[tsurba]

Yet understanding is necessary but not sufficient when you read university math, especially advanced courses.

Proofs assume you have the elusive thing referred to as ”mathematical maturity”, which means many algebraic manipulation steps are skipped because it’s assumed you can just see the result straight away.

This ability to see the connection is not understanding but learning by rote, having done the same tricks with similar equations a thousand times.

This is what makes advanced math books/courses slow for me as a CS phd researcher. I can very slowly progress through, but it takes a massive amount of time to work through what just happened. If you take 60 instead of 20 courses on math the routine you have is just completely different. I guess you can call it fluency in the language.

(For example now I’m reading optimal control & variational calculus along with the functional analysis it needs, its heavy.)