In mathematics, observation and reasoning are two important methods to solve problems. Observation refers to the method by which people obtain information about the mathematical characteristics of things or problems through vision, and dialectical their morphology, structure and quantitative relationship through thinking, so as to discover some laws or properties. Reasoning is a thinking form that draws another new judgment from one or several existing judgments.

For example, when solving geometry problems, we can use observation to describe the characteristics of graphics, and then use inference to prove the conclusion. In addition, when solving algebraic problems, we can use observation to find the relationship between formulas, and then use reasoning to prove the conclusion.