I suppose what would be really nice is for computerised mathematics to be marked up such that these interchanges can be made automatically, with libraries of ru

I suppose what would be really nice is for computerised mathematics to be marked up such that these interchanges can be made automatically, with libraries of rule sets shared online. You're reading a document and it has some funny triangle thing you don't understand? Click on it to get a menu of alternative representations, and you see it can be swapped to "log" notation. Further, you go to your reader preferences and add a rule "whenever you see this triangle thing, show me it as a log". A student finds some crusty old document with funny "heart monitor" symbols, clicks on them and finds they're just a particular kind of power triangle. They update their preferences to replace those symbols with power triangles. Of course, holy wars rage on mailing lists about whether the default rules should convert "tau" to "2pi" or "pi" to "tau/2" ;) Seriously though, too much time is spent making computerised mathematics look right in PDFs (e.g. TeX), compared to telling the computer precisely what it is/means. Thankfully there are some attempts at this (e.g. OpenMath), but they don't seem to be very widely used.