I know that Xcode still lets you write apps in Objective - C, but there is hardly any (new) documentation, and very few new apps are written in it.
To add to the question - how viable would it be to learn and write a new app in Objective - C in 2021?
It depends what you mean by "viable".
Is it possible to learn and write a new app in Objective-C?
It it worth it?
Unless you have specific reasons for using Objective-C (such as an existing code-base, or a client who requires it).
Swift has many improvements, and is a far better language.
how viable would it be to learn and write a new app in Objective - C in 2021?
Are you already familiar with C or C++?
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Quinn “The Eskimo!” @ Developer Technical Support @ Apple
let myEmail = "eskimo" + "1" + "@" + "apple.com"
to answer your subject question: NO