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Is there an area of computational science research that can be done on pencil and paper (with results written up for a journal format later on)?

I'm wondering if there is abstract proof-based linear algebra or abstract algebraic objects being developed for computational science. Seems like it would be really fun if such an area of research existed.

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    $\begingroup$ Computation science can be seen as an interdisciplinary area. If you consider the math branch of numerical analysis is done essentially by hand with pen and paper. Computations are made to investigate and test in more comfortable way the "theory". You use the tag of linear-algebra, for example see the last issue of the journal Linear algebra and Its Application you can find a lot of research by hand. This is only one example! $\endgroup$
    – Mauro Vanzetto
    Commented Apr 23, 2020 at 9:20
  • $\begingroup$ For instance, an interesting example is Crouzeix's conjecture. It is an abstract theoretical result that shows up in various bounds needed in the study of numerical algorithms. $\endgroup$
    – Federico Poloni
    Commented Apr 23, 2020 at 11:59
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    $\begingroup$ Lots of theoretical work in numerical analysis starts with pencil and paper. Whether this kind of research is "computational science" is certainly debatable. $\endgroup$
    – Brian Borchers
    Commented Apr 23, 2020 at 18:16
  • $\begingroup$ @BrianBorchers yes, it is an open arguments... :-) Obviously an interdisciplinary area as Computational science has not got definite border, and it gets contribute from different area, some can be archived as more theoretical and appear more distant. This can be the case of "numerical analysis", but this open another door: what is "numerical analysis"? I find very interesting the paper by Nick Trefethen THE DEFINITION OF NUMERICAL ANALYSIS that discuss the arguments, curious also the last sentence of the paper. $\endgroup$
    – Mauro Vanzetto
    Commented Apr 24, 2020 at 9:03
  • $\begingroup$ Well, in the old days, before electronic computers, numerical calculations were carried out by human calculators, possibly with pencil and paper, en.wikipedia.org/wiki/Computer_(job_description). $\endgroup$
    – Maxim Umansky
    Commented Apr 25, 2020 at 5:03

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