Maxime Bôcher (1867 - 1918)

I like to look at mathematics almost more as an art than as a science; for the activity of the mathematician, constantly creating as he is, guided although not controlled by the external world of senses, bears a resemblance, not fanciful I believe, but real, to the activities of the artist, of a painter, let us say. Just as one cannot become a painter without a certain amount of skill, so one cannot become a mathematician without the power to reason accurately up to a certain point. Yet these qualities, fundamental though they are, do not make a painter or mathematician worthy of the name, nor indeed are they the most important factors in the case. Other qualities of a far more subtle sort, chief among which in both cases is imagination, go to the making of a good artist or of a good mathematician.

Bulletin of the American Mathematical Society 11 1904, 133.