翻开一般的数学課本,就会看到:定义—定理—証明—推論,最多再举几个例,或者在定义前面有个小敍,说明一下理論发展的簡略情景。但要問,这个定理是怎么发現的?数学家怎样找到了証明?証明的过程为什么必須是这样的?如此等等数学家們真实的思維过程在写书时都被抽掉了。在一般的数学文献中,这样做也许是必要的,但在数学教科书与数学教学中,注意适当地发掘这种思維过程就显得很重要了,它将对培养初学者的数学能力起很好的作用。近来讀到一本书:“数学与似然推理”(原书是英文,有俄文譯本),是数学家波利亚(Polya)根据自己数学研究和教学的經驗写成的。这本书的主要目的在于肯定地回答諸如“在通常的自然科学中所应用的归納、类比、观察、实驗、概括等方法在严謹的科学,例如数学 Turning on the general mathematics textbook, you will see: Definition - Theorem - Proof - Inference, at most a few more examples, or a small narrative in front of the definition, explain the brief scenario of theoretical development. But to ask, how did the theorem be found? How did the mathematician find the proof? Why did the proof process have to be like this? Then the mathematician’s real thought process was taken away when the book was written. In the general mathematics literature, this may be necessary, but in mathematics textbooks and mathematics teaching, it is very important to pay attention to properly explore this thinking process. It will play a good role in cultivating beginners’ mathematical ability. effect. Recently read a book: “Mathematics and Likelihood Reasoning” (original book is in English, there is a Russian translation), is written by mathematician Polya based on his own mathematical research and teaching experience. The main purpose of this book is to affirmatively answer questions such as "Induction, analogy, observation, experimentation, generalization, etc., applied in the usual natural sciences, in rigorous science such as mathematics.