So I was looking up some stuff on Number Theory today and I saw that it is a form of pure mathematics, so I decided to look it up and here is the definition that I found:

"Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. It is distinguished by its rigour, abstraction and beauty. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics,[1] and at variance with the trend towards meeting the needs of navigation, astronomy, physics, engineering, and so on. Ancient Greeks were usually more fond of geometry than of pure mathematics."

Plato was the first one to distinguish between different forms of mathematics and he said that number theory was for the philosophers "because he has to arise out of the sea of change and lay hold of true being."

G.H Hardy compared pure mathematics to poetry and painting and is used to express truths outside the physical world.

I had never really heard of pure mathematics and I think it is interesting that this is supposedly more philisophical and only ture mathematicians studied it in the past.