11 About My Blog

This is the blog that I want to convince people that mathematics is really useful for the human beings. I love this blog and my favorite posts in this blog are Haiku and Three Things That Make Me Happy .


Haiku is a type of Japanese poems. For Chinese, poems are very common and they are one of the most important part of the study of Chinese. I like this kind of poems. They are brief and beautiful in the way to express what we want, just like what mathematics does. We can convey a deep meaning by several words, it is really a cool work!


To share some things I like to others is interesting. I always hold the opinion that the simplest things can also bring happiness for us. If you pay more attention to the concrete daily life, you will find that, what we have possessed is enough. Hope you can enjoy the life and be happy.


10 Usefulness and Teaching of Math



When we consider the usefulness of mathematics, usually the first one we want to ask is the math teacher. Therefore, I had an interview to professor Zaher Hani in Georgia Tech, who researches and teaches partial differential equations (PDEs).


professor Zaher Hani (the left one) and me (the right one)

Professor Zaher was very kind and glad to help us and he answered all my questions. He told me that what the PDEs lessons teach are very fundamental facts for science and scientific developments. The theories from PDEs are useful in physical phenomena, such as wave, heat and flow, especially widely used in engineering. We can see that, PDEs are definitely useful and they do improve our life, by promoting the development of technology.


a visualisation of the solution to heat equation (in 2-dimension)


a visualisation of the solution to wave equation

Also, professor Zaher enjoys teaching PDEs. As a student in his lesson, I have a say. His PDEs lessons are extremely fascinating and easy to understand, which may be owned to his concrete examples and according to my another interview, this is also agreed by the most other students who attend this class. He said that students have to start thinking about deep concepts which are fun to discuss, and he also held the opinion that, in a way it takes him more time to prepare for this class, on the other hand it is much more interesting for him to teach this class.


professor Zaher is teaching

Thanks again for professor Zaher’s enthusiasm about my interview. He is a really nice teacher and feels pleasure to help others. He loves math, and he knows how useful it is. He enjoys teaching and discussing with students. I would like to say, those who want to be a math teacher in the future, such as me, can learn some things from him.

9 Recommend Terence Tao’s Blog

Click here to read the Tao’s Blog

I am Ling Dai and my blog is about mathematics and shares my thoughts about math. I want to recommend a blog which is written by the famous Terence Tao, and it was introduced to me by my teacher.

I like this blog for Tao’s creativity first of all. He shares his thoughts about some mathematical questions in the blog, which provides many creative ideas to help people to overcome the mathematical difficulties. Also, this blog covers lots of different branches and situations of math, such as the updating “Polymath Project” nowadays, differential systems, linear algebra and even information about scholarship of UCLA (where Tao works). Last, Tao uses Latex to design a nice typesetting, which looks really neat.


these neat formulas can be written on wordpress

 Frequently updating, neat typesetting and deep thoughts make it hard for me to dislike it. I would like to claim that this blog would be better if Tao can share some books about his posts, which helps reader to get into the topics.

In conclusion, I think Tao’s blog is typically helpful for anyone wants some deep understanding of mathematical questions. I can give it full marks!





8 Cartoons

dog math

There are two dogs talking about how many bones one of them have. It is a simple calculate, but it is funny that the question is about how many fingers left instead of how many bones left. When we learn addition and subtraction in primary school, we always use our fingers to do calculate. I like it because it is a funny cartoon which can be observed by almost everyone.

7 Music Review

That’s Mathematics

The singer, Tom Lehrer, was a retired American musician, singer, song-writer and mathematician. He showed his talent in music when he was a child. He entered Harvard College at the age of 15 and got the Bachelor of Art in mathematics from Harvard University. He taught math and music in many famous universities, such as MIT and UCSC. His music owned a style of parodying various forms of popular songs, and he also dealt with social and political issues of  the day in the 1960s. Black humor can be found in his early songs.

I want to talk about this “That’s Mathematics”. This was a song which made to celebrate that the proof of Fermat’s Last Theorem was finally finished by English mathematician Andrew Wiles in 1993. This is a simple and positive song. The lyrics are easy to understand because we can see many samples which we are familiar with. It does imply that how math is powerful in our daily life. For example,


counting sheep when you’re trying to sleep

Close-up of the scales of justice

being fair when there’s something to share


being neat when you’re folding a sheet




Counting sheep
When you’re trying to sleep
Being fair
When there’s something to share
Being neat
When you’re folding a sheet
That’s mathematics!

When a ball
Bounces off of a wall
When you cook
From a recipe book
When you know
How much money you owe
That’s mathematics!

How much gold can you hold in an elephant’s ear?
When it’s noon on the moon, then what time is it here?
If you could count for a year, would you get to infinity
Or somewhere in that vicinity?

When you choose
How much postage to use
When you know
What’s the chance it will snow
When you bet
And you end up in debt
Oh try as you may
You just can’t get away
From mathematics!

Andrew Wiles gently smiles
Does his thing, and voila!
Q.E.D., we agree
And we all shout hurrah!
As he confirms what Fermat
Jotted down in that margin
Which could’ve used some enlargin’

Tap your feet
Keepin’ time to a beat
Of a song
While you’re singing along
With the rest of the guys
Yes, try as you may
You just can’t get away
From mathematics!

6 Three Things That Make Me Happy

I’d like to share three things that make me happy. There is nothing different, and in fact, they are simple things which can be done by nearly everyone.

The first thing is that, the thought that I live in a peaceful and developed times makes me feel happy. It seems nothing to do with me but I always feel lucky when this thought appear in my mind.There are lots of great mathematicians died in war or from illness which can be cured easily nowadays. It is a long list, such as Archimedes died in the war and Niels Abel died for tuberculosis. Maybe it is not the best times because even now these questions are not be solved completely. However, people are trying and struggling for peace and medical devices, and we have made great progress. At least, most of us need not to fight for politics or out of someone’s desires, and medical level did improve a lot compared with years ago.


Archimedes died in the war


Niels Abel, jobless and poor in his whole life, died two days before he

received the letter informed he had been admitted as

a professor at the University of Berlin

Next, taking an afternoon off and studying math at cafe relaxes me most and makes me happy. I love afternoon because I can sleep for an hour (maybe too lazy but it is true) and I can still do something else when I wake up. Usually go to cafe and read something about math is my favorite activity. A cup of coffee, pens and pieces of paper, enjoy the most beautiful deduction by the simplest tools. What a lovely life!

1 2

Last, going for a walk after dinner is also one of things which I can get happiness most. The beautiful math always is natural. The deep thoughts usually come from the easy things. Go for a walk will not only take a rest of brain but also sometimes get inspirations from the other kinds objects. I learned this habit from David Hilbert ( the greatest mathematicians in 20th century). Anyway, I found it did work for I could sometimes change my perspective to solve questions which might be right way to do this. Though it usually could not help to solve problems, take a walk after dinner is also a good habit for health.


Einstein and Gödel took a daily walk in Princeton

As you can see, the simple things can make me feel happy. I am proud of this: although I am not the greatest mathematician, I feel confident to be the most positive man in the mathematical world. I believe that this could the fourth thing that I’d like to share, which makes me happy.



5 This I Believe

I believe that mathematics is more than a tool to be applied to physics or physical problems.

For the people who get into the natural science or engineering, math is one of the subjects that they must learn. We all think that math provides a lot of help indeed, and also these subjects offer many interesting questions for mathematicians, which push an actuation in the way to develop math. However, from my perspective, math is much more than a tool to do this. It is an independent system which is also tightly associated with the other kinds of science and technology.

I’d like to talk about some history of calculus. Normally, Isaac Newton is the first name that comes to our mind when we talk about this. But if I mention Weierstrass, then I believe you probably have never heard of this name unless you have tried to get into mathematical analysis. In fact, Weierstrass is one of the mathematicians who reach the  true accuracy of calculus. The definition of limitation, which is one of the most important definitions, was invented by Weierstrass.


Isaac Newton


 the famous Weierstrass Function

To establish the accuracy of calculus is a long and interesting process, which started when it was invented by Newton and Leibniz, with the efforts of lots of famous mathematicians, such as Euler and Lagrange, finally ended by Weierstrass, Cauchy, Dedekind, and some others, and took about one and a half centuries to finish it.

I am not going to discuss some details about this process, instead, I decide to talk more about the motivation of this process. Why did people still want an accurate system when they were master of the tools of calculus? What is the purpose of the further research if the physical tools is known?

In my opinion, technology is above tools. I think this is the key purpose of this process: we can find more tools by establish accurate basis of calculus. When everything is clear, new tools in the same field will be found. This is the reason why mathematicians keep in finding the “useless” theory: only the basis are stable enough can we build a tall and majestic building. Also, the further research appeared in the later years, such as differential equations, complex analysis, real analysis and other subjects, which stood on the accurate calculus, showed great efficacy of the physical examples.


by Newton’s law of universal gravitation, the orbits of the solar system can be                                                 accurately donated by the differential equations

We should admit that math is more than a tool. Some basic research in math, which seems with nothing to do with the physical society, may become the first step of the future knowledge.

What is your opinion about math? Is it just a tool for you? Leave your ideas in the comments please.