How to self study mathematics for the sake of the subject?

[tuxscholar]

Hello all the intellectuals! how to learn mathematics utterly on your own in a very profound manner like the way mathematicians do also you can share the way you study it. I've graduated from high secondary school several years ago but at that time I've study Math only for acquiring good grades and it resulted nothing. But now I'm thoroughly interested in learning this subject like i want to know what mathematician deal with this subjects and why there are so many prestigious awards exists in mathematics e.g. Abel prize, Fields Medals etc. and why Mathematics seems to be a very special subject. But so far I've got a lot of eBooks to read pertains to different subject and I've read some of them but after some time I've find the majority of what I've learn very tedious to think about or things which seems to be very abstact up to the point of incomprehension, still I've want to have a very decent understanding to this particular subject because even after I know very little about this subject and mistakenly developed a notion that this subject is nothing but endless manipulation of symbols and memorizing of formula which otherwise will take forever to create on your own, I still always fantasizes that I'll become a mathematician or it will be intensely intellectually rewarding subject to learn and master, and also this subject seems to be a cheapest science you can learn or do (like you only need a pencil and a paper) and it can make your mind significantly engaged and it is mentaly healthy exercise for your mind. So what approach i should have to learn this subject consistently without loosing direction.

 

[fresh_42]

A list of several articles about "how-to-self-study-..." I once gathered and posted is here:
https://www.physicsforums.com/threads/self-teaching-gcse-and-a-level-maths.933639/#post-5896947

You could also surf the various insight articles we have about certain subjects, but that's more like an aperitif than an e-book. Here are some hints on how to use the internet effectively:
https://www.physicsforums.com/threads/how-to-use-the-w-in-www.1062388/

I would concentrate on a certain field you want to learn and start from there.

 

[martinbn]

There is a book by Richard Courant and Herbert Robbins called "What is Mathematics?: An Elementary Approach to Ideas and Methods".

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[sbrothy]

I know this is not a new post, but I've wondered the same. The conclusion I reached is that it requires an extreme amount of discipline to solve problem after problem to become aquinted with "nature's language" so to speak. Learning mathematics is like learning to ice skate or play the guitar. It's not exactly a question of training your so-called muscle-memory, but I think it's a closely related phenomenon.

I've found this book helpful understanding: Enchanted Looms: Conscious Networks in Brains and Computers.