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> you lose the ability to understand math as anything other than a human attempting to be a computer I get what you're saying and it's important, but I also di
by User23 4y ago
> you lose the ability to understand math as anything other than a human attempting to be a computer
I get what you're saying and it's important, but I also disagree with how you're framing it. It's desirable to get to the point where you can automatically do purely mechanical symbol transformations as you work through a problem, thus saving your higher reasoning for the conceptual problem of searching for which transformations will lead to a solution.
Frankly, I find the continuing concern with "intuition" with respect to purely mechanical transformations to be rather medieval. It is slowly changing though as the influence of computing science osmoses back into more traditional mathematics. Using Mathematica or similar tools makes it abundantly clear how distinct the mechanical and conceptual challenges are.
- mattwilsonn888 4y agoI don't believe layers should not be built on top of to the point of rarely, or even never thinking about the inner workings again. I just believe that when building those layers, having an intimate relationship in your mind with how they work and relate to each other will have positive effects, even after you start executing steps without regard for their deeper concepts. That's the case even for just the 'engineer' archetype, who uses math strictly as a tool. For any person doing theoretical work, discovery is often preceded by a fundamental understanding and tweaking of the most basic tools - so I believe the mindset is useful in both cases but borderline necessary for the second.