I am learning Python because it appeals to me as a mathematician but also has many useful libraries for scientific computing, image processing, web apps, etc etc.
It is frustrating to me that for certain of my interests (eletronic music or installation art) there are very specific programming languages which seem better suited to these purposes, such as Max/MSP, PureData, and ChucK -- all quite fascinating.
My question is, how should one approach these different languages? Should I simply learn Python and manage the others by using plugins and Python interpreters in them? Are there good tools for integrating the languages, or is the proper way simply to learn all of them?
I would say learn them all. While it's true that many languages can do many things, specialised languages are usually more expressive and easier to use for a particular task. Case-in-point is while most languages allow shell interaction and process control very few are as well suited to the task as bash scripts.
Plugins and libraries can bridge the gap between general and specialised languages but in my experience this is not always without drawbacks - be they speed, stability or complexity. It isn't uncommon to have to compile additional libraries or apply patches or use untrusted and poorly supported modules. It also isn't uncommon that the resulting interface is still harder to use than the original language.
I know about 15 languages well and a few of those very well. I do not use my prefered languages when another is more suitable.