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The title says it all. I often heard people say something like memory is unimportant in doing mathematics. However, when I tried to solve mathematical problems, I often used known theorems whose proofs I forgot.

EDIT Some of you may think that using theorems whose proofs one has forgotten does not seem to support importance of memory. My point is that it is not only useful, but often necessary to remember theorems(not their proofs) to solve mathematical problems. For example, you can't solve many problems of finite groups without using Sylow's theorem.

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    Yes, it is very important...but not in the same sense, imo, as it serves to recite all the spanish and english kings in the last 1,500 years. One needs to *remember* theorems, definitions, etc. in order to do mathematics and to advance with it, since otherwise we couldn't know, or remember, what's needed to do this or that. For example, it would be crippling mathematicswise not to remember what a function is, or what is $\,4\cdot 7\,$...2012-11-17
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    One can substitute lack of memory by other skills to some degree, but remembering stuff is of course important. How do you understand something if you don't rmember the definitions of the terms involved?2012-11-17
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    @DonAntonio, I don't know what $4\cdot 7$ is, honestly. I do know that $2\cdot7$ is $14$, from childhood, and then I double that. *Every single time*. I hope you are wrong!2012-11-17
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    Memory isn't something you have or don't have; there are meta-cognitive strategies and techniques one can use to enhance one's ability to recall information, when needed.2012-11-17
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    Bad, bad boy @MarianoSuárez-Alvarez. A mí todavía me tocó estudiar las tablas de multiplicar de memoria, hasta la del $\,10\,$ . I hope you're not having problems with more advanced stuff, like $\,9\cdot 6\,$ or $\,1/2 + 1/5\,$, say.2012-11-17
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    Some problems in Math. heavily rely on observing patterns. I assume that you need good memory to relate patterns and recognize them when you encounter them. You definitely need good memory to get good grades too!2012-11-17
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    @amWhy, I am cringing at "meta-cognitive" but I am curious what strategies you have in mind? Practicing log-space arithmetic algorithms is something I've personally considered. :)2012-11-17
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    @Dan I once read somewhere that world champions in competitive memory all used mnemonic devices in memorizing such as [the method of loci](http://en.wikipedia.org/wiki/Method_of_loci). I believe amWhy may be referring to such techniques. I'm curious, what's log-space arithmetic?2012-11-17
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    @EuYu, please see the answers to my question http://math.stackexchange.com/questions/75655/is-there-a-log-space-algorithm-for-divisibility2012-11-17
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    A true Platonist will have a definite answer on this question. He would argue that anything we learn is in fact remembered i.e. something we have already "seen" or "memorized". He would hence conclude that memory is not only important for doing mathematics, it is ***the only thing needed*** for mathematics.2012-11-17
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    Makato I think you "struck oil" with this question, as it seems to have struck a chord with many of us! Thanks for asking it here!2012-11-17
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    @MarianoSuárez-Alvarez I think you prove a point. Even tough DonAntonio is right and not remembering that 4 * 7 is 28 might slow you down in doing that kind of math, for more complex problems it seems that remembering the final answer is less important than the road to get there. Because roads are 'adaptable': I can calculate 6*7 and 8*7 with only memorizing two rules: " 2*7 = 14 " and " For any number divisible by two, I can add the amount of times it is divisible times the outcome of 2 * ? together to get a correct result" .2012-11-17
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    @amWhy I'm being surprised. You are welcome.2012-11-17
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    Makato: and no downvotes on your question, either! (Someone downvoted my answer, but that's irrelevant).2012-11-17
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    Hmm, I would like to argue that we could still go around finite-groups without Sylow theorems, just replacing by the class-euations of actions, as elementary as possible. Indeed, the three theorems of Sylow are proved directly by means of the class-equaitons.2013-02-11
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    Your question would be much better off if it distinguished short-term memory and long-term memory, as these are very different and their impact on a life of a mathematician must be considered separately.2013-11-25

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