> they were later put in rigorous mathematical footing in the theory of distributions
Yeah some French dude called Laurent Schwarz that got the Fields medal for it.
IIRC he built the set of distributions as the dual vector space of the tiniest vector space he could think of: extremely well behaved functions (C-infinite functions with finite support - weird mathematical beasts that go to zero at the extremities of their support with all derivatives also going to zero there as well).
I never really managed to grok the intuition behind the formalization of Schwarz, whereas the hand-wavy physicist way is pretty straighforward to understand.
Yeah some French dude called Laurent Schwarz that got the Fields medal for it.
IIRC he built the set of distributions as the dual vector space of the tiniest vector space he could think of: extremely well behaved functions (C-infinite functions with finite support - weird mathematical beasts that go to zero at the extremities of their support with all derivatives also going to zero there as well).
I never really managed to grok the intuition behind the formalization of Schwarz, whereas the hand-wavy physicist way is pretty straighforward to understand.