As lovely as symbolic mathematics is, it does have one major problem: it can not be parsed.
I do not mean the symbols cannot be drawn etc, but even a simple expression like "ab + c" can not be disambiguated. Is it "a*b + c"? or is there a variable "ab" added to c.
This requires the idea of "closures" .. i.e. history/state in which the expression appears. (Wolfram discussed it at a conference once, but I don't have the reference alas.)
So the solution is either to simply introduce new symbols to facilitate parsing (i.e. require multiplication symbols .. but there are more) or introduce heuristics that use history as the human does.
One promising technology is touch screens and sophisticated trackpads (Magic Pad for example) which lets us "draw" mathematics.
I do not mean the symbols cannot be drawn etc, but even a simple expression like "ab + c" can not be disambiguated. Is it "a*b + c"? or is there a variable "ab" added to c.
This requires the idea of "closures" .. i.e. history/state in which the expression appears. (Wolfram discussed it at a conference once, but I don't have the reference alas.)
So the solution is either to simply introduce new symbols to facilitate parsing (i.e. require multiplication symbols .. but there are more) or introduce heuristics that use history as the human does.
One promising technology is touch screens and sophisticated trackpads (Magic Pad for example) which lets us "draw" mathematics.