There is the much quoted story about David Hilbert, who one day noticed that a certain student had stopped attending class. When told that the student had decided to drop mathematics to become a poet, Hilbert replied, "Good--he did not have enough imagination to become a mathematician."

From p. 95 of Paul Hoffman's 'The Man Who Loved Only Numbers: The Story of Paul Erdos', 1998.

There's some masterful trigonometry in Erdos's paper on the optics of a two mirror imaging system, in Journal of the Optical Society of America. It took great imagination to even consider that such a treatment might be possible.