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I sometimes spend inordinate amounts of time memorizing math articles or theorems/proofs or formulas. My question is "am I wasting time?" and will 'active thinking' or 'working out problems' be faster way to master mathematics?

I am absolutely a beginner. So at an apprentice stage sometimes I find that best way to grasp a subject is through verbatim scribing. Also, memorization seem to be my forte.

Mathematics is a language and just like when trying to learn the basics one has to memorize grammar, does the same theory apply in this field?

I used to browse MO, this website, wikipedia but since "mathematics is not a spectator sport" I imagine more fruitful way would to be to isolate small problems and work on it?

I am sorry if the question is very general.

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    I would say your time is better served doing lots of problems. As you keep doing them, you'll eventually remember what you need to remember.2011-11-26
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    What J.M. said. The point of Maths if you want to do anything with it beyond passing exams is that you would need to learn how to figure out it by yourself. The best bet would be to do lots of problems and a ton of problems. On memorization I find it's very helpful to write down stuff even if it's useless. Like if you are trying a problem just write down what coming into your mind.2011-11-26
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    Making notes while reading is still essential, it helps you remember what you learned (and you gotta remember something to be able to do practice problems). Part of your jot notes should be trying to come up with examples, or doing some calculations as you go along, or putting theorems in your own words, modifying a proof etc. (not verbatim)2011-11-26
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    Doing math is the best way to get good at math. But, I had a professor that said "Memorize every proof of a main theorem so that I could ask you ten years from now to reproduce it." Some proofs are so instructive, it is good to memorize.2011-11-26
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    @GottfriedLeibniz Making notes is sort of passive. Reminds me of people I see just copying the notes neater, which is good handwriting practice however I don't see how they are learning anything.2011-11-26
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    Thank you. I understand many famous mathematicians had near photographic memory or eidetic imagery (for instance Poincare as mentioned by E.T.Bell) but that does NOT conversely entail that good memorization skill is a requirement. But my question was because since I am a beginner, if I memorize concepts and carry them around with me, will not insight follow when I am relaxing?2011-11-26
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    @ZeeshanMahmud E.T. Bell makes a lot of crap up(stuff he wrote on Cantor was mostly garbage). Also that is bad reasoning. You can't just pick one Mathematician and then generalize from it. Erdos was autistic, it doesn't imply you need autism to be a famous Mathematician.2011-11-26
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    @simplicity: I met Erdős a number of times (no paper). I have known a couple of autistic people. Erdős was not. Singular, yes. But sociable, capable of having perfectly normal conversations.2011-11-26
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    I would say that one of the most important skills for mathematics is to learn *what* needs to be memorized...2011-11-26
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    I want to emphasize what J.M. said. Doing a problem and having that "Ah-HA!!!" moment, when you apply a theorem or use an important concept for the first time, will sear that new knowledge into your head. If you're *working* on memorizing something, you're probably just wasting time (or cramming for a test ;-) ). It's the difference between asking for someone's name and sitting down, introducing yourself, and getting to know them.2011-11-26
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    In my opinion, mathematics student should memorize minimum primitive information, because only this information are not based or linked to your previous knowledge, therefore if it remains unlinked, we tend to forget it. In every topic try to see the big picture, try to link issues. Only LINKED information can be stored for a prolong period. For more motivation take a look at a great series of posts by professor Santo D’Agostino [How much mathematics should a student memorize, part 1](http://qedinsight.wordpress.com/2011/02/02/how-much-mathematics-should-a-student-memorize/)2011-11-26
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    I find it next to impossible to answer this question in a useful way, because I have met both people who overestimated memorization and people who underestimated memorization. Some skills not only have to be memorized, they have to be automatized. Among students, there are those who think that it is enough to know that a differentiable function is "smooth" and those who would learn $1+1=2$ by memorizing "a vertical line, a cross, a vertical line and two parallel horizontal lines have to be followed by a squiggly line".2011-11-26
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    All mathematicians now a days just memorize the set theoretic axioms and any definitions from their field. Then, they will just derive the results they need and forget them when they don't. It is the most efficient in terms of brain space.2013-09-05
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    @ArturoMagidin: nice comment. Should be turned into an answer I think.2014-05-25

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