I am learning classical Attic Greek at college, and we recently saw that, in a departure from the typical recessiveness of verbs, the accents for aorist infinitives always falls on the penult regardless of the ultima and is always a circumflex. Taking the verb παιδείομαι for example, the aorist infinitive is παιδεῦσαι, not παίδευσαι with the accent retreating as we might have expected (indeed this is actually the aorist imperative).
My question is, why is this the case for aorist infinitives? I hypothesized that perhaps, since infinitives are formally verbal nouns, the aorist infinitive keeps its accent on the penult and not the antepenult because noun accents are persistent. Obeying the accent rules of nouns would, at least, explain why it is a circumflex and not an acute. My professor said he wasn't sure of the reason, but added that aorist infinitives tend to have their accent on the same syllable as the masculine nominative singular of the verb's active participle. However, he did not know whether or not this is the reason why the accent of the aorist infinitive is where it is, whether it is just a coincidence, or whether there is some greater common reason for both.
If anyone had an explanation, or knows of any theories, I'd love to hear them. And if you do and added a link to a source I could read for more information, I'd greatly appreciate it. Indeed a related question could ask why second aorist infinitives also have peculiar infinitive accentuation, so an authoritative source on such matters would do brilliantly. Thanks!