Mathematical Thinking and Scientific Work

Mathematical can’t liberate from problem solving and number as mean of communication. Everyone can descriptive what about mathematics and also mathematicians have different definition about mathematics. Different mathematician said that mathematics is a science of axiomatic thinking established with deductive method consisting of definition, theorem, axiom, role, etc.

We usually have assumption when we solve some mathematics problem. It’s a concept or definition by theory and also it can built system of mathematics. We need a clear people as an object of mathematics. An object of mathematics must be clear. For examples are pen, paper, table, necktie, etc.

We can say that object of mathematics is our idea, because all of thing in our mind. An object of mathematics is Meta mathematics that is thinking about mathematics.

Two ways to get an object of mathematics (concrete thing) that is
1. Use idealization method
There are someone said that idealization method is assumption to get absolutely. Assumption all of thing is perfect. We put example a flat plane, no things in the world is really as a flat plane. Some examples for concrete thing that is she is a beautiful girl form of thing, size of thing, in the reality there are more than million characteristic of something. So, we know that object of mathematics not all can be touched, but the characteristic absolutely because it is only use an assumption.
2. Abstraction
In abstraction we only use a characteristic.
Just to learn a certain characteristic

 Thinking about mathematics must consistent.
Agree with first agreement reached that is the definition.
If a proof not consistent, the statement will be wrong.

 Mathematical logic
In mathematical logic catch with everything, we can difference easily which is small which is bigger, which is prime number which is perfect number, etc. For example six less than seven based the number but if we write number six bigger than number of seven, it will be six bigger than seven. If there are some random number that is eleven, four, seven it’s can be write in a series. We may write the first is four the second is seven and the third is eleven. In reality of mathematics that is relation. We can put for example that is what is the relation of nineteen and twenty seven? We can answer the question, nineteen plus eight is twenty seven or twenty seven minus eight is nineteen.
And also about relationship two sets. If there are two sets A and B, is it a relationship?
 Mathematical Operation
In mathematical operation usually use arithmetic that is addition, subtract, multiplication, and division. The statement is logic if the statement can be proofed. For example eleven plus nine is twenty. The other is radix, square root, square, power, exponent, etc.

 True or False Statement
We can know mathematics sentence, we can use the truth table. It is learned of logic of mathematics. The function is conjunction, disjunction, implication, and double implication. There is conclusion from the premise. For example the first premise if you are student of university then the second premise the next week go to campus so the conclusion from the premise is You are go to campus.

Thesis is sentence show truth.
For example is seven is odd number and also prime number.
Antithesis is opposite thesis.
For example seven is not odd number.
Hypothesis is not permanent assumption.
For example x, we can’t know x odd number or even number. The equipment is presumption.

Scientific work has some characteristics,
1. Impersonal
Not relation with personal.
Personal, for example is say OK, good luck
2. Have a standard or criteria
Scientific work must get a standard because it’s fixed work.
3. Objective
The reference is got by text book, proposal, or depend on.