The Diagrammatic Future of Mathematics

The Diagrammatic Future of Mathematics

[Ellis]

There is growing evidence that calculating with diagrams of labeled
dots and arrows instead of linear expressions suffices for many parts
of mathematics. For example, I cite "Categories, Allegories" by
Freyd-Scedrov, and "Exercices de style: A homotopy theory for set
theory," (in two parts) by Gavrilovich-Hasson, and I would add that
Voevodsky's Univalent Foundations project, although seemingly
implemented by linear expressions in Coq, is probably susceptible to
a diagrammatic translation.

Newly available tablets with high-resolution handwriting and drawing
input functionality implies that mathematicians -- among others --
may now collaborate in real time independently of their physical
location. It seems to me this capability must be important for the
future of mathematics.

Furthermore, it also seems to me the time is right for developing a
search engine which finds, among all freely available online
mathematics and physics papers, matches or partial matches of linear
expressions or of diagrams with labeled dots and arrows.

These actual hardware and potential software developments could
wonderfully change the history of mathematics. Do you agree?

Ellis D. Cooper



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