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I am, at best, a novice mathematician. I started teaching myself the subject while writing my thesis in computer science. I find that I have a strong urge to prove every relationship or formula that I come across while studying. I routinely find it hard to accept or understand a relationship that I cannot prove and often go to great lengths to do so. Is this practice normal or recommended or otherwise?

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I face the same problem sometimes, and I think the short answer (and I have learned this the hard way) is that it is not practical to try and prove every statement you come across. For example, I used to have the habit of trying to prove most propositions in a book on my own. While this is not a bad habit, it would often take me very long to finish even a single chapter of the book. And, of course, some of the propositions just had complicated or ingenious proofs. So, as a college student, always running low on time, this is an impractical practice during the semester. –  Rankeya Nov 3 '11 at 3:17
I still try to do this over the summer, when things are more relaxed. But, either way, you just don't end up learning enough math at a reasonable rate this way. –  Rankeya Nov 3 '11 at 3:18
But, may be you mean just those question of which you do not see proofs. So, in that case, if the statement is not immediately obvious, then yes, it is a good practice to pause and prove the statement or try to prove it on your own. But, then you don't have to write it all out in gory detail right? You can just note down the gist of the argument for future reference. –  Rankeya Nov 3 '11 at 3:24
Inside all mathematicians lies the hopeless romantic who wishes they could do this, but unfortunately it is highly impractical, and only the most brilliant minds have a chance of getting very far with it. –  Ragib Zaman Nov 3 '11 at 5:26
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up vote 3 down vote accepted

It is very highly recommended. Although when you begin doing things it is sometimes more fruitful to simply gaze at some ideas and accept them to let blossom more amazing ideas, at some point you just gotta start thinking and that is where foundation becomes important. It will never hurt you to start making some rigor go into your mind, as long as it does not stop it from finding new ideas. I believe that it takes much, much work to have both rigor and intuition, but that is the price to pay, because it's the best thing to do. Simply focusing on rigor won't get you anywhere though ; proving things is one thing, understanding why they're true is another.

Hope that helps,

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