Is Writing Really Necessary for Problem Solving?

[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?

 

[Pengwuino]

I try to write down as much as possible. I don't know how it is with other people, but a lot of times I'll have an idea in my head but my mind is incapable of visualizing complex equations and doing the manipulations in my head. So writing things down is important. Plus, a lot of the time when I write things down, I realize what I was thinking was wrong.

 

[Astronuc]

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?

It depends on the problem and/or the individual.

Usually proofs, mathematical or otherwise, require writing down steps, and perhaps erasing some. Similarly, derivations of physical models require writing steps down, just like one would do in a homework problem, starting with a problem statement, writing down relevant equations, then solving said equations.

I believe Andrew Weils did a lot of writing while working through Fermat's Last Theorem.
http://www.pbs.org/wgbh/nova/physics/andrew-wiles-fermat.html

 

[lisab]

I don't see what harm is done by writing things out, or using a diagram. Especially when thinking about a *physical* problem, a diagram is helpful. I don't see what is lost.

<snip>
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.
<snip>

That doesn't seem correct to me, or maybe I don't understand what you mean. Could you elaborate?

 

[Jimmy Snyder]

I do my best to follow all of the derivations in the books that I read. I do my best to do them in my head and if I can, then good. If I can't do them in my head I have no choice but to write them down and so I do. I write them down in the margins of the book so that when I read it again, I will be better able to do it in my head.

 

[Dale]

The argument would be that writing is mostly a post-insight process

writing helps me remember my insights later.

 

[arildno]

Writing something down de-emotionalizes the idea you have in your head, dissecting it, for example, from the excitement and conviction you have that it is great.

Thus, writing helps you to focus on those elements in your idea that are actually objectively significant.

A number of times, I had the idea that I had finally "figured it out", but when I got to writing it down, the bare content was a lot less persuasive than when the idea was just floating about inside my head.