Mathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians may express this pleasure by describing mathematics as beautiful or describe mathematics as an art form, or, at a minimum, as a creative activity.
Diagram from Leon Battista Alberti's 1435 Della Pittura, with pillars in perspective on a grid
Aesthetics is the branch of philosophy concerned with the nature of beauty and the nature of taste; and functions as the philosophy of art. Aesthetics examines the philosophy of aesthetic value, which is determined by critical judgements of artistic taste; thus, the function of aesthetics is the "critical reflection on art, culture and nature".
A man enjoying a painting of a landscape. The nature of such experience is studied by aesthetics.
Rainbows often have aesthetic appeal.
The Mandelbrot set with continuously colored environment