Abstract (a bridgement): Taking the Mathematical Olympics as the carrier, this paper expounds the meaning of mathematical thinking mode: mathematical thinking is to understand the essence of mathematical knowledge, a mathematical viewpoint extracted from some specific mathematical contents and excessive understanding of mathematics, the essence of mathematical knowledge structure and the commander-in-chief of the soul, which plays a leading role in mathematical knowledge. As it is used repeatedly in cognitive activities, it has universal guiding significance and is the guiding ideology for establishing mathematics and solving problems with mathematics. The index of mathematical method is the various ways, means and ways adopted in the process of raising and solving problems; The algebraic substitution method is enumerated, which creates conditions for effectively solving problems in mathematics competitions. It shows the beauty of unity, simplicity, symmetry and singularity in mathematics.

Key words:

Mathematical thinking

Mathematical method, mathematical method

Competition competition

Substitution behavior substitution method

Additional conditions. Additional conditions