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Doctoral programs in the fine arts, instead of coming up with their own ways of doing things, tend to adopt standards from the humanities, which themselves tend to adopt standards from science. Because of being preoccupied with trying to look like other disciplines, artistic thinking within artistic doctorates gets suppressed. But if we look into science directly and not through this second-hand approach, we can find aspects of scientific thinking that are closer to art than to the humanities. In this paper, I give examples of artistic thinking in the work of various scientists and mathematicians: a non-fiction book that uses fiction (Douglas Hofstadter's book Gödel, Escher, Bach), a linguistic analysis that concludes with a story (Livia Polanyi's book Telling the American Story), scientific lectures with unusual formal aspects (Roger Penrose's "VJing" of multiple layers of foils through an overhead projector, David Deutsch's Lectures on Quantum Computation), and a collective hiding behind a fictional mathematician (Nicolas Bourbaki). I also briefly introduce the problem of verbal overshadowing and the effects it may have on the creative process in art. [ABSTRACT FROM AUTHOR]