Back at university, one of my lecturers had a story about having to convince a company to cancel a contract they'd signed with a different lecturer, call them Bob, because the software Bob had agreed to write had provably impossible performance characteristics.

I forget the details, I think it was not quite as bad as "O(1) sorting for any length list" (not even 100% sure they actually told us the specifics) but it was something along those lines.