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Fontenelle has said: "Mathematicians are like lovers… Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him and from this consequence another." Ernst Mach in a less poetic vein adds: "The power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations" (Bell, 1937).
The present study is an attempt to bring together certain observations concerning the psychological process of "pure" mathematics and to formulate them in terms of the economic and structural concepts of psychoanalytic theory. That data is derived largely from the analysis of a gifted young graduate student in mathematics who is also suffering from a so-called "strephosymbolia" in reading and writing. The analysis of several episodes of mathematical "illumination" has given rise to the present thesis.
Pure mathematics is a creative process that stands midway between the arts and sciences. It attempts to conceptualize according to its own set of rigorous rules the properties of number and space that are too complex or beyond the ken of immediate apprehension by the sensory-perceptual apparatus. The following theoretical concepts will be developed: The concept of number arises normally in connection with certain stages of the maturation of the perception apparatus during the oedipal period. In those with a special mathematical "gift" it is probable that this maturational sequence takes place at an earlier period in ego development so