It will be hard to come up with an accessible general framework to express general problem situations without resorting to either (a) an explosion of templates

It will be hard to come up with an accessible general framework to express general problem situations without resorting to either (a) an explosion of templates for solving the N-most-common kinds of problems (the browsing through which will be worse than learning the math and the programming); (b) a set of elaborate but limiting special-purpose programs (much like iPhone apps that might help, for example, a metal welder to choose stock feed rate, gas mix/flow, and electric current depending on metal type and thickness to be joined; or mortgage calculators). Worse yet, it doesn't take much for interesting problems to get into the land of over- or under-constraint. In an under-constrained problem there are a multitude of solutions forming their own K-dimensional space, and then one likely should apply some secondary optimization criteria to determine the best solution. In over-constrained problems there is no exact solution, but again one needs to impose some optimization to get something "close enough" to the desired criteria, according to some norm. Explaining the need for optimization, letting the user explore the solution space, and having them express these optimization criteria will be tough. A Google search for "geometric constraint solver" leads to this paper: http://www.cs.purdue.edu/homes/cmh/distribution/papers/Constraints/CAD95.pdf http://www.cs.purdue.edu/homes/cmh/distribution/papers/Const... -- what appears to be a lot of work just in helping people/machines solve geometric problems (though surely more widely applicable when taken in the abstract). Coming up with even more general "hands-on" explorers/solvers will be a lot of work.