Theoretical fluid dynamicist here. I'm fairly decent with math, or at least solving differential equations. Related to the essay, I've always found it odd how many people with a CS background tend to "compute first, ask questions later." My experience has been that analyzing a problem first is generally a good idea, but CS folks typically don't in my experience. Exact or good approximate solutions to problems often exist, perhaps only for relatively simple problems, but still.
Sometimes computation is necessary, but that doesn't mean you'll save time by avoiding analysis entirely. When mathematical analysis succeeds, the time saved can be considerable. And you can combine both, e.g., recently I sped up a non-linear algebraic equation solver for my work by using an ansatz that I derived using the perturbation method. (Also probably helps the solver converge to the right solution.)
Sometimes computation is necessary, but that doesn't mean you'll save time by avoiding analysis entirely. When mathematical analysis succeeds, the time saved can be considerable. And you can combine both, e.g., recently I sped up a non-linear algebraic equation solver for my work by using an ansatz that I derived using the perturbation method. (Also probably helps the solver converge to the right solution.)
One possible explanation: https://en.wiktionary.org/wiki/if_all_you_have_is_a_hammer,_...