When I was learning Ancient Greek, I was taught that most verbs had three basic stems corresponding to the different aspects: imperfective -λυ-, aoristic -λυσ-, and perfective -λελυκ-. Adding an augment made them past-tense, removing it made them non-past.
This was a useful mnemonic. But historically, was there actually any connection between the sigmas in the future λύσ-ω ("non-past aoristic") and the aorist ἔ-λυσ-α ("past aoristic")? I had always assumed so, but then I came across the "S-future" while researching the Latin future perfect.