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Comment by amelius | Hacker News Reader

Mathematicians use operator overloading all the time. It would be nice to have a tool that explains to me what an equation actually means in a given context.

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You are talking about the semantics of an equation while this tool is already satisfying when understanding correctly the syntax (in LaTeX).

There are actually a number of ongoing research projects to establish standards of semantical mathematical representations. Probably one of the best funded running projects (budget ~10MEUR) which has a work package on this topic is http://opendreamkit.org/ . Work is going on at https://mathhub.info/ from my knowledge. I would like to provide a deep link but the site seems to be in a broken state. Apparently people are working on it right in the moment.

I’ve long had this dream of building a system that would allow for symbolic algebra manipulations, where the representation knows about the semantics. The idea is to replace long and tedious pen-and-paper symbolic calculations, while still having direct control over each step of the calculation. In looking for something like this I’ve found specialized proof verifiers, which are doing something different. At the other end of the spectrum there’s Mathematica, which does symbolic manipulation but doesn’t understand enough semantics.

Are these projects aiming at something like what I’m describing? Or are they more about something else like verifying proofs?

Well, in principle a CAS like Mathematica (or in principle every mature alternative) allows you to implement such a workflow (i.e. naming mappings or an algebra on your objects). I think what Wolfram is concentrating on since a decade is accumulating "knowledge" into their system, i.e. exactly this kind of semantic information we talk about. However, as an end user I don't really see that, it seems to be more well-groomed behind Wolfram alpha.

On the other hand, there are these research projects which however seem to concentrate on standards rather then actually accumulating semantic knowledge.

I would love to see an adoption of hypertext and semantic mathematical notation in scientific papers. Instead of writing $E=m c^2$ in a (LaTeX) paper, we would instead define the symbols machine readably with a code like

   set E = physics/Energy
   set m = physics/Mass
   set c = physics/constants/speed-of-light

I have never seen actual scientific papers which do this kind of stuff, i.e. which are machine readable.

Isn't that usually what the document is for? :)

The verbalization if most LaTeX commands can help learn to read the equations. Sometimes.

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