conjugations - What is the etymology of 〜ません（でした）?

I have always been interested in the negative polite (〜ません) and negative past-polite (〜ませんでした) inflections of verbs.

My understanding is that ます is an inflectable function word (助動詞), so I'm wondering why the negative form ends with ん. Is that a contraction of ぬ perhaps? (Also why is the 未然形 ませ rather than something more regular, like まさ?)

The really weird thing for me is でした (the past inflection of the polite copula), showing up for the negative past-polite form. Has this always been the way to handle this sort of semantics, even in Classical Japanese, or is this a recent introduction to the language?

Although I think there is probably no really satisfying answer to why things are like this, I do think it'd be interesting to know how things evolved through time, so any answers revealing some of that information are welcome!

Answer

My understanding is that ます is an inflectable function word (助動詞), so I'm wondering why the negative form ends with ん. Is that a contraction of ぬ perhaps?

Yes, the final -n is from negative -nu. This should make sense as -nu attaches to the irrealis, which is ma-se since mas- is サ変.

(Also why is the 未然形 ませ rather than something more regular, like まさ?)

masu is assigned the サ変 conjugation. As such, the irrealis is ma-se. Conjugation types can change over time, but サ変 is used in other words as well, so there is currently no motivation for such a change. That said, in the early stages of masu, there are a few extant usages of irrealis ma-sa indicating experimentation as a 四段 conjugation; though this form is rare and never prevailed.

The really weird thing for me is でした (the past inflection of the polite copula), showing up for the negative past-polite form. Has this always been the way to handle this sort of semantics, even in Classical Japanese, or is this a recent introduction to the language?

There were originally several competing negative past polite forms: masenkatta, masen datta, and masen desita. Early citations for masen desita appear around 1860s. As desu became more common and standard, the past polite standardized on masen desita by the 1890s. At this point, it is modern Japanese, not classical.