# Principia Mathematica

## Book on the foundations of mathematics (1910–13, 1925–27) / From Wikipedia, the free encyclopedia

#### Dear Wikiwand AI, let's keep it short by simply answering these key questions:

Can you list the top facts and stats about Principia Mathematica?

Summarize this article for a 10 year old

The * Principia Mathematica* (often abbreviated

*) is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. In 1925–1927, it appeared in a second edition with an important*

**PM***Introduction to the Second Edition*, an

*Appendix A*that replaced

**✱9**with a new

*Appendix B*and

*Appendix C*.

*PM*was conceived as a sequel to Russell's 1903

*The Principles of Mathematics*, but as

*PM*states, this became an unworkable suggestion for practical and philosophical reasons: "The present work was originally intended by us to be comprised in 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; moreover on many fundamental questions which had been left obscure and doubtful in the former work, we have now arrived at what we believe to be satisfactory solutions."

I can remember Bertrand Russell telling me of a horrible dream. He was in the top floor of the University Library, about A.D. 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down books, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of

Principia Mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated....

G. H. Hardy, *A Mathematician's Apology* (1940)^{[1]}

He [Russell] said once, after some contact with the Chinese language, that he was horrified to find that the language of

Principia Mathematicawas an Indo-European one.

John Edensor Littlewood, *Littlewood's Miscellany* (1986)^{[2]}

*PM*, according to its introduction, had three aims: (1) to analyze to the greatest possible extent the ideas and methods of mathematical logic and to minimize the number of primitive notions, axioms, and inference rules; (2) to precisely express mathematical propositions in symbolic logic using the most convenient notation that precise expression allows; (3) to solve the paradoxes that plagued logic and set theory at the turn of the 20th century, like Russell's paradox.^{[3]}

This third aim motivated the adoption of the theory of types in *PM*. The theory of types adopts grammatical restrictions on formulas that rules out the unrestricted comprehension of classes, properties, and functions. The effect of this is that formulas such as would allow the comprehension of objects like the Russell set turn out to be ill-formed: they violate the grammatical restrictions of the system of *PM*.

*PM* sparked interest in symbolic logic and advanced the subject, popularizing it and demonstrating its power.^{[4]} The Modern Library placed *PM* 23rd in their list of the top 100 English-language nonfiction books of the twentieth century.^{[5]}