You must first decide which mathematician to choose, and then combine his specific examples to write inspiration.

Mathematicians always publish papers in the form of reasoning, and it is impossible to write a lot of exploratory and experimental work he did before proving. However, before proving a theorem, mathematicians must go through a lot of concrete calculations, carry out various experiments or tests, and form the ideas and methods of proof. Only at this time can they be logically synthesized and expressed as a series of reasoning, that is, proof. Thus, there is "calculation" in "performance". On the other hand, there is "expression" in the "calculation" fully expressed in arithmetic and algebra. So there are two stages in mathematical research: experiment and proof. From the etymological point of view, the word "proof" contains the meanings of "attempt", "experiment" and "confirmation". They said: "English" prove "has two basic meanings, one is to try or experiment, and the other is to confirm." Of course, experiments in mathematics are abstract thinking experiments, which are different from this. Mathematical experiment is just a way to put forward conjecture and hypothesis. it

Only through logical proof can a conjecture or hypothesis become a theorem. M·F· Atia, a British mathematician and winner of Fields Prize, believes that, like other natural sciences, some discoveries in mathematics have to go through several stages, and formal proof is only the last step. The initial stage is to identify some important facts, arrange them into patterns with specific significance, and extract seemingly reasonable laws or formulas. Then, people use new empirical facts to test this formula. Only at this time, mathematicians began to consider the problem of proof. For Hardy, proof is only the facade of the mathematical building, not the pillar of the structure. Carry out mathematical experiments to stimulate their potential learning ability and make them invest in a high-level learning state. At this moment, students' learning is not just memorizing definitions, theorems and formulas, but constructing knowledge through operating experiments. Effective understanding of thinking methods in mathematical knowledge structure. Students can get more feedback information to learn mathematics through operating experiments and constantly improve their understanding of new mathematical knowledge. Carrying out mathematical experiments can further cultivate students' practical ability, ability to observe and analyze problems, make students enter the state of active exploration, change passive acceptance of learning into active construction process, and cultivate students' innovative spirit, innovative consciousness and innovative ability.