It's been a long, slow effort to "get up to speed" (or more accurately "a slow crawl") on the various subjects one needs to know to work on "computational mathematics" aka SANE.
A reading knowledge of a lot of areas is needed, including things like abstract algebra (to understand Axiom's category/domain) type theory (to understand first-order dependent types) proof theory (to understand Gentzen, sequents, etc.) category theory (to understand catamorphs, functors, etc.) metaobject protocol (to understand CLOS extensions) number theory (to understand finite fields) calculus (to understand field extensions for integration) programming (to understand typeclasses, CLOS, etc) philosophy (to understand polymorphic sets, etc) CPU hardware (to understand "down to the metal", FPGA, etc.) Specification (to understand consistancy, completness, etc) Verification (to understand decision procedures, etc) Proof tools (like Coq, Lean, etc.) and a few other subjects that won't come to mind at the moment. The usual academic approach, that creates a special "course of study", requiring classes in areas is probably best. There are a lot of good online courses, such as the UOregon summer school, that introduce the basic ideas clearly. There are some good introductory books like Troelstra and Schwichtenberg's "Basic Proof Theory" that cover Gentsen, Hilbert, and Natural Deduction ideas. It seems worthwhile to put together a full course of study with links to videos and books, so one can get up to speed on required knowledge. I'll start an outline with links to these on the axiom-developer.org website in the coming weeks. It's sort-of an "Axiom University" major in computational mathematics. (There are no degrees :-) But one does mathematics and programming for the joy of it anyway so who cares?) I welcome suggestions and online links. Tim