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In this paper, we demonstrate an integration of technologies aimed to "illustrate" and "expose" the mathematical content to readers. We are not covering technologies aimed to assist with "verifying" or "co-deriving" mathematical results, such as proof-assistants and automated theorem provers, although we consider them viable future integration projects with Authorea.   The preprint of this paper, and simultaneously the demonstration of all described capabilities, are cross-hosted on Authorea and can be found at \cite{live-math}.