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September 6th, 2011, 02:14 PM   #1
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Writing Things Out is Bad?

To what extent do skilled mathematicians/physicists write things out as they think? Could it be much less than one might initially suspect?

Suppose, for example, somebody argued that writing things down ought to be avoided when one is solving problems. The argument would be that writing is mostly a post-insight process, whereby one writes things down that one already knows to be true. But, in order to understand/figure out what is true, one has to visualize actual concepts in one's head where insights can actually be generated, not write things down where one's working memory has limited access. Thus, the purpose of writing things down is just to prove one's understanding and communicate ideas, but NOT to understand concepts and figure out solutions to problems.

Is there any truth to such an argument?
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September 6th, 2011, 03:33 PM   #2
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Re: Writing Things Out is Bad?

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Originally Posted by gwsinger
Is there any truth to such an argument?
I can't speak for physics, where it may well be true. But I suspect it is rarely true in math, where I find the arguments too large to fit in my working memory. I write things down because without access to that larger amount of space I can only consider ideas of where something might go, rather than actually going there (doing the calculations). So I might think "it looks like I could solve this with congruences, possibly covering hard special cases with a sledgehammer theorem like Catalan's conjecture" but until I actually put pen to paper I won't actually realize that the approach can't work for this problem ("Oh, right, -3 is a solution so there are always modular solutions... just need to find some way to rule out a positive one...".)

Generally, I think insight is overrated and hard work underappreciated. There are brilliant thoughts to be had, and bright minds to think them, but it's a long way from a good idea to a solution.
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September 15th, 2011, 06:25 AM   #3
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Re: Writing Things Out is Bad?

Quote:
Originally Posted by gwsinger
To what extent do skilled mathematicians/physicists write things out as they think? Could it be much less than one might initially suspect?

Suppose, for example, somebody argued that writing things down ought to be avoided when one is solving problems. The argument would be that writing is mostly a post-insight process, whereby one writes things down that one already knows to be true. But, in order to understand/figure out what is true, one has to visualize actual concepts in one's head where insights can actually be generated, not write things down where one's working memory has limited access. Thus, the purpose of writing things down is just to prove one's understanding and communicate ideas, but NOT to understand concepts and figure out solutions to problems.

Is there any truth to such an argument?
I disagree strongly. Writing things out clarifies them in your mind. Most "skilled mathematicians" keep a pad of paper and pencil with them and are always writing things down as they work.
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