D.W. Gotshalk. The Journal of Aesthetics and Art Criticism
Vol. 13, No. 1 (Sep., 1954), pp. 80-85
Expression is some elements of an artwork (materials, forms) making some other deeper or more critical elements manifest (i.e. suggestive). To achieve such an effect, the elements must cohere well enough. Once achieved, such an expression becomes an intrinsic property of the object, independent of the subjective experience of an observing mind (i.e. objective criteria in art). The expressiveness may be interpreted to convey diverging messages to observers, a phenomenon ascribed to differences in gender, class or culture.
Aesthetic expression differs from expressions in the natural sciences in that it draws attention to the perception itself instead of other higher-end interests, such as knowledge or other pragmatic ends. When it comes to Mathematics, however, similarities outweigh the differences. The a priori nature of mathematical knowledge make a distinction from science.
When the mathematical expression compounds values and properties to awaken a piece of knowledge intrinsic to the audience’s mind, the process is similar to an artwork creating a personal aesthetic experience appreciated in and of itself. The epistemic feelings of certainty and fluency generated through the process of understanding a mathematical equation or proof, the amazement at the novelty and creativity embedded in a particular theorem, and the “eureka” moment at the discovery of deeper insights in a geometrical diagram, all amount to qualities that draw attention to the mathematical object itself.
Hence, the aesthetic criteria used by Mathematicians may not be that different from those used in paradigmatic art after all.