The first chapter, the two sources of mathematical thinking methods, the first section, the original geometry of ancient Greece, the second section, China's nine chapters of arithmetic, the second chapter, some breakthroughs in mathematical thinking methods, the first section, from arithmetic to algebra, the second section, from constant mathematics to variable mathematics, the third section, from deterministic mathematics to stochastic mathematics, the third chapter, the truth of mathematics, the first section, mathematical proof and mathematics. Mathematical Axioms Section III The Third Mathematical Crisis Section IV Godel's Incompleteness Theorem Chapter IV Development Trend of Modern Mathematics Section I Unity of Mathematics Section II Increasing Application of Mathematics Section III Mathematical Revolution Caused by Computers Chapter V Abstraction and Generalization Section I Abstract Methods Section II Generalization Methods Chapter VI Conjecture and Refutation Section I Inductive Conjecture Section II Analogical Conjecture. I want to refute the counterexample in the third section. Chapter 7 The cultivation of guessing ability is deductive reduction. The first section is the axiomatic method. The second section is reduction method. The eighth chapter is calculation and algorithm. The second part is the calculation algorithm. Chapter 9 is application and modeling. The first part is the mathematical model method. The second part is the establishment of mathematical model. The third part is the teaching of mathematical model method. The fourth part is the modern application of mathematical model method. Chapter 10 Other Methods Section 1 Classification Methods Section 2 Combination of Numbers and Shapes Section 3 Specialized Methods Section 2 Chapter 11 Mathematical Thinking Methods and Quality Education Chapter 12 Mathematical Thinking Methods Teaching Chapter 13 Mathematical Thinking Methods Teaching Case Study Guidance Reference