Rózsa péter: recursive function theory’s founding mother

Abstract

Take a person who was a major founder of a thriving area of mathematical research. Say that this person wrote, in addition to papers that are still cited 50 years later, the first book in that field. And say that this same person also authored a classic book of mathematical exposition for the general public. Now say that this person was a woman. You would expect, even if her name were not a household word in the mathematical communi ty at large, that at least she would be frequently mentioned in the literature that details the significant achievements of female mathematicians. But such is not the case. R6zsa P~ter (1905-1977) is the person in question, a person w h o m Stephen Kleene once described as "the leading contributor to the special theory of recurs ive functions. ''1 We feel that P~ter's many contributions to mathematics deserve much greater recognition than they have received. P~ter had set out to work in chemistry, but during the course of her studies at Lorand E6tvOs University in Budapest she attended the lectures of Lip6t Fej~r. These talks sparked her mathematical interest, and she changed fields. By the time P~ter graduated in 1927, it was as a would-be seco n d a r y school t e a c h e r of m a t h e m a t i c s and physics. However, there were quite a few more mathematicians than openpositions in Hungary at that time. P~ter, like many of her colleagues, could not obtain full-time employment and made her living by tutoring and the like. Eighteen years later, in 1945, P~ter finally secured a full-time position, joining the faculty of the Budapest Teachers Training College, where she remained until the college closed in 1955. She then assumed a full professorship at Lorand E6tv6s University, a post she held until her retirement in 1975. Just as P~ter had switched from chemistry to mathematics, she also changed fields within mathema t i c s -o r rather, after abandoning one field, she helped found another! Originally, P~ter's research area was number theory. However, some theorems she obtained turned out to be independent rediscoveries of results that had already been proved by Robert Carmichael and L. E. Dickson. This discouraged P~ter so much that she backed away from mathematics altogether, devoting herself to writing poe t rymthroughout her life, P~er was also a talented poet and translator of poetry. ~ At the beginning of the 1930s, she was brought back into the mathematical fold by L~szl6 Kalm~. Kalm~tr had been a classmate of hers at Lorfind E6tvOs Universi ty , and they became lifelong friends and colleagues. He told P6ter about Kurt G6del's recent work related to incompleteness. Without knowing how G6del had proved various results in his landmark paper, she was able to devise her own, different proofs. This experience not only restored P~ter's self-confidence, but it also pointed her research in the direction she would follow from then on. P~ter realized that the primitive recursive functions 2 G6del used were important in their own right, not just as a tool for proving incompleteness. This insight led to her 1932 paper, 3 presented at the International Congress of Mathematicians in Zurich, in which P~ter became the first person to propose the study of recursive functions as a field in itself. She then proceeded to write many of the first papers in that field. Between (continued on page 61)