From Lev Grossman's Q&A today

At Quora:

The two things that most influenced the way magic works in The Magicians, apart from reading an eff-ton of other novels with magic in them, are these:

One, studying the cello for ten years. The physical rigor and at times discomfort of that, of trying to use your misshapen fallen body to produce transcendent beautiful music, has a lot to do with the way I imagine magic feels.

...

I feel some nostalgia for the days when magic was wilder. Gandalf for example: you never knew what he could or couldn't do, and that was kind of exciting.

...

I've studied [JK Rowling's] books over and over and over again.