What makes mathematics attractive ?

I think one of the interesting nature of mathematics is to find out same similarities between things.

Mathematics is a process from special to general and then from general to special. Say for example, when we write a simple arithmetic equation 1+2=3, in fact, its already a general concept of adding one entity and two entities together to yield three entities without explicitly state what is the entity.

Maybe before we have the equation, humans need to observe that one apple plus two apples yields three apples. One pen plus two pens equal three pens. So those are the special cases of the equation.

But usually after we have a generalization, when we need to apply it, then we will go back to the special case. Say if now we have one dollar, when other give you two dollars, then you know you with totally have three dollars -- thats again a special case.

So I think to be good in mathematics, you need to be sensitive about things. You need to observe and compare the similarities between the things, relationships or the rules. Then by guessing, you may have a hypothesis. And after logical proving, you will get the theory.

I think I really appreciate this process, as it involves your ability to analyse the things, your intuition and your logical mind. As usually when eventually it comes out the theory, it's precise and highly abstract, but it really summarise many logic behind within one statement.

Like you may familar with the following equation :

1³+2³+.....+n³ = (1+2+.....+n)²

Is it precise ? Simple ? True for all nature numbers ? And it hides the behind logic of proving say by mathematical induction.
 

What's the relation of math and my computer career ?

Thats a good question. To me, mathematics seems not really have direct impact to my computer career. As those differentiate equation, linear algebra, topology .... seems dosen't help much when I write a C program or a UNIX sheel script.

As when writing a program, I think we are looking for a method or a procedure that we may have already know or used in our human life, but just put it into the computer. So programmer is more like to implement a procedure or a process. While mathematics deal with logic proving that it depends much on observation, intuition and experience.

Yet, maybe one thing that mathematics really helps me. Since, mathematics really train up the analytical mind. In some sense, when writing a program, you also need to have the abstraction of things, say variables, which are generalization of some entities behind. For example, when you are asked to write a program to add up two numbers, then you may have something like :

read a, b;
print a+b

What is a and b ? Yes, they are the generalization of any two numbers. And you are manipulating the generalized entities, instead of explicitly adding two particular numbers.
 

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