My point of view on this is that it's all about whether progression in the subject gets more abstract or more concrete.

Law and medicine are both concentrations of much larger and more broad fields. Medicine is a particular corner of bioligy and law is a particular corner of the intersection between logic and political science. The further one goes in these fields, the more concrete and specific things get.

Math, unlike professional subjects, is the inverse. Math starts teaching you things that seem concrete, and then begins to generalize those relationships and algorithms.

Think about it this way: Arithmetic is algorithms for numbers, algebra is a generalization of arithmetic for that applies to large subsets of all numbers. Linear algebra is a generalization of algebra to multiple equations at once. Calculus is bridging the gap between discrete and continuous functions using algebra. And it just gets more general from there.

At some point everyone runs out of the intellectual skill needed to think in ever more abstract terms (Some sooner than others).

TLDR: Professional subjects are concrete applications of general concepts, math is generalizing from concrete observable use cases. Thinking in ever more abstract terms is a different problem with fewer systems to guide students versus thinking in ever more concrete ones.

My point of view on this is that it's all about whether progression in the subject gets more abstract or more concrete.

Law and medicine are both concentrations of much larger and more broad fields. Medicine is a particular corner of biology and law is a particular corner of the intersection between logic and political science. The further one goes in these fields, the more concrete and specific things get.

Math, unlike professional subjects, is the inverse. Math starts teaching you things that seem concrete, and then begins to generalize those relationships and algorithms.

Think about it this way: Arithmetic is algorithms for numbers, algebra is a generalization of arithmetic for that applies to large subsets of all numbers. Linear algebra is a generalization of algebra to multiple equations at once. Calculus is bridging the gap between discrete and continuous functions using algebra. And it just gets more general from there.

At some point, everyone runs out of the intellectual skill needed to think in ever more abstract terms (Some sooner than others).

TLDR: Professional subjects are concrete applications of general concepts. Math is generalizing from concrete observable use cases. Thinking in ever more abstract terms is a different problem with fewer systems to guide students, versus thinking in ever more concrete ones.