[szhorvat]

I should add that every time I asked WRI support about implementation details, I did receive an answer with references to the method used.

[reikonomusha]

Did they ever share any of their algorithms created in-house? (They claim many are.) If they share the method, why can't they share the code?

They do have some notes on internal implementation, that do not seem up-to-date, here [0]. Were they any more detailed than this?

[0] http://reference.wolfram.com/language/tutorial/SomeNotesOnIn...