An overview of the foundations of mathematics in the twentieth century

This thesis will begin by looking at a brief history of the foundations of mathematics. This will lead to an examination of the foundations after Russell announced his set theoretic paradox. At first three main viewpoints were presented: logicism, formalism and intuitionism. This thesis will give an overview of these three schools of thought. In the end, all three were incapable of satisfactorily laying out the entire foundations. In the latter half of the century, much of the philosophy of mathematics was developed with the realization that a reliable and infallible foundations is unlikely. This thesis will also examine two of these later foundations: structuralism and proofs and refutations.