MATHEMATICAL THINKING AND SCIENTIFIC WORK

MATHEMATICAL THINKING AND SCIENTIFIC WORK

Mathematics is divided into two categories. They are applied mathematics and pure mathematics. Applied mathematics is about mathematics and the application in our daily life. While pure mathematics is related to prove or find new theorems in Mathematics.
Thinking about Mathematics, we have an object here that is our idea. It is an abstract object that can not be touched and seen with our eyes. It is just can be found in our mind because we have ourselves idea. And in fact, our ideas can be different than others. While in our daily life, we have some concrete object. There are two ways to get some ideas from concrete object:
1. Idealization

It means that we should assume that something is perfect. In fact, there is no pointed thing in this world because everything consists of molecules and atoms which has rounded shape. So, even we say that needle is pointed, in fact it does not.
But to think in Mathematics, we have to assume something is perfect. To know whether an angel of a triangle is cute or obtuse, we have to assume that cute is really pointed so that we could count the size of an angel.

2. Abstraction

It means that we have to learn some theorems. I wonder when learning History of Mathematics in my last semester because long time ago, in the age that we usually call it as an ancient age. But in fact, there were so many mathematicians that found so many theorems with its proof. Even, they were smarter than mathematicians today. Look around! If we are asked to proof a theorem, we know that it is very difficult. While, the mathematicians long time ago could find many theorems and prove it. What ashamed!
In Mathematical thinking, there are some aspects that could affect it:
a. Consistence

In doing any mathematics problems, we have to be consistence. It will always accord to the beginning rules. If there is a mistake, it will not be used again forever. It teaches us that we have to be the one who always consistence. In doing our principles of our life or our mission or agreeing some promises.

b. Logic

It is included daily logic and formal logic. In our daily life, there will be always some relationships between mathematics operations and our life’s problem. We can use our logic to get some conclusions. In Yogyakarta State University, there is a lesson “Logika dan Himpunan Matematika” for Mathematics Education which can make us easier to get some conclusions. And it gives us a ‘training’ to use our logic in solving many problems in our life.

3. Thesis and antithesis

In a Physics rule, if there is an action, there will be a reaction. If there is a thesis, there will always be a antithesis.

The further action after Mathematical thinking is scientific work. We can make scientific work based on:

1. Characteristic

Scientific work has its own characteristic. Its characteristic can show the quality of the scientific work.
2. Impersonal

What means by impersonal is not related to any problems that we have (our feeling or our emotion) in doing scientific work. If we make some questions for a test, for example, we must not include our feeling in the statement there. Because it will be disturb the scientific work itself.
3. Standard

To have a good quality, scientific work must have a standard. It is not only about the quantity of scientific work that we did but also the quality is more important.