You're implying that if something can be outdone it doesn't have a purpose, which seems to rule out purposes for pretty much everything.
I'm sure there's always someone that can write books or maths papers or symphonies better than you. I don't think this robs you of purpose, unless your purpose is to be the absolute best at something.
Anyway, I find it curious that you would say logic is a quintessentially human trait, because humans are naturally quite bad at logic.
The difference between being outdone by another human and being outdone by a computer is that the computer's efforts are nearly infinitely reproducible, given the processing power.
So a more apt analogy would be if there was someone inside every cellphone who could write books, papers, or symphonies better than you. That day is coming.
I'm sure there's always someone that can write books or maths papers or symphonies better than you. I don't think this robs you of purpose, unless your purpose is to be the absolute best at something.
Anyway, I find it curious that you would say logic is a quintessentially human trait, because humans are naturally quite bad at logic.