DollaWilliam

Not a doctor, but I have spent ~10 years working with data on the reimbursement side of a large hospital. Please see my comment above.

That's not true, due to price discrimination. They can't precisely tell how much they can get paid for something until they submit invoices to insurers.

I can confirm that, at least for an N of 1. Contracts with individual insurers are typically negotiated to be set to a percentage of (known) Medicare reimbursement for a given procedure. As it is with any negotiations, more powerful insurers get better rates. The costs are usually monitored at a macro accounting level, since what really matters is staying in the black.

As an aside, in addition to other confounding factors, cost accounting would likely affect physician compensation since it would shine a light on their actual effort. Expect that to Just Not Happen in an organization with more than one provider. They enjoy their compensation, and they will fight to keep it.

Edit: perhaps the physician compensation scheme I am familiar with is wildly atypical. Hence the N=1 disclaimer.

> 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.)

That's a false equivalency. Mathematics, in practice, is more of a domain specific language that encapsulates more and more precise information as you increase the level of abstraction. The levels of abstraction layer upon one another to be able to handle more complex concepts while retaining all of the underlying precision.