There is a form of this critique which is correct, but requires a lot more mathematical sophistication than you can get from starting from this viewpoint. For

There is a form of this critique which is correct, but requires a lot more mathematical sophistication than you can get from starting from this viewpoint. For example, Fields Medalist Terrence Tao essentially believes the same thing, but sees it as an extension of having gone through a phase of rigour to understand how in particular to ignore the details of a system: https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/ https://terrytao.wordpress.com/career-advice/theres-more-to-... And modus ponens, modus tollens. Consider the view where if any approach to mathematics is valid, including your idiosyncratic version, it is also the case that the style they teach is going to be at least as valid. To actually understand why you would want to choose one mathematical system over another requires familiarity with both systems, and so some flexibility is demanded of you.