Mathematical truths are discovered Artistic truths are mediated.
Mathematicians generally agree on what is mathematically correct. Artists generally have no idea what is artistically correct.
Math illuminates the supportive skeletal structure of thought whereas Art illuminates the metaphoric wind, which blows through that structure.
Science reveals the body of "God" and Art reveals "God's" mind -- or is it the converse?
Pure Mathematics has no expression for metaphor however; it does provide us a structure that can be used for it.
In general, the mathematician is not interested in finding truths through nonsense as opposed to the artist who is.
The goal of art is to go beyond language. Mathematics is a language to describe what is beyond us.
Artists have an insouciant tendency to get lost in their imagination Mathematicians have an attentive tendency to map their imagination
A mathematical theory seems to come in a flash of intuition before the final product is rigorously constructed.
An artistic theory seems to come much after the artwork that has been constructed in a flash of intuition.
Mathematical creations are not unique in the sense that they could be discovered by anyone.
Artistic creations are uniquely invented by individuals.
Mathematics, among other things, is a language.
Art, among other things, uses language.
In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it’s the exact opposite. —Paul Dirac
Please feel free to add any other difference you can think of, and also to question the proposed ones.
This thoughts where originally written by Kaz Maslanka, in his blog called Mathematical poetry.