Abstract

In a recent paper, the mathematician Harold Edwards claimed that Euler’s alleged proof, that Fermat’s last theorem is true for the case n = 3, is flawed. Fermat’s last theorem is the conjecture that there are no positive integers x, y, z, or n, such that n is greater than two and such that xn + yn = zn. In this paper we shall first briefly explain the specific flaw to which Edwards called attention. After that we briefly explain the nature of mathematical proofs and with reference to such proofs explain the nature of gaps in proofs. Then we critically discuss an alternative view concerning the nature of proofs in mathematics and discuss the alternative view critically. Specifically we argue that advocates of this alternative view, which we call mathematical postulationism, have not provided a satisfactory account of the nature of gaps in proofs. The unsatisfactoriness of postulationist accounts of gaps in proofs is revealed through reflection concerning appropriate repairs to proofs with gaps.