The creation of calculus was a small step for man and a giant leap for mankind in its prospects for mathematics and the possibilities it created for future mathematicians. Before we understand calculus, we must first understand how it began and what it was inspired by. By understanding what calculus is used for, we can examine calculus with a more intense and understanding lense and explain why it was created in the first place. Exploring the ideas that calculus creates is an important step for our goal to become conceptually brilliant.
The ideas used in calculus had been in circulation since the times of ancient Greece, but it was the efforts of two men that brought it together to the modern world: Isaac Newton and Gottfried Wilhelm Leibniz. Fermat’s discovery of the maxima and minima, two concepts used in calculus, were implemented in Newton’s work and research. The fact of the matter is that calculus was not created by a single person, it was more accurately a combination of ideas left from past thinkers that was combined to reunite the different parts of mathematics. Pythagoras, who is wildly considered to be the forefather of math itself and inspiration to Newton, created the Pythagorean theorem, which related two sides of a right triangle to its hypotenuse. His contributions to geometry should not be understated as well. His additional discovery of the first mathematical proof set the stage for future opportunities for mathematicians and allowed calculus to implement proofs as well. Descartes’ unification of algebra and geometry was groundbreaking for its time, and skills from both these branches of mathematics are used in calculus. The first conclusive implementation of these ideas were created by the independent efforts of Isaac Newton and Gottfreid Wilheim Leibniz. They both created different parts of calculus independently, but their work combines to form the components we use. Newton’s teacher, Isaac Barrow, influenced Newton’s ideas and helped him with his early work and the Fundamental Theorem of Calculus. Newton’s previous research on physics and the laws of motion helped his development of calculus. His work concerning planets allowed the concepts of calculus to come quite easily to him. Further development of his ideas would help form the calculus that we know of today.
Calculus is the study of change, and it helps mathematicians analyze the world that we live in. Calculus is used by a multitude of different people and professions, especially in search engines, weather patterns, and architecture. It is used in algorithms for search engines to better refine results for people. The more searches a certain topic gets, the more the algorithm gets used, and the more calculus is enforced in improving the preciseness of the results people get. This allows search engines to always improve over time and helps keep their development fresh and inventive. Variables such as the user’s geography and web history are used to improve the restraints that produce the best results for the billions of internet users that surf the web daily. Calculus also improves the accuracy of weather prediction software. Computer models use calculus to predict weather patterns all around the world. They also use algorithms, along with search engines, compute variables and possibilities such as temperature and wind speed to improve their predictions. This allows weather prediction software, along with search engines, to constantly and consistently improve over time. They can never hit a wall or stop evolving because the conditions of the world are always changing. Meteorologists use differential equations from calculus to discover how changes in atmosphere and pressure affects the weather, which further improve predictions. Architects uses calculus to improve the structure makeup of buildings, and helps with the discovery of new materials to use. The process of building a bridge relies heavily on calculus in calculating the amount of weight the structure can handle at a given time. Algorithms deliberate factors such as the environment and distance to make sure the bridge is structurally sound. The pattern seen throughout the uses of calculus is that it consistently used to improve fundamental parts of our reality, and it is an ever-expanding field in the improvements it provides for search engines, architects, and countless other professions. The age-old question of “what is calculus used for” should be rephrased to a far more appropriate, “what is calculus not used for?” The world that we live in can constantly be expanded and improved upon with calculus.
Newton’s papers on calculus were published in the mid 1660s. He did not want to publish them immediately, because he feared he would be ridiculed by his peers for his unconventional and revolutionary ideas. He only sent them to friends and acquaintances rather than share them with the general public. His Principia, which contained his three laws of motion, along with explanations about his form of calculus, was published on July 5, 1687. He had ideas and had written several papers beforehand, but he never published them until much later in life. The foundation of Newton’s discoveries was the relationship between the derivative and the integral and essential theories of calculus. His discoveries and writings took place in England.
The demand for a more complex form of mathematics came from people’s desire to understand how the world worked. The limitations of mathematics at the time prevented other mathematicians from diving into the possibilities of this question. Innovative and inventive thinkers had come up with models throughout the centuries to create better models of nature and the universe, which allowed mathematics to become more advanced. Futurism’s article on Isaac Newton further explains the need for calculus when Isaac realized,” When trying to describe how an object falls, Newton found that the speed of the object increased every split second and that no mathematics currently used could describe the object at any moment in time.” This dilemma inspired him to find the antidote for change, a quantifiable measurement to describe this previously unexplainable phenomenon. Creating calculus allowed scientists and mathematicians to understand motion in a dynamic and ever-changing world. It could be used practically and efficiently. By understanding the world that we live in, he could use calculus to appreciate movement with a clearer angle and pave the way for future mathematicians. Branches in mathematics such as geometry and algebra were separate entities that did not build off of each other the way calculus does. The creation of calculus was a response to this demand and unification in the field of mathematics.
By using calculus, we as students become better mathematicians and understand more of the natural world by implementing these ideas and discoveries passed on from past generations. The uses of calculus range far and wide, from architecture and the building of bridges to accurately predicting weather. Using calculus makes us more human, more articulate, and understanding of the world around us. It contains the foundation of previous branches of math that we need to understand it properly, and it combines the physicality of our natural world to make it practical and used in many different situations.