At least in programming it's possible to step into a function and/or work at multiple levels of abstraction.

Getting a math degree just to be able to fill in the gaps created where 'it trivially follows' is equivalent to being required to memorize the API for a framework because clearly defined documentation is hidden behind a paywall.

so called 'intellectual power' has little to do with it. What you're describing is familiarity with navigating a minefield of poorly structured information and tapping a academia (ie at a very high cost of entry) for 'special access' to resources that bridge the gaps.

Of software development suffered from the same informational constraints and lack of innovation, we'd still be playing pong.