The Principles of Mathematics, Vol. 1 offers a clear introduction to Bertrand Russell’s rigorous approach to logic, numbers, space, motion, and the nature of mathematical reasoning. It frames how pure mathematics uses abstract concepts to model ideas independent of physical objects.

The book is written for both philosophers and mathematicians, and it sketches the connections between symbolic logic and mathematical theory. It discusses how definitions, predicates, and logical constants underlie much of mathematics, and it surveys topics such as real numbers, complete and incomplete series, and the correlation of infinite classes. The author also outlines the role of dynamics, geometry, and the philosophy of space, with emphasis on careful analysis rather than empirical details.
What you’ll experience

An overview of the logical foundations that support arithmetic, geometry, and analysis
Concepts like complete vs. incomplete series and how functions relate infinite classes
A discussion of real numbers as a way to understand number through rational classes
The relationship between philosophy and mathematics, and guidance for readers new to symbolic logic

Ideal for readers of philosophy and mathematics who want a rigorous, practitioner-friendly view of foundational ideas and their implications.

About the Author

Bertrand Russell (1872-1970) was born in England and educated at Trinity College, Cambridge. His long career established him as one of the most influential philosophers, mathematicians, and social reformers of the twentieth century.

"About this title" may belong to another edition of this title.

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