Rózsa Péter's original name was Rósa Politzer but in the 1930 she, like many other Hungarians, changed her German style name to a Hungarian one.
Rózsa Péter studied at Loránd Eötvös University in Budapest where her interest in mathematics was brought about by Fejér's lectures. Another one to have an important influence on Rózsa Péter was László Kalmár who was a fellow student at Loránd Eötvös University.
After graduating in 1927 Péter earned a living tutoring mathematics, unable to obtain a permanent job. Her first post, at the Budapest Teachers Training College, was obtained in 1945. Péter's years at the teacher's college produced the charming book Playing with Infinity (first in German, 1955). When the College closed in 1955 she became a professor at Loránd Eötvös University and remained in this post until she retired in 1975.
Her first research topic was number theory but she became discouraged on finding that her results had already been proved by Dickson. For a while Péter wrote poetry but around 1930 she was encouraged to return to mathematics by Kalmár. He suggested Péter examine Gödel's work and in a series of papers she became a founder of recursive function theory.
Walter Felscher, in a personal communication to me [EFR], described the context of Péter's work on recursive function theory:-
Recursive functions were invented during the 1920s in the Hilbert school, but nothing much was proved about them. Developing ideas of Herbrand, Gödel defined the more general 'general' recursive functions (to which Ackermann's function belongs) in his Princeton lectures 1933-34; soon after, the old functions received the name 'primitive recursive', and the general ones lost their adjective.
In a series of articles, beginning in 1934, Péter developed various deep theorems about primitive recursive functions, most of them with an explicit algorithmic content. I admire this work, and it may well be said that she forged, with her bare hands, the theory of primitive recursive functions into existence.
[On the other side, it was Kleene who, having attended Gödel's lectures, developed the theory of general (including partial) recursive functions; this is a much more conceptual than computational area.]
In 1951 Péter collected what was known by then, including her own work, in the book "Rekursive Funtionen". An English translation appeared only in 1967. It was the first book devoted exclusively to this topic, but
(1) there had been extensive chapters on this matter earlier in Hilbert-Bernays (1934-1939) where some of Péter's work was quoted, and
(2) the English speaking world did not read her book but read, instead, Kleene's book of 1952.
In 1952 Kleene described Rózsa Péter in a paper in Bull. Amer. Math. Soc. as
the leading contributor to the special theory of recursive functions.
From the mid 1950s Péter applied recursive function theory to computers. In 1976 her last book was on this topic Recursive Functions in Computer Theory.
Article by: J J O'Connor and E F Robertson