The Principia Mathematica is a 3-volume work on the founations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910–1913. It is an attempt to derive all mathematical truths from a well-defined set of axioms and inference rules in symbolic logic. One of the main inspirations and motivations for the Principia was Frege's earlier work on logic, which had led to paradoxes discovered by Russell. These were avoided in the Principia by building an elaborate system of types: a set of elements is of a different type than is each of its elements (set is not the element; one element is not the set) and one cannot speak of the "set of all sets" and similar constructs, which lead to paradoxes (see Russell's paradox).