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> if you need to see an implementation then you're not really understanding the idea for what it is. I 100% disagree. At the very least, I think you're wrong i
by CogitoCogito 5y ago
> if you need to see an implementation then you're not really understanding the idea for what it is.
I 100% disagree. At the very least, I think you're wrong if your assumption is that such a statement applies in general. That statement certainly doesn't fit me as well as many people I've taught in the past. I got my PhD in (pure) mathematics and I could only understand high level abstractions _after_ I worked through many concrete examples. I know the same applies for many successful mathematical researchers because we discussed the subject at length. Now such a statement certainly does apply for _some_ people (I've taught them as well), but certainly not all.
If you're someone that likes this sort of abstract thinking, that's great. If you're someone that needs concrete examples to understand, that's great too. The real lesson is that everyone learns differently.
- Koshkin 5y agoBut there's a difference between trying to understand, say, a theorem by applying it in concrete situations and by studying its proof.
- CogitoCogito 5y ago> But there's a difference between trying to understand, say, a theorem by applying it in concrete situations and by studying its proof. There may be a difference or there may not. You could study a proof within the context of a specific example. That is how I usually would do it. But yes of course it's possible not to do like that (many people don't study proofs that way). In any case, I don't really understand your point.
- Koshkin 5y agoI was drawing an analogy, in this particular context, between studying the proof and taking something apart.