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In certain situations, fundamentals may not matter, but very often, especially for long term learning, they really matter. Since this is a deeply held belief, perhaps moulded by experience, I find it tricky to articulate to an intelligent skeptic why they should bother learning fundamentals. They often have surprisingly strong rebuttals, including:

experts do not find such basic material interesting

I empathise: if someone in a specific niche is getting along just fine without understanding fundamentals, they may have no motivation to learn fundamentals, especially if they're already recognised as an expert (not necessarily by peers, but perhaps by students, clients, or consumers of their research).

Question

What lines of reasoning or resources (preferably canonical ones) do you use to demonstrate the value of fundamentals to those who may be sceptical of the value in learning them?

One Example

This happens to be from a physicist, Richard Feynman:

In physics, when you discover new things, it looks more simple

(when) We learn about a greater experience .. the laws look complicated ... but .. every now and then we have these integrations .. (and) it turns out to be simpler that it looked before

The corollary being that when we understand something on a fundamental level, it's actually much easier to communicate, understand, model and predict.

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    Can you give an example of a "fundamental" whose pedagogical value you doubt? – cag51 May 10 at 2:40
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    "if someone in a specific niche is getting along just fine without understanding fundamentals" What a strange premise. They might believe they are getting along fine but they actually aren't. This paper is a great example of not knowing undergrad fundamentals: care.diabetesjournals.org/content/17/2/152.abstract Personally, I'd rather try not to be embarrassed like that. "[E]xperts do not find such basic material interesting" Of course not. In order to become an expert, you need to master the basics. Once you have mastered them, they are not terribly interesting. – Roland May 10 at 7:16
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    @Roland I'd have said that was A-level, rather than undergraduate, mathematics. Nevertheless, I'd imagine the authors' embarrassment is somewhat moderated by having a paper with 436 citations. – Daniel Hatton May 10 at 8:00
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    @JochenGlueck but how many of those citations are from papers pointing out the mistake or using it as an example of lack of understanding? – astronat May 10 at 10:22
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    A left-field thought, though: the trapezium rule was first proposed before the invention of peer review, so it's possible that Tai's paper really was the first peer-reviewed paper to give a full description of the method. A bit like Osborne Reynolds' discovery that ice is slippery. – Daniel Hatton May 10 at 15:31

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