What do you think about mathematics? What is the real mathematics?

School mathematics and university mathematics are different. At school, we study a pure math, but at university we not only study a pure mathematics but also applied mathematics.

There are many definition of Mathematics. Mathematic is a science and truth. Mathematic is the body of knowledge. And mathematic just lies in mind. Mathematics do not need a concrete things because the mathematics objects are abstract.

There are two ways to get the mathematics objects, there are:

1. Use a technical abstraction ---> not a shape

For the example: if we think about 5 (five), there are many characteristic in five. But in mathematics, we think about the value of "five".

2. Use a technical idealism ---> assumptions

Prof. C. Stacy from Melbourne University said there are two step in mathematics, they are:

1. Conjure ---> to think and to predict.

2. Convince ---> to communicate the result to the other people.

Prof. Katagiri from Japan said there are three aspects in mathematics, they are:

1. Mathematical Thinking

2. Idealization

3. Analogy

There are two mathematics process in Realistic Mathematics, they are:

1. Mathematics Horizontal ---> process from the real life to the mathematics symbol.

2. Mathematics Vertical ---> systems of the mathematics.