That sounds like a cool project. Do you know of any transcendental number that does admit an intuitive proof of irrationality (or, more generally, of not being algebraic to any specific degree)?
My gut feeling is that this shouldn't typically be the case, but I'm tired and struggling to convey why without descending into downright criminal levels of vagueness. I'd be more hopeful about an algebraic number of degree >1 having a 'nice' reason for specifically being irrational.
My gut feeling is that this shouldn't typically be the case, but I'm tired and struggling to convey why without descending into downright criminal levels of vagueness. I'd be more hopeful about an algebraic number of degree >1 having a 'nice' reason for specifically being irrational.