> The lingo is half the battle for most things but for math it seems like the lingo is the entire battle.
There's a kernel of truth there.
To abuse the DSL metaphor further, even mildly complicated mathematics concepts are only expressible using layer upon layer of ever-more-abstracted DSLs. Lower-level expansions of the building blocks to improve clarity for reading would be useless in practice, since mathematics is intended to be written and understood by humans and such an expansion would exceed our ability to keep the entire intended concept in our working memory.
Proficiency in mathematics is proficiency with understanding and extending the lingo itself. Mathematics /is/ the lingo, which is why it can't be unraveled from it.
>"how I learned it so it must be the best"
Not at all. It is, however, a very practical approach to getting someone up to speed to be able to do actual mathematics (as opposed to the basic symbol manipulations that most people confuse with actual mathematics.)
There's a kernel of truth there.
To abuse the DSL metaphor further, even mildly complicated mathematics concepts are only expressible using layer upon layer of ever-more-abstracted DSLs. Lower-level expansions of the building blocks to improve clarity for reading would be useless in practice, since mathematics is intended to be written and understood by humans and such an expansion would exceed our ability to keep the entire intended concept in our working memory.
Proficiency in mathematics is proficiency with understanding and extending the lingo itself. Mathematics /is/ the lingo, which is why it can't be unraveled from it.
>"how I learned it so it must be the best"
Not at all. It is, however, a very practical approach to getting someone up to speed to be able to do actual mathematics (as opposed to the basic symbol manipulations that most people confuse with actual mathematics.)