Could learning shortcuts for maths such as the trachtenberg system has negative effects on your intelligence?
The idea of intelligence is that it is an inate ability (although which kinds of ability are the subject of much debate). So learning anything would not be able to change your intelligence. Specifically, though, systems of mental computation (such as Trachtenberg) seem to be of little practical benefit these days. But there is a lot of interest in the benefit of keeping your mind active by learning anything. If you have the time, I would think learning Trachtenberg would minimally be useful mental stimulation. Of much more use would be figuring out how the methods really work, meaning how the underlying mathematics (arithmetic) gives the correct result and how the Trachtenberg algorithms simplify the computational effort enough to be performed mentally.