People influence others, either for the better or for the worse. This fact is clearly seen in the priority dispute between Isaac Newton, an English mathematician and scientist, and Gottfried Wilhelm Leibniz, a German mathematician and lawyer, over the invention of fluxions, or differential calculus, calculus concerned with derivatives and differentials, as a result of both releasing their findings around the same time. Claiming priority was important because the person received the recognition for their accomplishment, thereby showing that anyone else that published similar theories was most likely copying. Newton and Leibniz had multiple areas of influence, including other mathematicians, journals, or colleagues. The men would not have gotten to the point they were at in their knowledge and careers if it were not for multiple parties. The priority dispute over calculus was heavily influenced by the people who supported or criticized Newton and Leibniz, whether in the early or later stages of life, and the two impacted others as well.
The early stages of life are some of the most influential moments, so these heavily shaped Leibniz and Newton. Newton’s father died shortly after his birth, and when his mother remarried, his stepfather sent him off. He, therefore, grew up isolated from his mother, which led to a temper and reclusion. Since he became a recluse, he took to building and experimenting, throwing himself wholeheartedly into his work. Leibniz’s childhood was more positive. One of Leibniz’s teachers, upon witnessing his brilliance, extracted the promise from the boy’s mother that she would allow him access to his father’s library. The volumes in it certainly helped to expand his thinking. His mother’s virtue and piety also rubbed off on him when he was young, and because of this he maintained a calm composure for a majority of the dispute. These experiences would shape the men’s learning later in life.
There were four mathematical giants that had a tremendous amount of influence on the two men, namely because the calculus the latter discovered was based on the math of the former, but also because of feedback provided. Even if some of them disagreed with the results of Newton and Leibniz, they recognized the genius of both men and expressed that. The first of these men is Christiaan Huygens, who influenced both of them, though it was greater in relation to Leibniz. He did read several of Newton’s publications, including his work on optics, which he thought very highly of at first. When he eventually attacked it, Newton threatened to leave the Royal Society, an organization devoted to scientific and mathematical experiments and knowledge. (Sonar 124). After all, Newton was a scientist who was supposed to be discovering great concepts, and instead he received criticism. Concerning Huygen’s relationship with Leibniz, Sonar writes that “Huygens must have really felt something for the young lad, since he corrected him and directed his attention towards the corresponding works of Pascal, Gregory, Descartes, Sluse, and others” after Leibniz solved some problems wrong (156). Therefore, Huygens had a tremendous impact on Leibniz’s mathematical knowledge, and if he had not done what he did, Leibniz might not have discovered integrals and differential calculus, since it was a result of a push toward mathematical truths. Unlike after accusations came from Robert Hooke, Newton did maintain a polite relationship with Huygens, which shows he had more respect for the latter. The second who played a role in the development of Leibniz’s mathematical knowledge was Blaise Pascal, whose works Leibniz was instructed he should study. Not only did his studies of Pascal lead to the calculus involved in the priority dispute, but he also gained inspiration regarding the quarter circle (Sonar 157). He was able to master mathematics partly with Pascal’s calculations. The last two influenced Newton, and they were Isaac Barrow and John Wallis. Sonar stated that “Barrow certainly had fueled Newton’s mathematical interests,” and this thought is very true (101). Barrow was a huge proponent of Newton, building the pupil’s knowledge through lectures and aiding in career advancements. When Barrow planned to retire from the Lucasian chair, a position for mathematics professors, upon seeing Newton’s brilliance, he advocated that he be his successor. John Wallis was key in convincing Newton to publish his treatise on light and colors. He wanted to promote English scientific work overseas, and when Newton finally responded after Wallis’ third letter, he received permission to go through with the process, meaning that Newton’s ideas would be circulated throughout Europe. Newton perhaps made an impression on Wallis, too, regarding math, for Sonar writes that “Wallis never came back to problems of applied mathematics” after reading Newton’s book, the Principia (269). Huygens, Pascal, Barrow, and Wallis all had an impact on Leibniz and Newton, and in some cases learned from the latter two.
Robert Hooke played a prominent role early in Newton’s career and in the outcome of the priority dispute. Hooke was a brilliant man. He was an engineer, draughtsman, and scientist, and he helped rebuild London after the Great Fire. According to Sonar, Hooke is one “[o]f the numerous persons in his [Newton’s] life whom Newton counted as personal enemies” (121). Newton had gained inspiration from studying Hooke’s work on the theory of light and decided to perform his own experiments. His results differed from Hooke’s. Hooke heavily criticized Newton’s work after publication, saying that “he had performed all of Newton’s experiments earlier, but that Newton had drawn incorrect conclusions from these experiments” (Sonar 123). As a result, Newton, who did not like becoming involved in disputes, chose to withhold further works from publication (Sonar 178). This action played into the priority dispute because, when he did choose to publish his method of fluxions, it was when Leibniz had discovered a similar method as well, referred to as differential calculus, and letters had been written between the two. If Hooke had not so heavily attacked Newton, perhaps this could have been avoided (Newton did not even become involved in the heated discussion until John Keill, an associate, accused Leibniz of plagiarism). There would have been less chance of fighting over who had priority because one would have published his findings already. An outcome of the dispute with Leibniz was that Newton chose to publish his other works later in life. In the interest of avoiding further confrontations and to secure his priority, doing so would have been in his best interest. There were those that criticized Leibniz’s calculus, but he did not let it affect him like Newton, so it did not sway the events of the priority dispute. Hooke’s desire to be the best made him criticize others’ findings since he wanted to publish first. This fact is seen when Leibniz presented a calculating machine to the Royal Society. While it did not work perfectly, it was the first that was able to add, subtract, multiply and divide. Instead of complementing the young man, Hooke immediately claimed he could construct a better one. When Newton published his Principia, declared the “birth of modern physics” by Sonar, and Hooke saw “his ideas mathematically developed and reflected,” he tried to claim he had invented this all first, especially in relation to the reflecting telescope, and eventually accused the fellow scientist of plagiarism. Needless to say, Newton did not take kindly to these attacks, and he was never cordial towards Hooke again. Negative influences can have ramifications in the long run that are not foreseeable at the time, as seen with the rivalry between Hooke and Newton.
The scientific and mathematic world is more manageable when there are friends to help, such as with publications or having a willingness to discover new knowledge. Newton had many supporters because they admired and believed in him before the dispute. Three of them aided him in editing and publishing his findings. Edmond Halley was a tremendous help to Newton in the publishing world, pushing his works to the printer. If he had not, Newton would not have printed as many books due to not taking well to criticism. When Newton considered removing Book III from the Principia due to conflict with Hooke, Halley was there, persuading his friend to leave it. He went so far as to positioning “himself and the Royal Society at Newton’s side,” showing that he had a desire for Newton’s works to be read by many people. (Sonar 263). Halley even paid for the publishing expenses when the Society’s funds were low. Roger Cotes was the second to help. He spent countless hours correcting errors in the second edition of the Principia, ensuring there would be fewer mistakes to attack (Sonar 398). The third was towards the end of Newton’s life when he was hoping to publish a third edition of the Principia before death. The lad’s name was Henry Pemberton, who mainly studied medicine but was knowledgeable in math, too. He was a strong supporter of Newton’s ideas, having written a paper praising him and criticizing Leibniz. Apparently, he “at least got some words of thanks in the preface,” whereas Cotes had not received any (Sonar 429). The publishers were also a huge level of support. After all, if the work is turned down for printing, it will not become widespread, so by passing the works for printing, the printers were helping Leibniz and Newton’s careers grow and helping them become known. John Collins sent many of Newton’s books to the printer, and he also sent correspondence between the island and continent. Leibniz’s contact with Collins enabled him to be introduced to more mathematical works, such as those of James Gregory and to become acquainted with Newton. Ehrenfried Walther von Tschirnhaus was a close friend of Leibniz’s who frequently discussed algebra with him. He thought very highly of his friend, for when he wrote a letter to the English, he praised his associate’s intellect. Unlike Newton, Leibniz published treatises often on his findings. He contributed much to the journal, Acta Eruditorum, and a few times he was even asked to send in works. Having support in a career is essential to being successful, as is publishing one’s findings in math.
Though support is usually good, some of the mathematicians’ supporters took matters too far. Leibniz and Newton were not the instigators of the priority dispute. It was actually men that thought one or the other deserved the credit for inventing the calculus first, which resulted in either condescending letters being sent or remarks being published. A Newtonian, Nicolas Fatio de Duillier believed Newton was more brilliant, thereby deserving the recognition for his achievements by being recognized as the first inventor (Sonar 347). On the continent, one of Leibniz’s companions was crafting similar remarks against Newton. Leibniz’s main supporters were the Bernoulli brothers. At one time, Jacob Bernoulli desired to see Leibniz’s discoveries in geometry, and upon seeing them he declared that they should be published (Sonar 194). This enthusiasm certainly helped Leibniz to circulate more of his research. When the argument became more heated, John Bernoulli wrote against Newton, though this act was partly due to Leibniz’s egging him to, so that when the latter responded he would not seem as rude, possibly as a result of his mother’s ethics (when Newton was angry, he gladly wrote against the party who wronged him). However, he thought Leibniz should have more recognition in one of Wallis’ books for his calculus and did begin to think Newton could have plagiarized, issuing his own attacks against the English because of this belief. In the end, John Bernoulli did try to make peace with Newton after the conflict was over, but their relationship never fully mended. The result of the attacks from these supporters was that “Fatio’s declaration of war on Leibniz made sure that fellows and partisans on both sides … began to arm and took [sic] a stand” and Leibniz’s friends believed that the English would try to claim his work for themselves (Sonar 362). Once again, Newton and Leibniz had no desire to dispute until those close to them started placing accusations which fueled the hatred. Fatio and the Bernoulli brothers were key in Newton and Leibniz’s lives, as well as in adding fuel to the flames.
When arguments occur, sides are chosen, and so when Newton and Leibniz began debating over who was the first inventor of differential calculus, many mathematicians and scientists stood behind one or the other. The continent was mainly behind Leibniz since they were all Cartesians, preferring Descartes’ vortex theory to explain planets’ orbits to that of Newton’s gravitation. More specifically, Germany stood behind Leibniz; Holland was behind both, printing articles for either side; and France did not care due to being in the middle of a war, though the Academy in Paris leaned towards Leibniz because he had acquaintances there. Originally, when Leibniz complained to the Royal Society about remarks made by Fatio against him, they were quick to issue an apology. However, when this situation happened a second time, with accusations of plagiarism, they were not as willing and began to lean towards Newton and started to view Leibniz with suspicion, even digging up old letters in an attempt to prove Newton had priority. Not only were the English fighting that Newton had priority, they were also hoping to be noticed in a scientific world that supported the vortex theory, not gravitation (Sonar 372). If a group of people is fighting for spotlight, then they will stand behind their countryman because he will best represent them. Beliefs play a major role in choosing a side, as seen with the countries standing behind Newton or Leibniz based on gravitation or vortices.
Not only was the support from others important, but the impact that Leibniz and Newton made as well. Naturally, mathematicians came along that attempted to disprove the calculus, and, as a result, there were those who rose to defend it. These people would not have rose to the occasion if they did not have respect for the calculus and the man or a sense of patriotism, showing that the men had greatness in them. On the flip side, the debate between Newton and Leibniz was a possible source of slowing down the progression of mathematics. If the two had worked together instead of becoming involved in a dispute, their genius combined could have furthered the knowledge of the time. Sonar writes that, “The priority dispute between Leibniz and Newton, fought at the turn of the 17th and 18th century, had a tragic aftermath for British mathematics which lasted for 200 years” (489). He makes this statement because, instead of pursuing new principles, like on the continent, mathematicians in Great Britain were busy trying to prove the validity of Newton’s fluxions, which they were successful in. Additionally, there were those that did not even understand the differential calculus, meaning they could not add on to what was known. Newton and Leibniz could not have foreseen this outcome, but it does show how actions have long-term ramifications.
The path the priority dispute took was largely affected by the support Leibniz and Newton received, as were their careers. Four mathematical giants contributed to their careers and thoughts, either by giving support or their math providing inspiration. Robert Hooke was one of the people to have a direct impact on Newton’s career due to his heavy criticism which affected what the other scientist published and when. His actions helped create a situation for the priority dispute. From printing to fighting alongside Newton or Leibniz, many people played an integral role in their careers and in the events of the priority dispute. Not only did others impact the two great men, but their disagreement also had ramifications on the progression of mathematics, showing that the world is indeed connected.
Works Cited
Sonar, Thomas. The History of the Priority Dispute between Newton and Leibniz: Mathematics in History and Culture. Braunschweig: Springer International Publishing AG, 2018.
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