Mathematicians have a distinctive sense of beauty: they strive to present their ideas and results in a clear and compelling fashion, dictated by (i) __________ as well as by logic.
The sentence begins by stating that mathematicians have a distinctive sense of beauty. This statement is then elaborated after the colon, where their presentation of ideas and results are said to be dictated by __________ as well as logic. Clearly since their beauty is being elaborated on, the word for the blank should be aesthetics, which is the branch of philosophy which deals with questions of beauty and artistic taste. The other element of their presentation is of course logic, and that is explicitly stated.