...what I mean is the capability to utilize them to do useful work.
In his case, useful work would be mean being able to actually decide on an algorithm that might, for example, to have a systematic way choose the general chemistry of a stationary phase based on what is called here, "Henry's law" constants, which generally are applied in introductory courses for gas liquid interfaces rather than, as here, solid liquid interfaces.
What bugs me is that I have no insight whatsoever to the general mathematics of discontinuous Galerkin approaches, for example, and many other techniques in the solution of differential equations. It turns out, on further investigation, that this particular branch of mathematics, Galerkin finite element methodology is very important in a completely different area than Langmuir adsorption, specifically, neutron transport, and many other only loosely related areas as well.
For example: Discontinuous Galerkin spatial discretisation of the neutron transport equation with pyramid finite elements and a discrete ordinate (SN) angular approximation...
...and...
Sensitivity Analysis of the Galerkin Finite Element Method Neutron Diffusion Solver to the Shape of the Elements
What I'd like for my son would be to be able to look at these titles and say..."that makes sense..." or "why didn't they just use..."
There was a time in my life I was there myself, but I feel it's gone and I miss the feeling, the connectedness.
But you're right, most people don't need that level of math, although your other point is well taken, innumeracy drives the world to some very, very, very bad places, the Fukushima tritium terror being only one such example of the triumph of ignorance.
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