Full Idea
What makes a question interesting or gives it aesthetic appeal is its focussing of the project of advancing mathematical understanding, in light of the concepts and systems of beliefs already achieved.
Gist of Idea
The interest or beauty of mathematics is when it uses current knowledge to advance undestanding
Source
Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.3)
Book Reference
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.206
A Reaction
Kitcher defends explanation (the source of understanding, presumably) in terms of unification with previous theories (the 'concepts and systems'). I always have the impression that mathematicians speak of 'beauty' when they see economy of means.
Related Idea
Idea 12426 The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher]