Bion frequently resorts to mathematical thought in his use of abstractions that account for “elements of psychoanalysis”; among these, the concept of extension plays a central role. The author's hypothesis is that Bion borrowed the concept of extension from Alfred North Whitehead, whose book An Introduction to Mathematics, published in 1911, Bion read. The examples that both Bion and Whitehead use to illustrate the process of extension are almost the same. It is on the basis of this concept of extension that Bion accounts for the psychic growth of each individual, and for the analytic process in terms of transference interpretations in three registers - the senses, the personal myth of the patient, and passion. Bion's description of extension in the psychoanalytical field helps to make explicit some aspects of the psychoanalytic process, with an emphasis on the intuition of the analyst. The author's argument is illustrated with clinical material from the analysis of an autistic child.