Gottlob Frege
He created mathematical logic all by himself in order to give firmer foundations of arithmetic. His studies on logic and the nature of language led to a new method of philosophy, now called "linguistic" or "analytical".
However, his program for reducing arithmetic and mathematics in general to logic (Logicism in the philosophy of mathematics) turned out to have great difficulties: the concept of set is needed even for defining natural numbers, and logic alone is not sufficient for defining it; a naive definition leads to a contradiction, as the Russell paradox shows (see Russell).
