Guest wrote:Old Remark: Often Nature works to achieve its evolutionary goals in an optimal way. So, scientists must prove or show quantum gravity makes sense.

And the detection of quantum gravity is paramount.

General Questions: How do things work in Nature? Why?

The more mathematics one can absorb (understand) the better. And it is best to have a problem/project at hand when studying mathematical theory since theory and practice (application) are mutually beneficial. Amen!

The quest to discover the existence of quantum gravity and to model it mathematically is a grand impetus to study and apply some advanced mathematical knowledge/theories. Good Luck!