最近菲尔兹奖得主Zelmanov来给我们讲了5个晚上的课，老教授很亲切和蔼，第一天晚上我坐在最前面，很直接的感受到他举手投足间散发的魅力。
但是我实在无法听懂他讲的课，不是因为他讲的不好，而是他讲的内容是抽象代数，我没学过。
我旁边的一哥们，整堂课和老教授对答如流，实在令我羡慕不已。下课和这位仁兄交流，方知他是数院研究生，抽象代数他之前学过。他还特别兴奋地跟我分享这位老教授带给他对数学的新认知，可见他的收获确实很大。
我们都很有幸遇到这样真正的牛人，可是他的收获远多于我，我和他的差距就在于之前的积累。
当你自己本身就不行的时候，就算有贵人倾力相助，你也只是扶不上墙的泥。就像这位老教授讲的是他认为最基础的抽象代数，可我还是听不懂。
而那些有所准备的人，就能借助这次机会获得意想不到的成长。
所以，要在平时就不断积累，保持进步，先成为那个配得上最好的人。
还好，虽然课听不懂，最后的结课论文并不难，谁对数学还没点看法呢 [笑。
以下就是我的结课论文，题目为“Mathematics:Sicence or Art?”。
本人的英文水平实在差，请海涵。
Mathematics:Sicence or Art?
Regarding what the teacher taught us in that class at primary school, I would like to believe that mathematics is a hard science, which is all about problem solving.
But now, I suppose that mathematics is a useful art, in which pure mathematics focuses on proving and finding the beauty of mathematics, meanwhile mathematics has its unexpected and important applications. In the twentieth Century, mathematics was divided into two major categories, pure and applied mathematics, which played an important role in finance, aviation and engineering.
Regardless of its being considered as science or art, mathematics is absolutely integrated into our life. When you’re programming, every function you use includes mathematics; when designing, lines you measure and patterns you create includes mathematics.
But thinking deeply into this problem, you will find that mathematics in different situations has different reflections.
In calculus, for example, mathematics is considered as a tool, whose primary goal is to solve differential or integral through several steps.
As for when I’m first contact with probability theory, I believe that it’s more like a model of thinking.
A book, named Fooled By Randomness written by Nassim Taleb, describes how people know nothing about probability are fooled by historical data. If we don’t refer to those “never happened history”, we can’t really understand the “history that has been realized”, which Taleb calls “Summing under histories”.
What’s “never happened history”? For example, when you see a monkey seated in front of a computer writing Shakespeare’s King Lear, you must be amazed. You imagine that this monkey must have special intelligence, or be Shakespeare’s reincarnation.
But you can think it through probability, imagining a myriad of monkeys typing in front of a computer. Because of the randomness, there is always one that can write a complete book.
So “never happened history” is a myriad of monkey, “history that has been realized” is the monkey writing a complete book. And you just see that one.
There are many ways of treating mathematics. In terms of the mathematics itself, still some important issues worthy of discussion exist.
I’ve seen Roger Antonsen’s Ted speech, which left so much impression on me.
Many of us think of mathematics as addition, subtraction, multiplication, division. But the essence of mathematics is that mathematics has to do with patterns.
The big sticking point is about finding patterns, which mean a connection, a structure, some regularity, some rules that govern what we see.
Second of all, it’s about representing these patterns with a language in mathematics. We make up language if we don’t have it. And in mathematics, this is essential.
It’s also about making assumptions, playing around with these assumptions and just seeing what happens.
For example, what I show you is a pattern, which actually emerges just from drawing circles in a very particular way.
So, we can represent some really cool stuffs with mathematics in a pattern.
Is mathematics science or art on earth? Different people have different views on this issue. If you consider it as science, you can create something high-tech; If you consider it as art, you can create something beautiful and concise.
