## The Principia Mathematica by Alfred North Whitehead, Bertrand Russell

The Principia Mathematica is a 3-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell. PM, as it is often abbreviated (not to be confused with Russell's 1903 Principles of Mathematics), 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 PM was Frege's earlier work on logic, which had led to paradoxes discovered by Russell. These were avoided in PM 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). PM is widely considered by specialists in the subject to be one of the most important and seminal works in mathematical logic and philosophy since Aristotle's Organon. The Modern Library placed it 23rd in a list of the top 100 English-language nonfiction books of the twentieth century.