Michael Atiyah quoted Hermann Weyl in the opening talk at the second Heidelberg Laureate Forum:

I believe there is, in mathematics, in contrast to the experimental disciplines, a character which is nearer to that of free creative art.

There is evidence that the relation of artistic beauty and mathematical beauty is more than an analogy. Michael Atiyah recently published a paper with Semir Zeki *et al* that suggests the same part of the brain responds to both.

The quote makes sense. Consider the construction of a mathematical theory. There are many parameters that can be chosen, such as what structures to add and what properties to endow to the various objects. They are not constrained by empirical input (such as in physics). The only thing remaining is aesthetic input: are the structures and the theorems that follow from them appealing? Thus, math has been consciously built to please the aesthetic parts of the brain.

This throws the “unreasonable effectiveness” problem into relief: why should structures chosen for their aesthetic appeal be so useful?