yes and this particular flavor of insanity has a name: pedantry.
>the meaning is engraved in dense equations
what's hilarious is that middling tier mathematically literate people worship mathematical formalism while truly mathematically literate people (i.e. mathematicians) eschew it because they understand that mathematics can't be formalized but also because it's natural language whose value is communication not codification. even here - ask someone to explain to you rigorously the definition of the fourier transform wrt dirac deltas. again the middling tier mathematically literate will assume that writing down an integral against a dirac delta is rigorous simply because you can write it down completely forgetting that the dirac delta is a tempered distribution not a function and thus that integral means something completely different. ultimately it is the case that the definition is consistent with a set of agreed upon definitions but the symbology itself is just a pun.
lol tell me you're a physicist without telling me you're a physicist :)
>with minimal confusion.
i think this the key thing that people that do a little math but not an immense amount don't understand: notation serves the same purpose as short hand in any other speech/communication. locally it's crystal clear, where local can be as small as that paper, that subsection, or just that paragraph (cf "the distinction is clear from context" lolol). i've written papers myself where i switch notations midstream for efficiency's sake (try defining tensors without bases but then try manipulating them without index notation...) but taking notation for granted is just as likely to get you into trouble as taking an API's promises for granted (in fact they're exactly the same things - leaky abstractions).
the value of [mathematical] language is not only communication, but also reasoning. It is remarkable, and sometimes unfortunate, how much mathematical reasoning you can do without knowing what you're doing, by pattern matching. Notation doesn't just allow you to communicate. It also allows you to manipulate e.g. truths that you know into truths that you do not yet know. In doing this abstract manipulation, you postpone (when necessary, and hopefully not indefinitely) thinking about semantics, while acting only syntactically.
A lot of people say something like "math is a universal language", and it sounds like we both agree that's nonsense. But I think we disagree on the extent to which math is a natural language. Your comment does not, in my opinion, recognize the symbolic manipulation (which doesn't have to be mostly-linear sequences of symbols, but can be e.g. diagrams too) that make math math.
yes and this particular flavor of insanity has a name: pedantry.
>the meaning is engraved in dense equations
what's hilarious is that middling tier mathematically literate people worship mathematical formalism while truly mathematically literate people (i.e. mathematicians) eschew it because they understand that mathematics can't be formalized but also because it's natural language whose value is communication not codification. even here - ask someone to explain to you rigorously the definition of the fourier transform wrt dirac deltas. again the middling tier mathematically literate will assume that writing down an integral against a dirac delta is rigorous simply because you can write it down completely forgetting that the dirac delta is a tempered distribution not a function and thus that integral means something completely different. ultimately it is the case that the definition is consistent with a set of agreed upon definitions but the symbology itself is just a pun.