I start learning mathematics in 2017, when I realize mathematics as trivial and obvious ideas, at that time it wasn’t clear for me what mathematics will give me, and makes me different in the following years.
First, mathematics made me somehow more imaginary guy, a guy who can “see” the solution, who can just by looking to a symbol understands the meaning behind it, and what is really going on under the hood. It makes me feel like I see what others don’t see, and understands relations between things seems unrelatable.
Secondly, in mathematics we create systems, we study things in a very abstract way, in a way that gives us the ability to understands and know every detail. At an early stage in my learning journey I wasn’t a details-oriented guy and I never been before, but now I care and found my self reply to my professors: “in which system you are talking? and did you define things precisely? – this is not a complete proof..etc”, I start to realize that mathematics is more about how much do you know about the subject than anything else, and like what Terence Tao once said:
“the devil is in the details in mathematics.”
Thirdly, I start reading many mathematical books in different subjects, that’s learning process makes me know how to deal with different mentality since each topic has his own mentality and each mathematician has his way of treating that subject, all mathematicians talking about the same subject, but each one have his own vision and his own way of thinking, and that comes from their different environments and their different personality, even some mathematician when they grow up they develop a very different vision for the same subject – and that’s learning in mathematics!
Fourthly, mathematics is “Freedom” at its heart, freedom in thinking, writing, treating, doing, and explaining your self through your developed ideas. You cannot be a good mathematician if you stay in that “standards” of thinking and doing. Mathematics learns me how to be more peaceful with things I’m not sure about, things that I could be wrong about it, and all of that comes from that freedom.. since that freedom stands on “proofs”.
Fifthly, there are many approaches to deal with problems, and always when you facing a hard problem, first look at its heart, and what are the tools you have and are these tools enough to solve your problem? many times, No. Then, you need to search for tools in your memory, in your life, in a book, in a research paper, just for a tool that you can apply it to solve that problem. In many fields in mathematics, we facing something like:”Algebraic Geometry”,”Topological Algebra”,”Algebraic Number Theory”, all of these fields comes since we don’t know how to solve a very very simple problem, many theorems we can’t prove it using an elementary tool, so we have to develop tools that give us that ability to solve. I see mathematics as the leader of the human evolution in dealing with this world, since we develop tools that everybody uses it after us.
Sixthly, it maybe something far from mathematics, but it’s related to it. Mathematics gives me the ability to learn quickly and learn other things faster than before. Why? and how?, I think -and this is a personal opinion- the reason is that mathematics is an abstract language, a language that anyone can talk it, so when you dealing with that language many times, your mind starts to see things in an abstracted way, so you can understand things at its heart in a very fast way. For example, when you dealing with Computer, if you are a mathematician you can see every movement you do on the screen as a “Function”, everything on the screen as a “repeated small squares”(which is Pixels), Videos, Images as “Geometrical Shapes”(Which is large set of Pixels), Networks and Devices as “Graph/Vertices/Edges”, and so on. you see things in a very different way, and that give’s you the ability to be a quick learner.
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