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I have always been good at math but even I struggle with visualizing numbers in my head. I am seeking help on this forum to see if any mathematicians here have experienced the same issue I currently have and overcame this problem. If someone where to recite "794 times 869" I struggle to retain the numbers pitch perfect in my head as I perform the calculations.

Are there any exercises one could perform to improve his/her visual retention of objects and numbers in their heads?

Can you hold the number 7859385 in your head for an extended period without the image of the number becoming distorted at any point?

Or is it that am I just plain stupid and there is no hope of improving visual retention??

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    $\begingroup$ I know this doesn't answer your question, but it's better to retain the underlying principles in your head rather than specific examples of numbers. Plus, isn't the key to mental calculations just rote algorithms? $\endgroup$
    – AnonSubmitter85
    Aug 30, 2013 at 19:51
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    $\begingroup$ I thought it might might better fit at cogsci.stackexchange.com, but you've already cross posted it: cogsci.stackexchange.com/q/4461/370 $\endgroup$
    – draks ...
    Aug 30, 2013 at 20:48
  • $\begingroup$ When given $794\times869$ you may first calculate an estimate $800\times850$, and note how far away $794$ is from $800$ and $869$ is from $850$. If I have to memorize a long string of digits, I imagine the process of typing it in a numberpad. I can retain the shapes on this mental numberpad (like the L-shape 785) longer than I can retain the string of digits. $\endgroup$
    – Karl Kroningfeld
    Aug 30, 2013 at 21:12
  • $\begingroup$ If you just want to memorize a string of digits, you could try translating it into natural language. This is how people are able to memorize several decks of cards. Something along the line of a $1$ being a place, $2$ an adverb, $3$ a color, $4$ an article, etc. This way a number like $8623813\dots$ becomes a story rather than a number. It would take some thought to derive a robust translation (e.g., how to handle two nouns in a row), but it could be done. $\endgroup$
    – AnonSubmitter85
    Aug 30, 2013 at 21:35
  • $\begingroup$ See here for a complete description of a method to memorize numbers. $\endgroup$
    – AnonSubmitter85
    Aug 30, 2013 at 21:41

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If you want to begin solving real math problems in your head, I think you would enjoy reading Lewis Carroll's "The Mathematical Recreations of Lewis Carroll: Pillow Problems and a Tangled Tale (Dover Recreational Math)".

These are math problems that he thought up and solved while lying in bed. It has inspired me to do similar things. One thing it has inspired me to do is to never write down any of my solutions to problems herebefore entering them; instead, I work them out as I enter them.

You can find it here: http://www.amazon.com/The-Mathematical-Recreations-Lewis-Carroll/dp/0486204936

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