Rózsa Péter on the Philosophy and Foundations of Mathematics: A Reappraisal

Rózsa Péter 1905–1977

Biography

The Hungarian mathematician and logician Rózsa Péter (1905–1977) is best known as a founder of recursion theory. Her works broke new ground and helped to establish recursion theory as a separate mathematical discipline.

Born to a Jewish family in Budapest on 17 February 1905, she attended Maria Terezia Girls’ School and studied at Pázmány Péter University (renamed Loránd Eötvös University in 1950) in Budapest. After her graduation in 1927, Péter was unable to find a permanent position, so she took jobs tutoring students privately and teaching in high schools.

László Kalmár, who was a fellow student at Pázmány Péter University at that time, called her attention to the subject of incompleteness theorems published by Kurt Gödel in 1931. In 1932, Péter presented her first paper on recursive functions at the International Congress of Mathematicians in Zurich, Switzerland. In 1935, she received her Ph.D. with summa cum laude. In 1937, Péter became a contributing editor of the Journal of Symbolic Logic. Just as her career was beginning to take off, her employment position became worse when the fascist government passed anti-Semitic laws and Jews were no longer allowed to teach. During this difficult period, Péter wrote her popular book Playing with Infinity, which was first published in Hungarian in 1944. Shortly after the war, Péter was granted her first full-time teaching position at the Budapest Teachers Training College. When the college was closed in 1955 she became a professor at Loránd Eötvös University and remained in this post until she retired in 1975. She died on 16 February 1977, at the age of 72.

Péter received many honors and became one of the leading figures who paved the way for the acceptance of mathematical logic in Hungary. She was a passionate teacher of mathematics, who helped to introduce logic as a subject to university curricula. In 1973, she was elected the first female mathematician to become a member of the Hungarian Academy of Sciences.

Selected Bibliography

(1932). Rekursive Funktionen. In: W. Saxer (Ed.). Verhandlungen des Internationalen Mathematiker-Kongresses Zürich, vol. 2 (pp. 336–337). Orell Füssli Verlag.

(1935). Über den Zusammenhang der verschiedenen Begriffe der rekursiven Funktion. Mathematische Annalen, 110, 612–632.

(1935). Konstruktion nichtrekursiver Funktionen. Mathematische Annalen, 111, 42–60.

(1941). Az axiomatikus módszer korlátai (The bounds of the axiomatic method). Matematikai és Fizikai Lapok, 48, 120–143.

(1951). Rekursive Funktionen. Budapest: Akademiai Kiado.

(1961). Playing with Infinity (trad. by Z. P. Dienes). New York: Dover Publications. (Originally published in 1944 as Játék a végtelennel. Budapest: Dante Könyvkiadó.)

(1981). Recursive Functions in Computer Theory. Ellis-Horwood.

Abstract

Stephen Kleene (1909–1994) once praised the Hungarian mathematician and logician Rózsa Péter (1905–1977) as “the leading contributor to the special theory of recursive functions” (Kleene, 1952). Her works broke new ground and helped to establish recursion theory as a mathematical discipline. Today, Kleene is much better known in the philosophy of mathematics than Péter. In this chapter, I provide an overview of Rózsa Péter’s work and describe her active role in communicating these results to a broader audience in her book Playing with Infinity (1944/1961). First, I will briefly summarize the content and key statements of Péter’s book, including an overview of its reception. Second, I will focus on a case study: Péter’s popular sketch of Gödel’s proof. Third, I will contextualize this case study against the historical background of Hilbert’s program and the decision problem. This includes Péter’s research on recursion theory. Last, but not least, I will discuss Church’s thesis and Péter’s interpretation of it. I conclude with some reflections on the relevance of Péter’s work from a philosophical, conceptual and practical perspective.

When I began my college education,

I still had many doubts about

whether I was good enough for mathematics.

Then a colleague said the decisive words to me:

it is not that I am worthy to occupy myself with mathematics,

but rather that mathematics is worthy

for one to occupy oneself with.

Rózsa Péter*

* This is a quote from Péter’s essay “Mathematics is Beautiful” (Péter, 1990, 58). The essay dates back to a lecture delivered to high school teachers and students which Péter held in Rostock, German Democratic Republic, in 1963. The lecture was first published in 1964 in the German journal Mathematik in der Schule. The English translation by Leon Harkleroad appeared in the journal The Mathematical Intelligencer in 1990.