The story was that Einstein had an idea about the curvature of space time. However, he was a physicist. The concepts of Differencial Geometry were beyond his mathematical skills to understand. Therefore, he got help from somebody that he was friendly with while still in college. It was Marcel Grossman. From what I read, Grossman taught Einstein the necessary math needed to create his spacetime theory. Even after Einstein had the necessary mathematical knowledge he still was not able to fully arrive at the conclusions. This time Einstein got help from somebody else (this time a physicist) who knew this topic well, Schwarzschild.
Then after all of that, Einstein finally completely his theory. However, it was not "rigorous" enough and some people had trouble accepting it at first.
Now, imagine, Einstein did study Diffferencial Geometry at a mathematical level, rather than on how to apply it, he would have been more succesful in doing his work, and perhaps, not requiring help from other people because his mathematical theory knowledge will assit him.
..... And much of the credit of course goes to one of my favorite mathemations, Riemann. Without him, Differencial Geometry would not exist, and the mathematics behind relativity will not exist. And Einstein would only have been famous for the photoelectric effect rather than relativity. Again, if Riemann had your approach, none of this would have happened.
Calculus, is not really used by mathemations. Of course, they know it, but they do not use it in the work that they do. They use an analouge called, Analysis.What about the Math we learn and use, that is not standard Math? It's sub-standard Math?
If it is the applications, that you care about then:
.Originally Posted by Wikipedia
I have a sense, that you despise advacned mathematics is because you do not know it.