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Why do many languages have grammatical gender? Why do different nouns – including those for inanimate objects – take different forms of article and adjective, corresponding to 'masculine', 'feminine' and (in some languages) 'neuter'? How did this phenomenon evolve?

It seems to add an unnecessary complication to language, to no expressive purpose (since the gender of particular nouns cannot be varied). One would have thought that the development of a language would take the simplest path to a given level of expression, without any seemingly pointless inflections. At what point in the evolution of a given language did it become necessary for an article or adjective to 'agree' with a noun, and why? Why not use a single form of article and adjective for every noun, as in English?

The situation is further complicated where a language inflects for case, as in German and Latin. Different genders have a different set of case-forms to be learned, and there can be many different cases. How can these gender differences have arisen, given that a language initially develops 'upwards' from uneducated people, and not 'downwards' from academic institutions?

It is interesting that in both German and Latin all 'neuter' nouns and adjectives have the same form for the subjective (nominative) and objective (accusative) cases. Why is this? Could it be because the neuter gender is assigned to nouns referring to things for which the case is not so important? And why do a few nouns have the 'wrong' gender (e.g. la recrue (recruit) in French)?

Any explanations would be welcome.

Broadly speaking, grammatical gender is a kind of noun classification system. Structurally, such systems "can be a valuable tool of disambiguation", rendering clarity about antecedents. In addition to the masculine/feminine/neuter system found in Germanic languages or masculine/feminine in Romance languages, there are systems based on animate/inanimate, human/nonhuman, common/neuter contrasts. According to this article in Wikipedia, there are some languages with up to 20 gender categories
https://en.wikipedia.org/wiki/Grammatical_gender

At university, our field work class introduced us to Swahili which has 18 noun classes, as mentioned in this article on noun classes
https://en.wikipedia.org/wiki/Noun_class

You can think of gender as functioning like singular and plural in English to disambiguate an utterance. For example "I have a dog and three cats. It likes to run but they sleep a lot". The singular/plural distinction allows you to determine which behavior applies to which animal(s). I have heard it said that English which generally lacks gender classes has a stricter word order requirement than Latin with its five noun declensions. The inflections required by the declensions allow the word order to vary more freely.

Thanks for the links.

The Wikipedia article on grammatical gender points out that not all assignments of gender to inanimate objects are arbitrary; they may be based on natural features. But some do seem arbitrary, and it would be interesting to know how these arose.

Regarding the (partial) avoidance of ambiguity, I would have thought there were simpler and more reliable ways of achieving this, e.g. short words meaning "the latter" and "the former" (perhaps the words for "this" and "that" respectively).

"Gender" is a misnomer for "lexical category". The human lexicon can't work without categorization in "fuzzy categories", i.e. with fuzzy boundaries. Stol "table" and ulica "street" in Russian obviously have no literal gender, yet the former belongs to the "masculine" lexical category and the latter, to the "feminine" one.

Gendered languages also have agreement systems, so that adjectives and verbs must have the same or similar endings. This allows more flexibility in word order, so word ordering can be used for other meaningful things.

In Russian, for example, "chelovek prishel" means "the man came", but "prishel chelovek" means "a man came". Russian has no definite-indefinite noun morpheme(s) but the category is still there in Russian minds, so they use word order to signify the same categories as English the and a do.