- For Isaac Newton's book containing basic laws of physics, see Philosophiæ Naturalis 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..."
- Irvine, Andrew D. (2003). "Principia Mathematica (Stanford Encyclopedia of Philosophy)". Metaphysics Research Lab, CSLI, Stanford University. Retrieved 5 August 2009.
- "The Modern Library's Top 100 Nonfiction Books of the Century". The New York Times Company. 30 April 1999. Retrieved 5 August 2009.