The long-standing discussion of whether Physics is possible without Mathematics has pestered many and drawn many crazy
People often talk about the "unreasonable effectiveness of Mathematics" — a phrase coined by the physicist Eugene Wigner in 1960 to capture the idea that Mathematics describes the physical world far better than you would 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, Mathematics is an essential tool.
What is surprising, however, is that even Mathematics that has been developed for the pure pleasure of pure Mathematics can prove to be uncannily useful in Physics, sometimes a long time after it was first thought of.
A fascinating example is a particular geometric notion of curvature developed by the mathematician Bernhard Riemann in the 19th century. Riemann cared nothing about Physics when he came up with his ideas, and he certainly did not predict the dramatic developments in Physics that were to flow from Albert Einstein's pen at the beginning of the 20th century. Yet, Riemann's ideas turned out to be just what Einstein needed to formulate his general theory of relativity. According to general relativity, the force of gravity is the result of massive objects bending the fabric of space-time. To describe this bending, Einstein needed to define the curvature of a geometric object without reference to a surrounding space the object is embedded in and this is exactly what Riemann had done before him.
Mathematics provides an elegant and satisfactory framework to support the theories of Physics known to date, in particular the theory of relativity and quantum mechanics. In Ancient Greece, Physics was considered to be nothing but Natural Philosophy, a branch of Philosophy used to describe nature, and by extension, our physical universe. Many philosophers and thinkers, such as Aristotle, wrote extensively about Physics without actually using any Mathematical tools. But in those days, it was pure Philosophical thought, and using Mathematics to describe physical phenomena was not necessary. In our times, Mathematics is an essential part of Physics. In every college/university Physics course in the world, one of the first things you learn is the role of Mathematics in Physics. You need a good understanding of mathematical tools in order to comprehend Physics on a higher level. Math is a tool which improves the precision of physics. It took until Newton developed calculus before physics really started.
You find interference fringes when you pass light through slits. You know that you see fringes, but now you want to know how they form and what the factors that affect these fringes are. How they form is part of Physics, but now you want to find its width and its dimensions and factors that affect them. So here you need mathematical equations. With these equations you can see how u can change the length or width or colour of these fringes. And due to these equations you can find the use of this phenomenon in day to day life.
But there is another side to this coin. Michael Faraday used no Mathematics at all to create the laws of electromagnetism. Einstein used mathematics to express his theories because there was no other medium to do so. However, he famously said in 1949, “Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.” Most of the great physicists used abstract thought, mental experimentation and the power of their imagination to create their theories. For them, Mathematics is merely the language in which it is expressed. For them, Mathematics is not required to understand Physics any more than an anthropologist is required to learn a native language to understand another culture. There have been inventors who were practical. Crude experimentation, time after time enabled them to manipulate forces and materials for new knowledge, and discoveries. There have been ‘philosophers” who used just observation and logical thought processes to draw conclusions about the world around them.
The long-standing discussion of whether Physics is possible without Mathematics has pestered many and drawn many crazy. People bear the burden of Mathematics to do well in Physics. Others fail to get the whole picture of Physics for they are not good at Mathematics. This situation is a dilemma. It is like Shakespeare’s Hamlet. We are often confused about whether “to do or not to do”
(Author is a Student )