Many of the most effective people I know—alive and dead—seem unable to do serious thinking without a writing surface in front of them. It seems to extend cognition somehow: perhaps it effectively extends one’s Span of working memory, or perhaps moving the fingers somehow contributes to the thinking.
For instance, in an interview with Charles Weiner, Richard Feynman said that for him (1973) the paper’s not just a record of work done in his head:
Weiner: (Referring to Feynman’s journals) And so this represents the record of the day-to-day work.
Feynman: I actually did the work on the paper.
Weiner: That s right. It wasn’t a record of what you had done but it is the work.
Feynman: It’s the doing it — it’s the scrap paper.
Weiner: Well, the work was done in your head but the record of it is still here.
Feynman: No, it’s not a record, not really, it’s working. You have to work on paper and this is the paper. OK?
Grothendieck, an eminent 20th century mathematician, is said not to be able to think without writing (2007):
He was improvising, in his fast and elegant handwriting. He said that he couldn’t think without writing. I, myself, would find it more convenient first to close my eyes and think, or maybe just lie down, but he could not think this way, he had to take a sheet of paper, and he started writing. He wrote X → S, passing the pen several times on it, you see, until the characters and arrow became very thick. He somehow enjoyed the sight of these objects.
Feynman, R. (1973, February 4). Interview by C. Weiner. Niels Bohr Library & Archives, American Institute of Physics. https://www.aip.org/history-programs/niels-bohr-library/oral-histories/5020-5
Illusie, L. (2007, January 30). Reminiscences of Grothendieck and his School (S. Bloch & V. Drinfled, Interviewers) Personal communication.
Correspondence with Stephen Malina, 2020-05-05. Re: Question about a question