The Diagrammatic Future of Mathematics
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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Ellis