Wilfred Bion frequently resorts to mathematical thought in his quest for abstractions that are able to account for “elements of psychoanalysis”. Among the mathematical concepts to which he resorts, the concept of extension plays a central role. The author’s hypothesis is that Bion borrowed it from Alfred North Whitehead, whose book An Introduction to Mathematics, published in 1911, he is known to have read. The examples given by Whitehead and Bion to illustrate the process of extension are almost the same. It is on the basis of this concept, arising from the theory of numbers, that Bion accounts both for the psychic growth of each individual starting from his early sensory experiences and for the analytic process thanks to transference interpretations in three registers, namely, 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 in conducting the analysis. This is illustrated by clinical material from the analysis of an autistic child