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数学家波利亚将其著作《数学与猜想》的第一卷命名为《数学中的归纳和类比》,并在其第三章中直接引用了拉普拉斯的下述断言:“甚至在数学里,发现真理的主要工具也是归纳和类比。”波利亚十分重视类比方法对于建构数学知识的作用,认为“类比”实际上“是合情推理的一种思维形式,即是由两个或更多的思考对象在某些属性上的相同或相似,从而推出它们在另一属性上也相同或相似的一种推理方法。”在他看来,类比和归纳一样,都是合情推理的主要方法,是教学发现的重要源泉。
The mathematician Polyana names the first volume in his book Mathematica and Conjecture “Induction and Analogy in Mathematics,” and in its third chapter directly quotes Laplace’s assertion that “even In mathematics, the main tools for discovering truths are inductive and analogous. ”“ Polia attaches great importance to the role of analogy in building mathematical knowledge, arguing that ”analogy “ in fact ”is a form of thinking that is plausible reasoning, That is, two or more thinking objects are the same or similar in some attribute, so as to deduce an inference method that they are the same or similar in another attribute. “” In his view, analogy and induction , Are the main method of reasonable reasoning, an important source of teaching discovery.