The main representative of logicism is Russell. In Principles of Mathematics and Principles of Mathematics, Russell's goal is to prove that "mathematics and logic are congruent", which can be analyzed into three parts:

1, every mathematical truth can be expressed as a language that is completely expressed or expressed by logic. In short, every mathematical truth can be expressed as a real logical proposition.

2. If every logical proposition is a translation of mathematical truth, then it is a logical truth.

3. Once every mathematical truth is expressed as a logical proposition, it can be deduced from several logical axioms and rules.