What math applications did it have in past centuries and how have uses evolved?

Geometry was developed by Egyptian farmers to survey their farms. In those days it was called To Mer, "The Measured Land". Later the name was changed to Hut Ka Ptah, "The Resting Place Of The Soul Of Ptah". The Greeks pronounced that "Aigyptos", the French changed the Greek to "Aigypte", and Americans changed the French to "Egypt".

A Greek philosopher named Euclid traveled to Egypt to learn what he could and got interested in the rules used by farmers to accurately locate farm borders in the mud left by the annual floods. He wrote down all the rules and developed standard ways to prove their correctness and to develop new methods. His book, in all its editions, is the second best selling book of all time, after the bible.
www.google.com/search?q=euclid

Euclid was never sure about his fifth postulate. It was two thousand years before Nikolai Ivanovich Lobachevsky figured out what was wrong with it: it only applied to plain geometry. If you wanted to do geometry on some other surface, you had to use a different fifth postulate.
en.wikipedia.org/wiki/Nikolai_Lobachevsky