Many people in engineering believe that to understand something, it is necessary and sufficient to have a low-level mathematical description of that thing. That you need to "know the math behind it". In nearly all cases, it is neither sufficient nor at all necessary - far from it
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Similar to how, say, you can always reinvent the Pythagorean theorem on the fly if you think about geometry through the lens of vector products, or how you don't need to memorize the quadratic formula if you understand what an equation is and the general process for solving them
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I think in a lot of cases the most efficient way to build the right mental model is via implementation. It’s so easy to fall prey to the Dunning–Kruger effect and fool yourself into believing you understand something until you actually need to use or implement it somewhere.
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I suppose it depends on the situation. If one is a time traveller thrown back in time and tries to reinvent technologies - then, yes, nothing less than prefect command of all details will serve. But innovating in one's own requires, imho, more breadth than depth of knowledge.
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It might not be necessary to understand the deep math to apply the method, but I also think it would be hard to use it intelligently with no understanding of the math behind it. Hard to judge that if you already know the math, as you do.
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