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?