Is calculus a discovery or an invention?

As an expert in the field of mathematics, I can provide a nuanced perspective on the question of whether calculus is a discovery or an invention. Calculus is a branch of mathematics that deals with rates of change and the accumulation of these changes over time. It is often considered one of the most powerful and fundamental areas of mathematics, with applications in physics, engineering, economics, and many other disciplines. The distinction between a discovery and an invention is an interesting one. A discovery typically refers to the recognition of something that already exists in the natural world or in the realm of ideas, while an invention refers to the creation of something new that did not previously exist. When we apply these definitions to the field of calculus, we can see that there are elements of both. Step 1: English Answer Calculus, in its essence, can be seen as a discovery because it deals with the fundamental concepts of change and accumulation, which are inherent properties of the universe. The mathematical principles that underlie calculus, such as the concepts of limits, derivatives, and integrals, are not constructs that were created out of nothing; rather, they are formalizations of patterns and processes that have always been present in the natural world. For instance, the idea that a curve can be approximated by a tangent line, or that an area can be computed by summing an infinite number of infinitesimally small rectangles, are observations that can be made by studying the behavior of physical phenomena. However, the invention aspect comes into play when we consider the formalization and systematization of these concepts. Before the work of Isaac Newton and Gottfried Wilhelm Leibniz, who are often credited with the development of modern calculus, there were indeed mathematical techniques that were used to perform tasks that would later be understood as applications of calculus. For example, ancient Greek mathematicians like Archimedes used methods that resemble integral calculus to calculate areas and volumes, and the Chinese mathematician Liu Hui employed similar techniques in the 3rd century AD. But these methods were not unified under a coherent theoretical framework. The formalization of calculus by Newton and Leibniz can be seen as an invention in the sense that they created a systematic method for dealing with these mathematical concepts. They provided a set of rules and principles that allowed for a rigorous treatment of limits, derivatives, and integrals. This systematization was a creative act, akin to the construction of a new machine or the formulation of a new scientific theory. It allowed for the application of calculus to a wide range of problems and laid the foundation for much of modern science and engineering. The nomenclature "calculus" itself is an example of an invention. Before Newton and Leibniz, the term "calculus" was used more generally to refer to any form of mathematics involving calculations. It was only after their work that the term came to be associated specifically with the branch of mathematics dealing with the mathematics of change and accumulation. In conclusion, calculus as a field of study is a blend of both discovery and invention. The concepts and ideas that form the basis of calculus were discovered in the sense that they reflect universal truths about the nature of change and accumulation. At the same time, the formal system of calculus that we use today is an invention, created by mathematicians to provide a rigorous and consistent way to apply these concepts to solve problems. The development of calculus is a testament to the power of human creativity and the ability to build upon and refine the understanding of natural phenomena. **

While the nomenclature may have been invented the math itself (concepts and ideas) was discovered. Before Newton and Leibniz, the most famous creators of modern calculus, all mathematics were referred to as calculus. After their work, calculus referred to infinitesimal calculus.Dec 20, 2014