1. For people who don't understand philosophy, they often myth philosophy, saying that philosophy is the highest science, which is higher than all sciences; This is not objective and practical;

2. For people who are obsessed with mathematics, it is not objective to say that mathematics is "the language of God (Gauss)";

3. Mathematics and philosophy are the knowledge of understanding and transforming nature in human development. This kind of cognition can only be found that it does not change with the change of people, that is to say, mathematics and philosophy have objective characteristics and are not transferred by human will;

4. Mathematics and philosophy are both related and different: because they are both reactions to objective things, mathematics and philosophy are both discoveries of the material world, and they are bound to be related; And there are differences between them, because objective things are developing and their appearances are not only the same, so they must be different in mathematics and philosophy;

5. It is not that mathematics is a subject that studies concepts such as quantity, structure, change and spatial model, and some research methods in mathematics are also applicable to philosophy; Similarly, the methodology in philosophy also inspires and helps the study of mathematics. So mathematics and philosophy can complement and transform to some extent, because objective things can also complement and transform.

6. It is unscientific to say that philosophy is ontology and a summary of all thinking and methods; Things are constantly developing, and the methods of studying things need to be constantly developed. But focusing on the development of things will form an independent discipline, and there will be new research methods and thinking summaries, which is not the category of philosophy; Therefore, philosophy and all disciplines are equal, not antagonistic, nor superior to other disciplines; They all focus on the objective cognition of their respective fields, with the continuous development of objective things.

7. To correctly understand the relationship between mathematics and philosophy, we must oppose the view that mathematics is a tool and means of philosophy. This view obliterates the characteristics of mathematics as a methodology and virtualizes the "highest scientific theory" of philosophy. It is a metaphysical theory that does not understand philosophy, a challenge to the cognition of different aspects of objective things, and an ignorance of the dialectical unity of objective things!