This is remarkably accurate and resonates with me a lot. I did mathematical olympiads in high-school, where intuition to crack problems plays a major role. Then went on to college to study an undergraduate degree in maths (concentration in analysis). Analysis requires, at least in its rigorous foundations, to be careful and have a skilled knowledge of logic/quantifiers (more than elementary abstract algebra in my humble and biased opinion), often very scrupulously. Then in my graduate studies intuition along with the maturity of rigor work to produce new theorems. I'm impressed that several times I look at a paper or series of results and can read them "diagonally" to get the motivation without scanning all the text (of course, if the aim is to cite/build on top of/generalize/apply it then close attention to reasoning should be paid).
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This is remarkably accurate and resonates with me a lot. I did mathematical olympiads in high-school, where intuition to crack problems plays a major role. Then went on to college to study an undergraduate degree in maths (concentration in analysis). Analysis requires, at least in its rigorous foundations, to be careful and have a skilled knowledge of logic/quantifiers (more than elementary abstract algebra in my humble and biased opinion), often very scrupulously. Then in my graduate studies intuition along with the maturity of rigor work to produce new theorems. I'm impressed that several times I look at a paper or series of results and can read them "diagonally" to get the motivation without scanning all the text (of course, if the aim is to cite/build on top of/generalize/apply it then close attention to reasoning should be paid).