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There is in this field of thought [mathematics] a type of creativity found only in the fine arts. The men who first constructed the various systems of non-Euclidean geometry participated in a creativity quite similar to that of Rembrandt or Michelangelo. Mathematical imagination at least equals and often surpasses that required by the other fine arts, since the mathematician is neither aided nor confined by material forms of expression. His is a world of pure abstraction....the creative mathematician often generalizes the original solution of a question and from it builds himself a logical edifice, posing and investigating questions of abstract structure without any regard to their connection with the world around him. He designs and constructs with a taste for order and harmony, pattern, symmetry, precision and generality.

William Berlinghoff
Mathematics: The Art of Reason
1968, p. 2