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It turns out that my adolescent son might have numeric synaesthesia-- numbers have specific colors and possibly other distinguishing characteristics for him. He has shown that he can commit long sequences of numbers to memory, apparently by breaking them into three-digit chunks and then just forming a visual memory of them.

First question: sure this helps him recall numbers, but it also means there is a bit of irrelevant information attached to each number he encounters, and that could be confusing or distracting while learning math (e.g. two numbers "clash" so the answer feels wrong even though it isn't). Does anybody have any advice for me or him on good practices, on problems to be alert for, etc.?

Second question (a fun one): can anybody think of practical/entertaining things he can do with the ability to recall long strings of numbers?

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I don't know that this forum is the place to ask your first question. I suspect there may be forums available for parents with children who have numeric synaesthesia; though you might want to consult an educational psychologist for advice on this. For your second question, that is perhaps appropriate here: it would seem that your son might do quite well with combinatorics, or perhaps more so, problems involving numeric sequences. –  amWhy Nov 5 '12 at 15:32
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If you have not already, then I would suggest watching the documentary about Daniel Tammet. –  EuYu Nov 5 '12 at 16:23
    
Born on a Blue Day is an amazing book! –  Sniper Clown Nov 5 '12 at 19:21

2 Answers 2

(1) For your first question, perhaps start at Wikipedia - if for no other reasons that perusing the references and resources available.

Just a brief search of potential forums/blogs related to your first question:

(2) For your second question, perhaps the best route to answering your own question would be to experiment with various recreational math problems. (E.g., see Ian Stewart's collection of math problems in many of his many books: they provide a great variety of problems, appealing to various modes of problem-solving, and include solutions. Simply look up author=Stewart, Ian in a public library's catalog for a listing of some of his books, or Google his name. Note, if you click on the "Ian Stewart" link, there's a list of his many publications, many of which are compilations of recreational-math-problems.) Such experimentation will help you and your son hone in on the types of problems your son finds easy to solve, and those that are particularly challenging for him.

(2) continued... I mention in a comment below your question that your son might do well with and/or enjoy combinatorics and studying numeric sequences. To be more specific, your son may find a niche in enumerative combinatorics. I'll also add that he may very well enjoy elementary number theory. (Note: my use of "elementary" in the link does not imply number theory that is less sophisticated or difficult than number theory in general. Wikipedia may clarify this.)

Cheers!

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Give him pie! (Pi)

who knows maybe 20 years on he'll be in guinness book or records.

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