How I view theorems on Mathematics.
Consider a sculptor who is building a statue ,you didn't know where did he start and how did he proceed step by step and suddenly it will come into a full fledged shape that will kindle a suprise shock inside your mind when did he finish and how did he got that shape.
For me ,theorems are just like that where theorem is the statue and sculptor is the mathematician.
Mathematics and oops
Object-oriented programming is considered as as the dominant programming methodology for years.But how I consider it as follows.
"Generally if you ask any csc fellow about classes and objects,what he will say as follows.
classes are the templates from which objects are derived and each object is different from another one and also they will give a classic example such as car in order to explain oops concept.They will say that oops is an programming abstraction like in a car if you want to stop a car ,you will just put a brake for that you don't need to know what is going on the backend.
Theorems are seen by people just like that .But in order to understand the elegant structure of it ,you have to dive into the theorem in more depth then only you will realize that it is like a fractal which can't be realized until you go deep inside.
I will conclude by saying that for me class is like an graph say eqn
x2 + 2x+8=0
where objects are nothing but an value at a point ,for each no you will get an distinct graph at that point.
Also as I said Programming(specifically ooops) is an abstraction where the user just calling the method without awaring of backend process where excellent mathematical structure is going on.
And one more excellent point which I want to mention is that
how programming and theorem are organised
But before that it is good to metion what is meant by a theorem from wikipedia for you
"In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms. The derivation of a theorem is often interpreted as a proof of the truth of the resulting expression, but different deductive systems can yield other interpretations, depending on the meanings of the derivation rules. Theorems have two components, called the hypotheses and the conclusions. The proof of a mathematical theorem is a logical argument demonstrating that the conclusions are a necessary consequence of the hypotheses, in the sense that if the hypotheses are true then the conclusions must also be true, without any further assumptions. The concept of a theorem is therefore fundamentally deductive, in contrast to the notion of a scientific theory, which is empirical."
so in order to prove a new theorem you can use previously accepted theorems or definitions .Mathematics is constructed like that.
In a similar fashion in programming ,the programmer use a concept something called code reusability what is meant by that ,in order to achieve a specific goal they will use a previously constructed modules from some other programs which may help to achieve their goal.
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Consider a sculptor who is building a statue ,you didn't know where did he start and how did he proceed step by step and suddenly it will come into a full fledged shape that will kindle a suprise shock inside your mind when did he finish and how did he got that shape.
For me ,theorems are just like that where theorem is the statue and sculptor is the mathematician.
Mathematics and oops
Object-oriented programming is considered as as the dominant programming methodology for years.But how I consider it as follows.
"Generally if you ask any csc fellow about classes and objects,what he will say as follows.
classes are the templates from which objects are derived and each object is different from another one and also they will give a classic example such as car in order to explain oops concept.They will say that oops is an programming abstraction like in a car if you want to stop a car ,you will just put a brake for that you don't need to know what is going on the backend.
Theorems are seen by people just like that .But in order to understand the elegant structure of it ,you have to dive into the theorem in more depth then only you will realize that it is like a fractal which can't be realized until you go deep inside.
I will conclude by saying that for me class is like an graph say eqn
x2 + 2x+8=0
where objects are nothing but an value at a point ,for each no you will get an distinct graph at that point.
Also as I said Programming(specifically ooops) is an abstraction where the user just calling the method without awaring of backend process where excellent mathematical structure is going on.
And one more excellent point which I want to mention is that
how programming and theorem are organised
But before that it is good to metion what is meant by a theorem from wikipedia for you
"In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms. The derivation of a theorem is often interpreted as a proof of the truth of the resulting expression, but different deductive systems can yield other interpretations, depending on the meanings of the derivation rules. Theorems have two components, called the hypotheses and the conclusions. The proof of a mathematical theorem is a logical argument demonstrating that the conclusions are a necessary consequence of the hypotheses, in the sense that if the hypotheses are true then the conclusions must also be true, without any further assumptions. The concept of a theorem is therefore fundamentally deductive, in contrast to the notion of a scientific theory, which is empirical."
so in order to prove a new theorem you can use previously accepted theorems or definitions .Mathematics is constructed like that.
In a similar fashion in programming ,the programmer use a concept something called code reusability what is meant by that ,in order to achieve a specific goal they will use a previously constructed modules from some other programs which may help to achieve their goal.
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