I am going to use higher level mathematics as made computationally feasible by the Mathematica ecosystem of products and solutions. (I'm not interested in arguing this personal choice; Steven Wolfram is not interested in reorganizing his ecosystem.)
As a simple example (and examples are my primary focus) consider what it means to "solve a problem" in a Hopf Algebra. Solution recognition is complex enough just for starters (see http://people.duke.edu/~ccc14/sta-663-2018/notebooks/S09B_Optimization.html). Some issues are generic to any Hopf Algebra, after confirming that the target domain is the genuine article. Some solution steps are likewise generic. Some issues and steps differ dramatically by specialization. (If you need convincing, follow the pointers from https://mathoverflow.net/questions/84161/hopf-algebras-examples.)
I don't want Neo4j to learn to manipulate Hopf Algebras, but I do want to interpret Hopf Algebra information. Mathematica knows the math; Neo4j can be taught to expose meaning in an external context.
Has this been done already? Is it known to be too hard to try?
Some problems can be solved spectacularly better, faster, cheaper when formulated in one mathematical context rather than another. Helping people with problems find better solutions is worth batting a formulation back and forth between the math-realm and the consequences-realm. Or so I believe.
