Abstract: Whether the propositional formula“2+2=4”is a judgement based on experience and intuition or the result of rigorous process of mathematics? Barnes and Bloor insist on the examination of the above formula ascribe to the vision of sociology, unfortunately it’s unmatched with the nature of mathematical knowledge. Mathematics has the features of deep difference under the multiple fields of vision such as idealization and virtuality as well as the association with the reality and experience world. The genealogy among the rigorous, deductive, empirical, applicative aspects was correlated with diversity internalization and hierarchy identity of mathematical knowledge.