Mathematical Thinking and Scientific Work

This whole article will explain about the correlation from mathematical thinking and scientific work. Mathematical thinking is thinking by consistent and always paying attention about the principle and the procedure when we solve some problems especially in mathematics. And if we do a fault or a step that it is not consistent with the assumptions, so the whole procedure is failed. As we know that mathematics consists of two ways which are pure mathematics and applied mathematics.
The school mathematics is the mathematics that learned in some grades of school, for example mathematics for junior high school or may be mathematics in senior high school. In this case, the school mathematics as the teacher’s task to explain to the student is having a pattern, solving problems, having some investigations of formulas, and also has the mathematics communications. And then the pure mathematics is sometimes interpreted by formal mathematics, and the characteristic of formal mathematics that is axiomatic mathematics. In formal mathematics sometimes each mathematicians are having a different thinking about mathematics too.
Mathematics established by deductive method consist that method itself, the definitions, some theorems, the axioms, rules, and procedure to proof, and etc. And then our first question is how to start establish mathematics as a system?
First we should have an assumption. Usually assumption is a concept of definition. All people can establish mathematics if they have a strong ground in mathematics, but to make we have a strong ground in mathematics is not too simple. So it is our tasks to always improve our ability in mathematics by always develop the mathematical thinking. To make the strong foundation in mathematics we also must paying attention with the definitions, the axioms, rules, and the procedure.
Second we must know the object of mathematics. And the object is your own idea in your mind. And then the second problem is how to get mathematical object? We can get it from the whole thing in the world, but be careful because some things in the world just being the example not the really object in mathematics. So, the examples of example in mathematics are maybe paper, pen chair, pyramid, and etc. The most difficult problem in here is how to make the example in mathematics being the object of mathematics? And it is what that did by Meta mathematics or thinking about mathematics. To make it can be the real object there are two ways.
The characteristics of real object are can be touched or can be tasted by us. And difference of real object and the mathematical object is mathematical object is abstract object, it can not be touched and can not be tasted, we can not manipulate it with sensory tools.
To make it can be the real object there are two ways. The first way is the idealization method. Idealization method is the method that we must always think the object is perfect because in mathematics sometimes we need the perfect object, for example the line that absolutely straight, the circle that absolutely circle, absolutely plane, and etc. The second way is by abstraction method. The abstraction method is just learning the one or some characteristics from all of characteristics that owned by that real object. For example the characteristics of a paper are it is light, flimsy, maybe the color is white and etc. But in mathematics we just learn the shape and the size of that paper. We just concern with the shape, for example it is rectangular paper, it is circle, it is triangular paper and etc. Well, the next characteristic that used in mathematics is size because in mathematics we just use the size or the value of something real. So the most important characteristics in abstraction method are the shape and the size.
Mathematical thinking is thinking by consistent and always according the early agreement. Consistent is always holding the principles of procedure. If we make a step that it is not consistent with the agreement, so the whole procedure is failed. And then mathematical thinking is always thinking by logic. Logic is consisting of two parts; they are daily logic and formal logic. Logical mathematics used very large in the world, for example comparison (seven more than four, and three less than ten, etc). The essential thing in logical mathematics is relationship, for example is nine equal ten minus one, four is three plus one, twenty five is five square, and etc. Mathematics operations are arithmetic operation for example addition, subtraction, to the power, square root, the radix, and etc. In mathematics we also must know about the “if then statement”. “If then statement” is usually write in if a then b, and the ‘a’ and ‘b’ are some simple statements or prepositions in mathematics. The sentence in mathematics can be the close sentence and open sentence. We also can see the truth table to understand what the relations of those statements are.
The table of truth is like that shown below:
If a is true and b is true, so a or b is true, a and b is true.
If a is true and b is false, so a or b is true, a and b is false.
If a is false and b is true, so a or b is true, a and b is false.
If a is false and b is false, so a or b is false, a and b is false.
How to get conclusion of some sentences? We must have some premises; mega premise (major premise), or minor premises.
In a procedure or to get the conclusion of some sentences sometimes we also find the antithesis, thesis, and hypothesis. The thesis in mathematics is a sentence that showing the truth, and then the antithesis is sentence that it becoming the contradiction sentence from the thesis. The hypothesis is a temporary assumption to make we can solve the mathematical problems by easier. And to proof the hypothesis we need the tool called conjecture.


The relationship between mathematical thinking and scientific work
Before we talk about the relationship between the mathematical thinking and scientific work, it can be wiser if we know that the scientific work has some special characters. Those characters are:
First, scientific work is impersonal work or it not related with personality or the maker. It not too much and it fulfilling standard definition, and also it is clear enough to can be able read by all people.
Second, scientific work has the standard of criteria; it can be just for local consumption, national, or maybe international standard. It also fulfilling the writing rule and it must become objective work.
The examples of scientific work are a report, paper, proposal, note, text book or presentation and etc. For scientific paper is consisting of abstractions, an introduction, and the background, discussion, conclusion, recommendation, ways of head, and preference. And also it must fulfill the ethical code that is far away from plagiarism and we must mention the sources and the references.
So, the relation of mathematical thinking and the scientific work is, if a mathematician makes some researches, and it proofed true, it can become the scientific work too. Because in the fact mathematics also as a science knowledge. And it can be used to all people to make them richer with new knowledge in mathematics. And we must always believe that if we want to be a good mathematician, please do not always want the other people helps us in mathematics, but we must think that mathematics is us and just we and ourselves that can make we become the good mathematician like what Mr. Marsigit said.

It is the end of this sixth article in my blog, I wish it is good for us and we can use it by maximal.
Regards…