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Do you think you can really reach higher levels of thought when studying subjects outside of Mathematics, Physics, and Philosophy?

I define "higher levels of thought" in relation to those rare moments (less than 10 in my life) when I felt like a concept was beyond my mental limits and really felt like it was beyond the scope of my understanding. All of these instances were with Math or Physics problems (and I've gotten pretty close with some Philosophical ideas). This is much different than the typical "this is a bit complex" or "I have to remember a lot to understand this" or "I will have to think about this for at least 3 minutes until I can say I really understand it". If you can break a complex theory in the Humanities into small parts that are each easily understandable, it's not what I'm talking about (because the corresponding mathematical ideas cannot be broken down into "simple" parts). And to clarify, I am comparing THEORIES in the Humanities with IDEAS in Mathematics (not "problems", like "solving world hunger" vs. "solving a integral"). From my (very limited) experience, I think that the Humanities open up your perspective and change the way you see/live in the world, but can they really make you exercise your mental muscle to its fullest? (I am aware that Philosophy falls under Humanities, I added that to the list after my initial thought so maybe it doesn't belong there) And which do you think is ultimately more valuable (is it even valid to compare the two?)-- new perspectives or deeper thought patterns?

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What do you think?
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