Calculus Critical Thinking Task

Calculus Critical Thinking Task Question 1: With reference to two additional sources, construct a case for who should be credited with the invention of calculus. Prior to this assignment, I never considered who the inventor of calculus might be. In class, we use it to solve practical problems such as determining the slopes of curves or finding maximum and minimum values. However, when I learned that there was a controversy over Newton and Leibniz claiming to be the inventors of calculus, I realized that calculus, like all other branches of mathematics, contains imagination and even conflict. After conducting research, I now support the claim that calculus was invented by Isaac Newton, considering the controversy surrounding the two mathematicians. Although Leibniz published his work first and created the symbols we use nowadays, Newton developed the concepts of calculus in the 1660s, while studying motion and gravity. He would later go on to explain how objects accelerated downwards due to gravity. According to the MacTutor History of Mathematics (University of St Andrews), Newton used what we now know to be calculus, although he called it ‘fluxions’ or ‘flowing’ describing how planetary bodies would move. The connection between physics and math was astonishing to me, as it opened a new field of possibilities. Most importantly, what distinguishes Newton’s work from others is how he managed to use abstracted concepts in mathematics in conjunction with the real world. In class, while doing textbook questions, many students forget that math can extend to other fields of study, hence combining it with imagination. This is not the case for Newton who used calculus to describe the universe. This is something important. It explains why math isn't just something we learn for exams, it's something that explains the world around us. Honestly, that’s why my perception of calculus has changed. It is not just a subject, it’s a way to comprehend concepts that are otherwise imperceptible, like speed, change, and growth. This invention did not just help Newton in seeing physics. From these inventions grew modern science, engineering, and most of the technology we rely on today. Today, calculus serves as the pillar for so much: medicine, architecture, artificial intelligence, and even in the emerging field of economics. In the absence of calculus, modeling pandemics, launching satellites, or video game designing would be impossible. When I think about who should be awarded for such a revolutionary tool, I think the person who first thought about how to compute change in motion, Newton, should be given credit. Without appreciating Leibniz impact on this issue would be unfair. His works on calculus helps the notation differentiate easier, making it easier to explain and understand where it can be taught helping in its growth. Without his impact, maybe calculus wouldn't go mainstream. It's one thing to say ‘good rebranding’, but invention is something different. And that idea was in fact first explored by Isaac Newton. This shred of controversy actually opened my eyes to realizing something else, that mathematics should not only be viewed as numbers, but as a science of exploration and discovery. Just like calculus helped Newton understand the world, I hope we can use it to solve problems like space travel, climate change and advancements in medicine. This belief is why I see Newton as deserving credit, not only for being the first to devise something, but for revealing the wonders of mathematics. Works Cited “Calculus.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 2 Apr. 2024, https://www.britannica.com/science/calculus-mathematics. Accessed 19 Apr. 2025. “Leibniz’s Philosophy of Mathematics.” Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, Stanford University, 13 Jan. 2020, https://plato.stanford.edu/entries/leibniz-logic-influence/#:~:text=For%20him%20%5BLei bniz%5D%2C%20the,is%20a%20calculus%3B%20formulas%2C%20relations. Accessed 20 Apr. 2025. “Newton and Leibniz.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., https://www.britannica.com/science/mathematics/Newton-and-Leibniz. Accessed 19 Apr. 2025. Newton, Isaac. “Newton’s Dark Secrets.” NOVA, PBS, 15 Nov. 2005, https://www.pbs.org/wgbh/nova/video/newtons-dark-secrets/. Accessed 20 Apr. 2025. O’Connor, J. J., and E. F. Robertson. “A History of Calculus.” MacTutor History of Mathematics Archive, School of Mathematics and Statistics, University of St Andrews, https://mathshistory.st-andrews.ac.uk/HistTopics/The_rise_of_calculus/. Accessed 19 Apr. 2025. Wilford, John Noble. “The Calculus Wars.” Smithsonian Magazine, Smithsonian Institution, May 2005, https://www.smithsonianmag.com/history/the-calculus-wars-15076352/. Accessed 20 Apr. 2025.