Happy Ada Lovelace Day!
Rózsa Péter (1905-1977) was a Hungarian mathematician and early contributor to the theory of (primitive) recursive functions. She received her PhD in 1935 from (what is now) Eötvös Loránd University in Budapest. Her fellow student Laszlo Kálmár had introduced her a few years earlier to the then brand-new work of Gödel, and she proceeded to study the class of (primitive) recursive functions first clearly defined by Gödel in his 1931 incompleteness paper. In a number of articles in the 1930s, she laid the groundwork for the study of hierarchies of sub-recursive functions and clarified the notion of primitive recursive function. I’ll just mention four of her contributions on the subject: In her paper, “Über den Zusammenhang der verschiedenen Begriffe der rekursiven Funktion” (Math. Ann., 1935) she showed that course-of-values recursion and nested recursion can be reduced to ordinary primitive recursion. In “Konstruktion nichtrekursiver Funktionen” (Math. Ann., 1935), Pétér simplified and expanded on Ackermann’s work, and proved that there are multiply recursive but not-primitive recursive functions. In “Über die mehrfache Rekursion” (Math. Ann., 1937), she studied multiple recursion in more detail and showed that the hierarchy of k-recursive functions is proper. In “Zusammenhang der mehrfachen und transfiniten Rekursionen” (JSL, 1950), she proved the equivalence of k-fold recursion and transfinite recursion along ωk. Her early work on primitive recursive function theory is set out in her monograph, Rekursive Funktionen (1951), translated into English as Recursive Functions (1967). She also wrote a popular book on mathematics, Playing with Infinity, which was translated into 14 languages.
Pétér was barred from teaching in 1939 due to her Jewish heritage, but obtained positions at the Budapest Teacher’s College in 1945 and at her alma mater in 1955. She was the first female mathematician to be elected to the Hungarian Academy of Sciences. She retired in 1976.