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　　Why Learn Mathematics?

　　By Mr. Geoffrey Shen

　　沈鸣

　　（数学学科主任）

　　沈鸣出生于上海，香港籍，复旦大学数学与应用数学专业学士，香港城市大学数学专业博士。他在香港留学和工作近八年，能运用流利的英语、粤语、普通话和沪语进行交流。他曾在大学任教，并且执教过A-Level国际课程，有近十年的教学经验。他热爱教育事业，相信身教胜于言传，教书更要育人。性格开朗的他，喜爱运动和阅读，注重生活平衡。他很欣赏的一句座右铭是：破万卷书，行万里路，识万种人。

　　Last evening, an unidentified flying object came to the earth for a visit. It came across a gym where people were doing all kinds of exercises. On treadmills, people were running. Some were moving their legs quickly and sweating out. But none of them were moving a single step forward and stayed in the same spot. “What on earth are they doing?” The aliens wondered.

　　Many people ask the question, why learn mathematics? As a math teacher, I agree that most math you learn in high school will probably never be used again in your future life, unless you choose to work in a math-related field. So is it a waste of time to learn math? Definitely not. Doing math benefits our mind as running benefits our body.

　　Math helps us to be meticulous, or very careful.

　　Let’s look at this paragraph in Chinese.

　　Can you identify any wrong characters? Well, I am sure that some of you are good enough to find all the mistakes. Even if you cannot find one, you still get the meaning without any misunderstanding. When it comes to math, things are quite different. Look at these examples.

　　Even the smallest mistake is intolerable. A math problem can have different methods but the final answer is always unique. One must be very careful in each step to get the right conclusion. Any misread or miscalculation should at best be avoided. When a math teacher designs a test, he must check several times because a tiny mistake could make a math problem unsolvable. When we deal with math, we tend to be extra careful, which also shapes our character during the course. Thanks to all the math we went through over the years, we become more careful than we used to be.

　　Some may say why bother to be careful. If anyone should run into a dentist who pulled the wrong tooth out of your mouth, or be charged ten times more because of the wrong decimal place, he will think otherwise.

　　Math builds our logical mind.

　　We now live in an era of information explosion. We can gain access to tons of information in a few clicks. Some are true but more are misleading. How to tell the right from the wrong? More often than not, logic reasoning is the key.

　　The foundations of math were nothing but a few intuitively correct ideas called axioms. All the rest theorems were obtained through the process of logical deduction or induction; hence the pyramid of mathematics was constructed. As we follow the mind-steps of those great mathematicians and go up, we are constantly exposed to logical thinking and our minds are fine-tuned to be more logical. Due to the nature of math being most pure and theoretical, logic is more widely and rigorously used in math than in any other subjects. While attempting math problems, our logic skills are sharpened. Such skills can be transferred to all other subjects. Whenever a person wants to make an argument or assertion, he must at least explain the reason and justify himself, in which logic plays a pivotal role.

　　Math makes things simple.

　　It is always said that math language is a universal language. A Chinese may have difficulty understanding an article written in English. But mathematicians can understand each other’s works well. For one reason, math language is so simple that it is generally accepted and understood by mathematicians of all nations. Let’s look at this example. What is the sum of [twenty thousand five hundred and thirty-six] and [seven thousand one hundred and eighty-two]? Without resorting to math language, one need more than a few seconds to figure out the right answer. If it is translated into math language, one can almost tell the answer immediately. You can see how powerful these simple notations really are.

　　Great mathematicians are truly genius. Not only they discovered many theorems, but they also designed the simplest language that ever exists. While learning math, we are taught to cancel out common factors and combine like terms because the answer should be made as simple as possible. In math, we get used to simple notations that are without ambiguity. And we always try to reduce unfamiliar and complicated problems to familiar and simple cases. To be simple is no easy at all. It is from these simple symbols and notations that the most amazing formulae were discovered and great laws unveiled.

　　The greatest truths are the simplest. To be simple is to be wise.

　　Although not everyone can appreciate the beauty of math, everyone can benefit from learning math: to be meticulous, logical and simple. Take the subject of math seriously, you will be amply rewarded with a well-trained mind that are open and ready to embrace greater wisdom.

　　By 林飞扬

　　学习数学的体验，对我来说就是不停地了解和承认自己的天赋和智商不够用的过程。

　　我很早就大概了解，我并没有和表象的成绩相匹配的智商，也对自己的思维定势深有体会——比如，我曾经很坚定地觉得圆只有四条直径——所以每次沈老师掷地有声地叩问Are you a genius，我都会惭愧地低下头反省自己。当数学还只是中考的一门科目，而还没有成为我的追求时，我只需要被动地理解我需要理解的知识，因此智商一直够用，也对数学本身没有美学上的欣赏。

　　进了高中之后，我开始把数学定位成未来比较可能的专业方向。这个决定背后，是很模糊的几个原因的混合：这是我喜欢、可以称之为擅长的一门学科。我开始花更多的时间主动地接触数学，包括自学和写exploration。在这个过程中，我才对我的智商和时间的有限感到越来越沮丧。比如，在写exploration的时候我接触到极限的定义，但我不能触类旁通地迅速理解它在证明中的应用；又比如我对黑白棋、二十四点等桌游第一次上手的时候，常常逊色于同伴。我开始了解，有人，有很多人，能够一眼想通我冥思苦想而不得其解的问题。所谓超人并不是尼采形容的那样难得一见的事，而仅仅是概率和基数的产物。我花了很长时间适应这件事。由于周围人对女孩子将数学作为学习方向的质疑，加之来自生活的种种明示暗示，我也开始不断地问自己，我到底适不适合学数学，我为什么要学数学。与此同时，我也更加了解了正向回馈在学习过程中的作用：过去的成功和失败影响心理，而心理影响未来的成功和失败。

　　幸好数学本身能够给我以宽慰，不然，在正向回馈的匮乏和周围竞争者的压力下，也许我早就放弃了。对我来说，数学的知识是固体的、大块的、唇齿留香的，让我能够吃饱喝足，并且一直stay hungry的。因此，独自进食是快乐的，我就像一个孤独的美食家。

　　夏校的周五是research day，我们的任务是在结束时做一个十分钟的presentation，我选好了一本叫Markov Chains and Stopping Time的书，然而看不懂。我每周周五都坚持看，在最后一周，我终于了解了它的一小部分。这很了不起，因为刚开始的时候里面的很多符号都是我没见过的。写拓展论文时的文献也是这样，只要想懂，在知识允许的范围内的就一定可以懂，区别只在于花费的时间长短。

　　好消息是，现在玩二十四点我轻松许多，黑白棋也可以偶尔获胜，这无疑是多次训练造成的。我最感谢数学这门学科的一点就是，很多内容，懂了就是懂了，不懂就是不懂，所以无所谓和他人比，也没有天才或不天才之说。我逐渐尝试把他人从我的正向回馈中剥离，把我的愉悦和自信回归学科本身，回归自己的懂得。我现在所希望的，就是即使我不能通过学习成为超人，也可以成为一个“唯手熟尔的卖油翁”。

　　上海七宝德怀特高级中学

　　2017年4月18日

　　QDHS

　　上海七宝德怀特高级中学