Richard Paul Thomas is a pure mathematician working in several areas of geometry.
Bendixson started out very much as a pure mathematician but later in his career he turned to also consider problems from applied mathematics.
The pure mathematician's life is, according to Pythagoras, the life at the highest plane of existence.
He later trained as a pure mathematician at Princeton University.
I cannot call myself a "pure" mathematician; too often have I been tempted by outside problems.
To a "pure" mathematician like Hilbert, this was both "ugly" and difficult to understand.
On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research.
In recent years this trait has also been observed among many pure mathematicians (who have an independent tradition of numbering from 0).
He was a pure mathematician, not interested in problems that had applications in science or business.
It is the mainstream way of looking at mathematics for academic pure mathematicians.