1. Species relationship: Mathematics and philosophy are both thinking activities of human beings to know and explore the world, and they are both part of ontological things. Philosophy discovers and produces ontological things from chaos, while mathematics discovers and produces non-ontological things-numbers from chaos. Both explore and understand the real world in their own way.

2. Logic and abstract thinking: both mathematics and philosophy emphasize logical reasoning and accuracy. Mathematics deduces laws and theorems through symbols and formal language, while philosophy explores human thinking, existence, value and truth through logic and reasoning. Both need abstract thinking and creative thinking.

3. Historical crossing: Historically, many famous mathematicians were also philosophers. Their contributions in the field of mathematics have promoted the development of science, and they have also put forward important viewpoints or conducted logical research in the field of philosophy. For example, Cauchy is both a mathematician and a philosopher. His work has an important influence not only in the field of mathematics, but also in the field of philosophy.

4. Philosophy as a mathematical method: In some cases, mathematics can be regarded as a philosophical method. It discovers and verifies laws and theorems through reasoning and proof, and this way of thinking is also very important in philosophy. The spirit and practice of mathematics is a concrete form of philosophical thinking.