Is Mathematics Problem Solving or Theorem Proving? 数学是“问题求解”还是“定理证明”? 

1 引⾔

2 数学家对数学方法的看法

3 分析方法

4 分析的与公理的

5 问题与定理

6 对⽴还是强调的不同?

7 希尔伯特论数学方法

8 打破平衡

9 公理⽅法与哥德尔不完备性定理 

10 实现希尔伯特目标的不可能性 

11 分析⽅法和哥德尔不完备性定理 

12 公理方法的其他缺点

13 分析⽅法的其他优点

14 公理方法和教科书

15 《数学与确定性》

16 回答两难问题 

1 Introduction

2 Mathematicians’ Views on the Method of Mathematics

3 The Analytic Method

4 Analytic Versus Axiomatic Method

5 Problems Versus Theorems

6 Opposition or Different Emphasis?

7 Hilbert on the Method of Mathematics

8 Breaking the Balance

9 Axiomatic Method and Godel’s Incompleteness Theorems 

10 The Impossibility of Achieving Hilbert’s Goal

11 Analytic Method and Godel’s Incompleteness Theorems 

12 Other Shortcomings of the Axiomatic Method

13 Other Advantages of the Analytic Method 

14 The Axiomatic Method and Texbooks 15 Mathematics and Certainty

16 Answering the Dilemma 

problemSolvingOrTheoremProving.pdf