Abstract: Constructing machine thinking mechanisms that are understandable to humans is the ultimate goal of this paper.Ma-thematic is an important thinking tool for humans to describe the state and running laws of the objective world,and is also a tool for machines to automatic resolving,interpretable running,and intermediate steps generating.The description language of the objective world has diverse forms,huge scale,and sparse features.Its semantic representation,semantic accumulation,semantic analyzing,and the implementation of machine thinking mechanisms are all based on progressive clarity and perfection by use cases.In the field of automatic humanoid solving elementary mathematic application problem,machine thinking mainly relies on basic mathematical concepts and their underlying computation theories,including set,proportion(fraction),unequal relationship,enumeration,and data induction and derivation(trend discrimination).Taking the semantic gradual accumulation and recognition of set elements and their proportions as the example,this paper discusses the application technology of mathematical principles in machine thinking systems from the perspective of machine thinking system implementation.Finally,an example is presented to illustrate the complete process and intermediate steps of machine automated humanoid resolving a specific elementary mathematic application problem.The methods and prospects of using mathematical tools such as inequality,enumeration,number axis,coordinate system,and mathematical induction and deduction in machine thinking are discussed.

Key words: Machine thinking, Set, Proportion, Mathematical object, Mathematical concept