Principia Mathematica

The Principia Mathematica is a three-volume work on the foundations of mathematics by Alfred North Whitehead and Bertrand Russell. It was published in 1910, 1912, and 1913. In 1927, it appeared in a second edition with an important "Introduction to the second edition", and different notes at the end. It is often known as "PM".
The book was an attempt to describe a set of axioms, inference rules and law of noncontradiction in symbolic logic from which all mathematical truths could in principle be proved. This ambitious project is of great importance in the history of mathematics and philosophy. The authors believed that such a project could be done. However, in 1931, Gödel's incompleteness theorem proved that "PM", and any other attempt, could never reach this goal. For any set of axioms and inference rules proposed, either the system must be inconsistent, or there must in fact be some truths of mathematics which could not be deduced from them.
One of the main inspirations and motivations for "PM" was the earlier work of Gottlob Frege on logic.
"PM" is not to be confused with Russell's 1903 "Principles of Mathematics". "PM" states: "The present work was originally intended by us to be ... a second volume of Principles of Mathematics... But as we advanced, it became increasingly evident that the subject is a very much larger one than we had supposed..."
The Modern Library placed it 23rd in a list of the top 100 English-language nonfiction books of the twentieth century.