In the philosophy of mathematics, there are many different schools and viewpoints. Some of these schools think that mathematics is a purely symbolic system, which has nothing to do with the real world; Others think that mathematics is an abstract description of the real world and has objective significance.
In addition, mathematical philosophy also discusses the essence of mathematical truth. Some philosophers think that mathematical truth is absolutely unchangeable, while others think that mathematical truth is relative and depends on our interpretation and application.
In mathematical reasoning, logicism and intuitionism are two main schools. Logicians believe that mathematical reasoning should follow strict logical rules, while intuitionists believe that mathematical reasoning should rely on human intuition and imagination.
In a word, philosophy of mathematics is a complex and profound subject, which involves many important issues and viewpoints. By studying the philosophy of mathematics, we can better understand the essence and significance of mathematics and provide guidance for our future research and practice.