There is an almost inevitable comparison to science when you start talking about magic(k) in a non-theorectical manner. Now its going to be fairly hard to avoid some generalisations so please, bare with me.
For the most part a mathematician or scientist of most any type will have… issues with the idea of magic as a practical method of achieving certain ends. However, the overall concept behind their methods are not all that dissimilar to those behind the use of magic(k). Maths uses thought processes in the form of number strings, formula and equations to manipulate the materials of the universe to cause a certain effect.
Magic(k) uses thought processes based around symbols, language, and perception to manipulate the materials of the universe. Thought becomes words spoken or written, symbols become representative of complex metaphors and ideas. Perceptions of concepts directly affect a persons thought – what one person sees as distinctly ‘black’ and ‘white’ magic(k) another person might see as choosing the right tool for the right job.
Which makes me wonder: could what pagans-heathens call magic(k) be advanced in a similar way to science?