottfried Wilhelm Leibniz.” Stanford Encyclopedia of Philosophy. 2007. Retrieved February 10, 2021, from https://plato.stanford.edu/entries/leibniz/#Life.

This webpage provided an overview of Leibniz, and it contained links to other relevant sources related to Leibniz’s life. This article was very helpful during our research, and we used an excerpt from this article that described the Stepped Reckoner, the mechanical calculator that Lebiniz developed.

Greer, Rita. “Portrait of Robert Hooke.” Oxford University. 2004.

This is a modern painting of Robert Hooke based on descriptions of his appearance from primary sources created during his lifetime.

Griffith, John. “The Forgotten Mind of The Calculus Controversy. ” University of Houston. 2017.

This short article summarizing the life of Gottfried Leibniz was useful in our project because it allowed to get a better understanding about how Newton was successful in tarnishing Leibniz’s reputation by the time of his death. This was included in the final section of our project to emphasize the negative effects the controversy had within the mathematics community.

Gunderman, Richard. "Robert Hooke: The ‘English Leonardo’ Who was a 17th Century Scientific Superstar." The Conversation. 2019. Retrieved February 2021, 20 from https://theconversation.com/robert-hooke-the-english-leonardo-who-was-a-17th-century- scientific-superstar-119497.

This web article about English astronomer Robert Hooke was important in our research because it provided precedent that scientific priority rules in the 17th century caused major disputes over ownership. Reading about Hooke’s disputes with Newton was very interesting because we were able to see parallels between Newton’s disputes with both Hooke and Leibniz.

Hall, Alfred Rupert. Philosophers at War: The Quarrel between Newton and Leibniz. Cambridge University Press. 1980.

This book contains a detailed history of the calculus controversy. The chapter in this book about the legacy of the calculus controversy was especially helpful during our research because it allowed us to understand how this dispute had long-term impacts. We used a quote from this chapter to explain how Newton and Leibniz both received credit for the discovery of calculus.

“House of Leibniz.” Hannover Tourism & Culture. 2019. Retrieved on February 2, 2021, from https://www.hannover.de/en/Tourism-Culture/Event-Highlights/Specials/Year-of-Leibniz- 2016/House-of-Leibniz.

This web page about the House of Leibniz contains a photograph of the house that Leibniz worked in up until his death.

“Isaac Newton (1643-1727), English Physicist and Mathematica.” Colnect.com. Retrieved on February 12, 2021 from https://colnect.com/en/stamps/stamp/33532-Isaac_Newton_1643-1727_english_physicist _and_mathematicia-300th_anniversary_of_the_gravity_theory_by_Isaac_Newton-Monac o.

This web page contains a photograph of a Monaco stamp of Isaac Newton in celebration of the 300th anniversary of the discovery of gravity.

“Isaac Newton at the Age of Twelve.” Harper’s Young People: An Illustrated Weekly. Vol. 2, No. 102, 1881, pp. 1.

The front cover of this magazine article contains a drawing of Isaac Newton as a twelve-year-old. This image was used on the page regarding Newton’s early life.

Jolley, Nicholas. Cambridge Comparison to Leibniz. Press Syndicate of the University of Cambridge. 1994. Pg. 20.

This book is a detailed biography of Gottfried Leibniz, and it helped us understand his work before his inquiry into calculus. Although this work focused mostly on philosophy, it helped us to understand Leibniz’s areas of study outside of calculus. A segment from this book was used to show Leibniz’s area of study during his time at college.

Kreiling, Frederick C. “Leibniz.” Scientific American, Vol. 218, No. 5, 1968, pp. 94-101.

This article focuses on Leibniz’s contributions to philosophy. Despite this, the subject of calculus frequently makes an appearance in this article because Leibniz heavily believed that calculus could act as a tool to better understand the fundamental philosophical truths of the universe. To us, Leibniz’s motive for studying calculus seemed very interesting, and we included an excerpt from this article in the introduction section to show this.

Kumar, A. “Newton’s Contributions to Optics”. Reson. Vol. 11, 2006, pp. 13. https://doi.org/10.1007/BF02903080.

This article provides a summary of Newton’s work on optics, which was a precursor to his work on gravity and calculus. Although the subject of this article did not relate to our research on calculus, it was nonetheless interesting to see Newton’s contributions in other fields of science, and we used a segment of this paper to demonstrate Newton’s aptitude with scientific thinking in general.

Mahoney, Michael S. “The Beginnings of Algebraic Thought in the Seventeenth Century.” Princeton University. 2009. Retrieved January 30, 2021, from https://www.princeton.edu/~hos/Mahoney/articles/beginnings/beginnings.htm.

This article provides a brief summary of the advancements in algebraic thinking since the Classical era. We found this paper to be interesting because it helped us understand the significance of the 17th century in regards to mathematical development. We used a section from this article to provide more background information to European mathematics before the development of calculus.

Meli, Domenico Bertolini. Equivalence and Priority: Newton versus Leibniz. Clarendon Press. 1997.

This book analyzes several unpublished manuscripts created by Leibniz. Most of these papers were related to the calculus controversy, and this book was important in allowing us to gain a more thorough understanding of the events that occurred during the controversy. In addition, this book had an incredibly helpful chapter on background information related to the controversy, and some information from this section was used to further describe the way scientific priority operated during the 17th century.

More, Louis Trenchard. Isaac Newton: A Biography. C. Scribner’s Sons. 1934.

This book provides a detailed biography of Isaac Newton’s life, and it includes excerpts from many letters between Newton and other mathematicians and scientists. Specifically, this book contains a transcript of Newton’s 1676 letter to Leibniz, which contains the encrypted message. In addition, the same section of the book contained an analysis as to how this encrypted letter was used by the supporters of Newton in order to attack Leibniz’s claims. In general, this source was very important in letting us get a better understanding of how this encrypted letter played a key role in the controversy.

Nauenberg, Michael. “Visiting Newton’s Atelier Before the Principia, 1679-1684.” Annals of Science, Vol. 76, No. 1, 2018, pp. 1-16.

This article focuses on the Principia , Newton’s famous publication on gravitation. This article was interesting because it made it clear that Newton was thinking about mathematical concepts related to calculus before his first publication regarding calculus. We used an excerpt from this article to provide background on Newton’s work before his inquiry into calculus.

O'Connor, J.J. & Robertson, E.F. "Luca Valerio." MacTutor History of Mathematics Archives. 2009. Retrieved February 2, 2021 from https://mathshistory.st-andrews.ac.uk/Biographies/Valerio/.

This webpage provides a brief biography of Luca Valerio, who was an Italian mathematician from the 17th century. He had made several advancements in mathematics related to limits and volume, which are ideas closely related to calculus. We included a portion of this article related to these advancements in the background page to provide further context for the calculus controversy.

Orlin, Ben. Change is the Only Constant: The Wisdom of Calculus in a Madcap World. Running Press, 2019.

This book contains an introduction to calculus, and it presents many concepts in a humorous manner. A quote from this book was used to introduce the background section of the website.

Robert A. Nowlan. Masters of Mathematics: The Problems They Solved, Why These Are Important, and What You Should Know about Them. SensePublishers. 2017.

This book contains a lengthy chronology of great mathematicians throughout history. The specific chapter regarding Leibniz and Newton helped during our research because it gave a detailed description of Leibniz and Newton’s contributions to mathematics. Thus, a quote from this section was included in the portion of our project about the legacy of the calculus controversy.

Roinila, Markku. “G. W. Leibniz’s Philosophy and Practical Projects.” University of Helsinki. 1997. pp. 17.

This article focuses on Leibniz’s work within the field of philosophy. We were able to better understand the personal interests of Leibniz through this article, and we included a quote from this paper to show his background in philosophical inquiry and the humanities.

Schrader, Dorothy V. “The Newton-Leibniz Controversy Concerning the Discovery of the Calculus.” The Mathematics Teacher, Vol. 55, No. 5, 1962, pp. 385–396.

This article provides a broad overview of the calculus controversy. During our research process, this article was by for the most important because the works cited section provided many sources that would help us delve deeper into various aspects of the calculus controversy. In addition, various quotes from this article were used to provide background for the calculus controversy as well as the historical and mathematical impacts this argument had in the long-term.

“The Newton-Leibniz Controversy.” Australian Mathematical Sciences Institute. Retrieved February 2, 2021, from https://amsi.org.au/ESA_Senior_Years/SeniorTopic3/3b/3b_4history_2.html.

This web article contains a very brief description of the calculus controversy. From this article we used a quote showing that the Royal Society inquiry used falsified information to conduct its analysis of the ongoing dispute.

“The Royal Society Supports Newton in the Dispute with Leibniz over the Invention of the Calculus.” History of Information. 2012. Retrieved January 21, 2021, from https://www.historyofinformation.com/detail.php?id=1726.

This brief web article contains a description of the inquiry by the Royal Society of London. From this article, we used a quote that explained some of the background information regarding the inquiry.

Westfall, Richard S. Never at rest: A biography of Isaac Newton. Cambridge University Press. 1983. pp. 494.

This book is a lengthy biography of Isaac Newton. Page 494 contains an illustration of Nicolas Fatio de Duilier, which we used in the section talking about his role within the controversy.