One interesting connection between science and art is that they are both concerned with the question of what is irreducible.
Science asks what is irreducible in the world around us. The great figures in the history of science, from Euclid to Einstein, produced beautifully simple explanations for complex observations.
Similarly, art also looks for the irreducible truth, stripping away all that is inessential. Except that in the case of art, what is considered essential is not the world around us, but rather our own human condition. In this regard art differs from entertainment, which merely seeks to divert and amuse.
A work of art, such as Becket’s Endgame, Picasso’s Guernica, Munro’s Passion or Beethoven’s ninth symphony, may indeed entertain, but its primary purpose is to illuminate some essential truth about ourselves.
In other words, both science and art seek truth, but they do so in very different ways. For example, both can teach essential truths about pain. Science will show you the connection between sensory stimulus and cognitive effect. Art will punch you in the nose.