History of Calculus: Part 3 - The Historical Motivation

Video Description

This is part 3 of the series: History of Calculus. Where I talk about the origins of calculus from ancient times to modern history. In this video I talk about the motivations that led to the discovery of calculus. To support this channel: - Buy me a coffee: https://www.buymeacoffee.com/tareksaid - Patreon: https://www.patreon.com/tareksaid - Super Thanks: You can find it by clicking the 3 dots under the video Notes: - 0:05 The work of the ancient Greek mathematicians was forgotten and was confined to libraries scattered around the mediterranean. Almost a thousand years later, Arab and Muslim scholars translated the works of the ancient Greeks and revived some interest in studying curves, and although they made great contributions to the study of curves, they stayed within the limits of the method of exhaustion. - 0:05 During the 2000 years' gap, mathematicians in India, particularly in Kerala school of Astronomy and Mathematics, made discoveries similar to what we may call today calculus, while their work is brilliant and has elements of calculus, it can not be called calculus. I will make a separate video about their brilliant work in a later video in the series as it gives an understanding of calculus from a different perspective. One based on arithmetic more than on curves. - 1:13 It is important to note that many mathematicians are not necessarily motivated by the practical applications of mathematics and are interested in mathematics as a form of art, however, when other factors like political, cultural and economical are at play, we can see how the absence of the practical applications of geometry shifted the focus away from it. - 7:25 Galileo later found that the motion of objects in free fall is uniformly uniform. - 13:34 Such a rod doesn't exist in nature and is used for demonstration purposes only. - 15:07 Finding the differential equation of the water from a tap is not possible since it is assumed to be done randomly. -17:06 The origin of the cycloid is not clear, some historians proposed that it was known to the ancients, while others think it was discovered in the 15th century and others proposed that it was only discovered in the 17th century. - 20:29 The Copernican model was already known at the time but it wasn't accepted. Another model that also existed was proposed by Tycho Brahe. Tycho assumed that the planets revolved around the sun, but the sun revolved around the Earth. Having said that, the most commonly accepted system at the time was the Ptolemaic system which is the one shown in the video. References: - The Historical Development of the Calculus | C.H. Edwards - The Origins of Infinitesimal Calculus | Margaret E. Baron - The History of the Calculus and its Conceptual Development | Carl B. Boyer - Infinite Powers | Steven H. Strogatz - Calculus Reordered | David M. Bressoud - Historical Stages in the Definition of Curves | Carl B. Boyer