Combinatorial enumeration might work. Isn't Deep Learning a spectacular victory of dumb brute force (in the form of Gradient Descent and overparameterisation) over elegant theory? Seemingly if you do a brute-force search to solve a problem, the number of possibilities you need to look through should be overwhelming, but a lot the time this isn't the case.

[Edit] The origin story of DL is also full of shallow dismissals, for perhaps not dissimilar reasons to the ones you're seeing here.