These kind of heuristics are supposedly a prerequisite to the formal study, but sadly most textbooks don't spend the time talking about it (since logically it's

These kind of heuristics are supposedly a prerequisite to the formal study, but sadly most textbooks don't spend the time talking about it (since logically it's not necessary). Instead of reading up on functional analysis (Banach spaces and Hilbert spaces), read bits of its history to get a taste. Here's one that's not too long http://courses.mai.liu.se/GU/TATM85/FA-history.pdf http://courses.mai.liu.se/GU/TATM85/FA-history.pdf