Russell not only made remarkable achievements in philosophy, logic and mathematics, but also made achievements in many fields such as education, sociology, politics and literature. Great changes have taken place in his philosophy. He believed in the New hegelianism in his early years, believed in the existence of absolute and universal phases, and regarded mathematics as evidence of Plato's thought. Later, he defected from absolute idealism to new realism with Moore.
As a philosopher, Russell's thought experienced several stages, such as absolute idealism, logical atomism, new realism and neutral monism, and mainly contributed to mathematical logic, from which he established logical atomism and new realism and became one of the founders of modern analytical philosophy.
Russell has made great contributions to mathematical logic. He and Whitehead co-wrote the book Principles of Mathematics, which is recognized as the basis of modern mathematical logic. His "Russell Paradox" promoted the development of logic in the 20th century, and the logicism he advocated also promoted the development of the history of mathematics to a certain extent.