“庖丁解牛”数学方法

庄子讲庖丁(butcher)解牛有三个功夫階段：

1st Level: 看见一只全牛 (Whole Cow)

2nd Level: 三年后，不见全牛，只见牛的生理结構(Anatomy) ：骨骼，肌肉，筋腱。

3rd Level: 不以目视而是神视，＂与桑林之舞合拍，与经首之会同律。＂达到了”物我”两忘的境界。Intuition.

数学的方法也如此。

1st Level: **Whole** Math (Primary school to High School)

2nd Level: Component **Structure** – (Undergraduate Math)：

Macro- structure (Algebra : Group, Ring, Field, Vector Space… );

Micro-structure (Analysis : Calculus, Topology, etc)

3rd Level: 无处不数 **Ubiquitous** Math – (Graduate Math)

eg. Fermat’s Last Theorem used all Math theories available today to prove.