The Meaning of Mathematics

Mathematics always has a lot of meaning. Between school and university, mathematics has different types/characteristics. In the university, we learn pure an applied mathematics. In the university, mathematics being the body of knowledge. Mathematics just in our mind.

There are two objects of mathematics:

1. Abstraction
2. Idealization

The word “abstraction” has different meaning with “abstrack”. Abstrack mean not concrete. But, if we can’t see or we can’t touch something, it’s called abstraction. Abstraction has a lot of characteristics, there are price, material, color, smell, etc. For example, the number of 5, has 1001 types. 5>5, 5<7,>

The second characteristics is idealization. We know that there is nothing perfect. Ex: there is nothing truly straight lines. There is nothing truly sharp angle, and etc. But we are always assume that the lines truly straight and the sharp angle truly sharp. And then, our assumptions make idealization.

The structure of mathematics build deductively, consist of definition, aksioma, theorema, lemma, formula, rule, and pattern, compose logicly can’t contradiction. The characteristics of mathematics are logic and consistent. Prof. Kayashteshi (Melbourne) deviding two characteristics of mathematics,to think, to predict and convince (communicate the result to the other person).

Prof. Katagiri (Japan) define that mathematics is thinking. He said that mathematics have 3 aspects:

1.Mathematical attitude

2.Mathematical metode

3.Mathematical content

Mathematical attitude mean always have a question, consistent, critical, and regard.

There are a lot of mathematical metodes:

§ Deduction (general to specific)

§ Induction

§ Incomplete induction

§ Silogism

§ Logic

§ Proof (direct/indirect proof)

The content of mathematics is that objects.

There is an action in Netherland called by Realistic Mathematics, in Indonesia it’s called by PMRI. This action deviding mathematics by horizontal (daily mathematics) and vertical (abstract, pure, that expanded at university).

The power of mathematics is critical thinking.So, if that thing was disappear, mathematics will be burn too.