What is the point of studying maths at a very high level?

[AlephZero]

You divide a mathematician by a physicist and you get a sum?

True story about the difference between a mathematican working as an engineer (me!) and a physicist who really wanted to be a mathematian (my boss).

I had written the specifcation for putting some new gizmo into a finite element analysis code, full of details of numerical integration, how to evaluate Jacobians, etc.

It came back from my boss with the comment "You could make this a lot shorter by <insert half a page of divs, grads, curls, and double and triple integrals here>"

So I sent a note back saying "OK, but if this is a spec for a computer program, how would you actually write the code"?

The answer: "You do it your way, of course".

 

[ilmareofthemai]

For most of the mathematicians I know, in one way or another, their interest in math comes down to its aesthetic quality. Doing math because you find it beautiful or because you like the way it makes you think seems like a perfectly rational decision to me.

Agree!
I recently read A Universe in Zero Words, a book about the history and influence of important equations (if you want some examples of crazy mathematicians, read the chapter about the types of infinities-the outcome for a couple of those mathematicians, i.e. Godel, was not so great) and developed a strong appreciation for mathematics, especially geometry. A great read.
Also, as someone else mentioned, math and physics sometimes develop at different rates, and the math Pauli needed was already developed, etc. For more examples, read Euclid's Window, a book about the major mathematical revolutions and their connections with physics. Is mathematics inherent, or a construct? It has to do with the definition but maybe we'll never know...It has already been proven that math can't be proven (Universe in Zero Words)!