So, a student comes to you asking to do a project on the applications of Laplace transforms, and under gentle cross-examination turns out to have very little idea what a Laplace transform is or what it’s for. Never mind: over the course of a term, you patiently guide him through the mysteries of setting up a diffusion problem, transforming it, solving the transformed problem and finally obtaining the solution to the original problem using the inversion theorem. In the course of this, the student learns the machinery of Bromwich contours, double Fourier series and the calculus of residues; as a final masterpiece, he brings everything together to produce an exact solution to a genuinely non-trivial three-dimensional initial–boundary-value problem. You feel quite pleased with yourself, and him.
Then you see the Conclusions section of his dissertation, where he’s written something like this:
The Inversion Theorem is very effective, but it is very costly and time-consuming and requires so many manipulations that by the time the expression is at a point that it can be computed, it would be easier to solve by hand.
I’d love to know what my student means by that Mrs Joe Gargery turn of phrase. Does it indicate a skulking suspicion that, after all, all this effort was somehow a blind intended to conceal the existence of a simpler form of solution? (And if so, what on earth does he think that solution looks like?) Is this yet another case of all-answers-are-simple syndrome? Or does he, like Mrs Joe, nurture a belief that there is no problem that can’t be resolved by means of a heavy hand and a Ram-page?
Maybe I should lessen my expectations, and be grateful if I don’t find out.