Personally I'd say an Art with the personality of a Science. A very different intellectual urge is satiated when you do maths to when you do science.
The most mysterious thing about mathematics is how useful certain, seemingly abstract, areas of it are.
For instance the fact that certain techniques in Algebraic Topology, invented solely for classifying spaces in pure mathematics have a use in modern particle physics is very bizarre.
Although I'm always impressed by how the different areas are used in proofs from other areas. For instance there is an analytic, topological and algebraic proof of the fundamental theorem of algebra. That connectedness between branches of mathematics that were conceived for entirely different reasons is what I find most unusual, probably more so than its applicability to science.
Edited by Son Goku, : Title