mathematicians usually think that if a theory can be used in theoretical physics, it is directly useful. After that, he had to say that theory
Physics is useful only if it is useful in experimental physics. After that, it is certain that if a concept of experimental physics is judged by the usual criteria
Useful in engineering, it's really useful. Even after the entire project, you can further. Therefore, the concept of these usefulness
There is a great limitation, and with this concept we can only assume that every science is used outside its own domain, and that this series of applications
There is some kind of general orientation------------------immediately. But if people are not picky, but--like math
The standard of home----that usefulness refers to anything that is not part of mathematics, that people will certainly find useful in most fields.
Similarly, according to the sum of all these standards, it can be said that a very wide range of areas are actually directly useful. Indeed, our lives
The world has changed a lot, although the impact is not very direct, but there is always a mathematical vitality behind the field!
In general, a mathematical discovery will have a time difference between its applications, possibly from 30-100 years or more
--Excerpt from "The Role of Mathematics in Science and society" von Neumann
Math is useful, what's the use?