From 19 10 to 19 13, Russell and Whitehead completed a three-volume masterpiece, Principles of Mathematics. In this book, they further clarified that mathematics is a branch of logic, mathematical concepts can be defined by logical concepts, mathematical laws can be deduced according to some premises of logic, and mathematical theorems can be proved as logical theorems; Starting from this logical thought, a huge symbolic formula system has been formed. This work is of epoch-making significance to philosophy. It examines the position of mathematical knowledge from a new angle, promotes the development of mathematical logic, and is also the most important logical work since Aristotle in ancient Greece.