In my belief and opinion magic is transcendent, similar to what beit mentioned however I believe that magic is all the greatness that which science cannot calculate, compute, and formulate. Magic/k is the science or higher reasoning and consciousness, something that cannot be confined to a single definition.
Magic is a level of physics that go beyond the limited pathways and constructs of ordinary minds, and yes even some brilliant scientists and geniuses have ordinary minds. If you look at an empty Venn Diagram science would be in the left side, mathematics would be in the right side, and magic... well that would be left in the overlapping area of the Venn diagram.
Many people have tried to prove the existence of magic, through science and facts, however that is such a limited construct of reasoning and proof. Does one need to see it to believe it, well with scientists more often than not yes. So to compare the two is pointless if you sit down both a scientist and a person who believes in and practices magic, ask them to debate it until they could both come to a conclusion that they can agree on, preferably yes it exists or no it does not. However that would be a never ending debate, the most probable outcome is that one or both will become exhausted and come to a draw with no energy to continue.
Magic is what is is, and science is science, they play similar rules, use formulas and equations and such etc. I would have to say that science is physical law where magic would be spiritual law, and that's my final thought and conclusion.
Brightest Blessings, Peace Be With You,