 Of equal significance during this period was Russell’s defense of logicism, the theory that mathematics is in some important sense reducible to logic. First defended in his 1901 article “Recent Work on the Principles of Mathematics,” and later in greater detail in his Principles of Mathematics and in Principia Mathematica, Russell’s logicism consisted of two main theses. The first was that all mathematical truths can be translated into logical truths or, in other words, that the vocabulary of mathematics constitutes a proper subset of the vocabulary of logic. The second was that all mathematical proofs can be recast as logical proofs or, in other words, that the theorems of mathematics constitute a proper subset of the theorems of logic. As Russell summarizes, “The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself” (1903, 5).