Meetings of the New York Psychoanalytic Society

June 23, 1953. ON MATHEMATICAL 'ILLUMINATION' AND THE MATHEMATICAL THOUGHT PROCESS. Victor H. Rosen, M.D.

A gifted young graduate student in mathematics provided the opportunity for a study of the psychological processes of pure mathematics, here formulated in analytic economic and structural concepts. Pure mathematics conceptualizes the properties of number and space. Its power rests on its evasions of all unnecessary thought and on its wonderful economy of mental operation. Autonomous ego functioning cannot explain the mathematical process, and certainly cannot explain the mental event known as 'illumination' which Kris describes as 'controlled regression' and which appears to be its decisive feature. As with wit, humor, fantasy and other experiences, the preconscious process is re-enforced with id energy. In one of the two experiences of 'illumination' studied, the patient wrote his father, requesting a book needed to solve a complex mathematical problem. When the package arrived but before it was unwrapped, he had a sudden inspiration for a short-cut method of reaching the same result by an original method. The other episode of 'illumination' occurred while he was brooding about an acute disappointment with his girl. Analysis of the first experience revealed that the process of illumination condensed at least three acts of seeing, gratifying, scoptophilic impulses. A considerable variety of other gratifications was represented in the receipt of the book: passive feminine strivings, access to unconscious fantasies, and a wealth of fantasy about interfering in the parental sexual relationships. The latter was re-enacted in the transference. In both episodes, mathematical thinking was also substituted for aggressive feelings. With those who have a special mathematical gift, it is probable that maturation is precocious in such a way as to allow the coexistence of a primitive conception of number and quantity with certain archaic mechanisms, which later