"If a painting contains no abstraction nor impressionistic elements, it is a kite that will never fly. But if the painting completely breaks the connection between human feeling and the object portrayed, the kite string has been broken. I try to keep the line unbroken."

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In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency towards intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations.

— David Hilbert