What was the goal of logicism in the work of Frege and Russell?

In the context of analytic philosophy, the goal of logicism, as championed by Gottlob Frege and Bertrand Russell, was to establish a firm, certain foundation for mathematics by demonstrating that it is entirely reducible to logic.21

Logicism contends that all mathematical truths are ultimately logical truths. The objective was to show that mathematical concepts and modes of reasoning could be defined and derived from purely logical notions—such as propositions and classes—without requiring specifically mathematical concepts like numbers or sets.123

This project was driven by a desire to prove that mathematics, as practiced, was reliable and trustworthy. Russell and Alfred North Whitehead attempted to execute this program in their monumental work, Principia Mathematica, which sought to derive the whole of mathematics from a few simple logical axioms. While the program faced significant challenges—most notably Russell’s paradox and Kurt Gödel’s incompleteness theorems—it remains a foundational effort in the development of mathematical logic and the philosophy of mathematics.13