Due to the effects of the Great Depression, many university graduates could not find work and Péter began private tutoring.

However, she was convinced to return to mathematics by her friend László Kalmár, who suggested she research the work of Kurt Gödel on the theory of incompleteness.

[5] Péter presented the results of her paper on recursive theory, "Rekursive Funktionen", to the International Congress of Mathematicians in Zürich, Switzerland in 1932.

In 1936, she presented a paper entitled "Über rekursive Funktionen der zweiten Stufe" to the International Congress of Mathematicians in Oslo.

[3] These papers helped to found the modern field of recursive function theory as a separate area of mathematical research.

During World War II, she wrote her book Playing with Infinity: Mathematical Explorations and Excursions, a work for lay readers on the topics of number theory and logic.

[4] In 1951, she published her key work Rekursive Funktionen,[9] the first book on modern logic by a female author, later translated into English as Recursive Functions.