How can I keep multiple profiles for Emacs?
In a single init file. As others have suggested in the comments above, this is easily done in emacs without having multiple profiles.
A single init file can keep the settings for multiple modes. Based on your question, those modes would be Clojure, Mathematica, and Text modes, and perhaps others in future. Depending on which file is currently being edited/active, those settings, configurations, keyboard shortcuts, etc., become active. In emacs terminology, grouping such behaviors is called modes, of which there are major and minor kinds.
The effect of this flexibility is that you don't have to restart emacs with different profiles. Nor do you have to run multiple emacs instances. This common misunderstanding comes from other editors, but not emacs. In emacs you switch from a clojure buffer, a mathematica buffer, and a text file without restarting.
You don't have to go into intricacies of modes to just start using them to great benefit. The easiest approach is to load pre-prepared init files that contain those modes. One place to start is the emacs starter kit. It comes with many modes ready for use and has an easy approach to customization for new emacs users.