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I'm very curious as to know how a person who pursued a formal, strict and rigorous education in mathematics would fair in comparison with a person who learnt applied math by "intuition" (that is without doing any proofs and relying more on the computational part), when confronted with problem solving.

For example, suppose a person follows a rigorous education in pure mathematics (let's say at a Graduate level), takes part in Math Olympiads, proves every theorem she encounters in her homework and is generally pretty math savvy. I assume such a person would have a good grasp on abstract reasoning and generalization.

Now, how would such a person, who learnt to think in an abstract manner would fair when confronted with "hands-on" problems, like designing an electronic amplifier circuit? What is her thought-process like? Since the calculations required to design an amplifier are just a special case of a broader set, would it be de facto an easy task to perform?

I never had the opportunity to take formal math courses and I can't help but wonder if taking more abstract math courses gives an edge on solving "simpler" applied math problems.

EDIT:

Question is directed towards applied maths disciplines problem solving, specifically how a theoretical point of view helps when solving more practical problems (for example, engineering related problems).

For example, suppose a person follows a rigorous education in pure mathematics (let's say at a Graduate level), takes part in Math Olympiads, proves every theorem she encounters in her homework and is generally pretty math savvy. I assume such a person would have a good grasp on abstract reasoning and generalization.

Now, how would such a person, who learnt to think in an abstract manner would fair when confronted with "hands-on" problems, like designing an electronic amplifier circuit? What is her thought-process like? Since the calculations required to design an amplifier are just a special case of a broader set, would it be de facto an easy task to perform?

I never had the opportunity to take formal math courses and I can't help but wonder if taking more abstract math courses gives an edge on solving "simpler" applied math problems.

EDIT:

Question is directed towards applied maths disciplines problem solving, specifically how a theoretical point of view helps when solving more practical problems (for example, engineering related problems).

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