I believe that mathematics is more than a tool to be applied to physics or physical problems.
For the people who get into the natural science or engineering, math is one of the subjects that they must learn. We all think that math provides a lot of help indeed, and also these subjects offer many interesting questions for mathematicians, which push an actuation in the way to develop math. However, from my perspective, math is much more than a tool to do this. It is an independent system which is also tightly associated with the other kinds of science and technology.
I’d like to talk about some history of calculus. Normally, Isaac Newton is the first name that comes to our mind when we talk about this. But if I mention Weierstrass, then I believe you probably have never heard of this name unless you have tried to get into mathematical analysis. In fact, Weierstrass is one of the mathematicians who reach the true accuracy of calculus. The definition of limitation, which is one of the most important definitions, was invented by Weierstrass.
the famous Weierstrass Function
To establish the accuracy of calculus is a long and interesting process, which started when it was invented by Newton and Leibniz, with the efforts of lots of famous mathematicians, such as Euler and Lagrange, finally ended by Weierstrass, Cauchy, Dedekind, and some others, and took about one and a half centuries to finish it.
I am not going to discuss some details about this process, instead, I decide to talk more about the motivation of this process. Why did people still want an accurate system when they were master of the tools of calculus? What is the purpose of the further research if the physical tools is known?
In my opinion, technology is above tools. I think this is the key purpose of this process: we can find more tools by establish accurate basis of calculus. When everything is clear, new tools in the same field will be found. This is the reason why mathematicians keep in finding the “useless” theory: only the basis are stable enough can we build a tall and majestic building. Also, the further research appeared in the later years, such as differential equations, complex analysis, real analysis and other subjects, which stood on the accurate calculus, showed great efficacy of the physical examples.
by Newton’s law of universal gravitation, the orbits of the solar system can be accurately donated by the differential equations
We should admit that math is more than a tool. Some basic research in math, which seems with nothing to do with the physical society, may become the first step of the future knowledge.
What is your opinion about math? Is it just a tool for you? Leave your ideas in the comments please.