"The aim is to be happy."
Translation:Amaç mutlu olmak.
Because that would mean: To be happy is a goal.
Not THE goal. And since there is no way to mark the "the"… the only recourse is to circumvent the problem by paraphrasing.
the cases (except for possessive) are never for subjects, "the aim" is the subject of this sentence. If you say "amacı mutlu olmak", it means "his aim is to be happy"
Ok, actually it would be completely fine to say that in English (although I take Ektoraskan's point below about why it doesn't work with the Turkish). Leading off with the infinitive is common in general or gnomic statements like this one, as, for example, in Lady Bracknell's famous pronouncement in The Importance of Being Earnest: "To lose one parent, Mr. Worthing, may be regarded as a misfortune. To lose both looks like carelessness".
i think it's fine in turkish too. you can say mutlu olmak amaç. since you don't say 'mutluk olmak BİR amaç(tır).' it may mean to be happy is an aim or the aim. it depends on the context. but i think they are not quite interchangeable. the emphasis is changed if you change their places.