I feel that the fields of art and science often overlap.
Major scientific breakthroughs have been products of scientists' creative imagination rather than their meticulous,
analytical research. Perhaps art is descriptive and revealing, while
science is more reductionistic. When it comes to the generation of
concepts and novel frames of reference, creative thinking, rather than
critical thinking, comes into play. However, this does not mean one should
belittle the analytical strength of science. Leonardo da Vinci grasped geometry and perspective effortlessly and used creative thinking to
conceptualize and then add detail. Still, that does not
necessarily mean the airplane he designed could have actually taken
flight.
My point is that dichotomies arise because we try to use common
frames of references. Science has aesthetic appeal in its images and phenomena, and art can be as rigorous as science when it comes to
perfection, as in music or painting, for example. Studying mathematics involves the
manipulation of complex abstractions, as does composing a symphony. For both
the mathematician and the composer, it can be an equally creative
experience.