Mathematics Thinking and scientific work

The definition of Mathematics from some lecture:
•mathematics is problem solving
•mathematics is investigation
•mathematics is creation
•mathematics mean of communication
pure mathematics is formal mathematics. The characteristic of formal mathematics is axiomatic, axiomatic mathematics different mathematic.
There are some definition of deduction mathematics is concept, definition, theorem, proof, axiom, procedure to proof theorem.
To starting point mathematics is system we should have assumes. The assumes can be a concept or definition of formal mathematics. The formal mathematics have base axiom, theorem and definition. Before definition you have clear picture or concept of object mathematics. Object mathematics can be your main or idea from the possibility object meta mathematics.
How to get mathematics object from the object concert:
1.idealism
idealism is assume that something is perfect, but perfect is God’s. We assume that something is sharp, but truly there is nothing which is sharp perfectly. We assume that line is straight. But truly there isn’t a perfect straight line.
2.Abstraction
A concert object have a lot of characteristic. In mathematics we just learn a few of the characteristic. Let : to learn about plane, we just learn about the shape and the size, to learn number, we just learn about the value. Mathematics is easy because just learn a few of the characteristic.


- Characteristic of mathematic thinking
1.Consistent
same with the first formula
2.Logic
We can know about the difference of big and small, relationship, mathematic separation or arithmetic, if than statement, the table of proof, how to get conclusion (premise), thesis, antithesis, hypothesis, let, etc.
- Scientific work
Example: report, proposal, text book, etc.
The characteristic of scientific work:
1.objective
2.have criteria or standard.

The characteristic paper:
1.abstract
2.recommendation
3.free from plagiarism
4.reference