It took a long time in the history of humankind before it occurred to anyone that mathematics is useful - even vital - in the understanding of nature. Western thought was dominated from antiquity to the Renaissance, turn by turn, by Plato and Aristotle. Plato taught that reality consists of idealized "forms", and our world was a flawed, inadequate shadow of reality - hardly worthy of passing notice, let alone study. Aristotle thought that the intricacies of nature could never be described by the abstract simplicity of mathematics. In the text section 1.
The Physics Of Mathematics And Mathematics Essay - Words | Bartleby
You can see a video of the lecture below. People often talk about the "unreasonable effectiveness of mathematics" — a phrase coined by the physicist Eugene Wigner in to capture the idea that mathematics describes the physical world far better than you'd expect from a mere human-made tool. Indeed, many physicists feel that mathematics expresses something deep about the nature of physical reality. That mathematics should be useful in physics is no surprise. Whenever we need to measure, count, and understand patterns or relationships in the world, maths is an essential tool. What is surprising, however, is that even mathematics that has been developed for the pure pleasure of pure maths can prove to be uncannily useful in physics, sometimes a long time after it was first thought of.
The relationship between mathematics and physics has been a subject of study of philosophers , mathematicians and physicists since Antiquity , and more recently also by historians and educators. In his work Physics , one of the topics treated by Aristotle is about how the study carried out by mathematicians differs from that carried out by physicists. Before giving a mathematical proof for the formula for the volume of a sphere , Archimedes used physical reasoning to discover the solution imagining the balancing of bodies on a scale. Some of the problems considered in the philosophy of mathematics are the following:.