Whereas painters and musicians are likely to be embarrassed by references to the beauty of their work, mathematicians enjoy discussions of the beauty of mathematics. Professional artists stress the technical rather than the aesthetic aspects of their work. Mathematicians, instead, are fond of passing judgment on the beauty of their favored pieces of mathematics. A cursory observation shows that the characteristics of mathematical beauty are at variance with those of artistic beauty. Courses in "art appreciation" are fairly common; it is unthinkable to find any "mathematical beauty appreciation" courses. We will try to uncover the sense of the term "beauty" as it is used by mathematicians.