*To infinity and beyond*

**Name: **Rózsa Péter**Nationality:** Hungarian**Lived: **1905-1977**Fields**: Mathematics**Claim to fame:** One of the founders of recursive function theory

In a time of great political upheaval, the Hungarian mathematician Rózsa Péter (1905-1977) overcame the obstacles put in her way and went on to a successful career in the subject that she loved. Building on the work of Kurt Gödel, she carried out innovative research in the field of recursive functions and wrote a number of successful mathematical texts.

### The end of an empire

When Rózsa Politzer was born to a Jewish family in Budapest on 17 February 1905 the city was still part of the vast and powerful Austro-Hungarian empire. By the time she left Maria Terezia Girls’ School in 1922, the empire had crumbled and Hungary was in political turmoil. Like many of her compatriots with Germansounding names, Rózsa changed hers to a more traditional Hungarian surname.

#### Inspired by numbers

The young Rózsa had been fascinated by science at school and so she enrolled at the oldest and largest university in Hungary, the Pázmány Péter University (renamed Eötvös Loránd University in 1950) to study chemistry. She soon found that her passion lay elsewhere, in the field of mathematics, and switched degree course to pursue this. Rózsa was taught by some of the most eminent mathematicians of the day, including Lipót Fejér and Jósef Kürschák. Whilst at university, she also met László Kalmár, with whom she would collaborate for years to come.

### “Mathematics is beautiful”

Graduating in 1927, Rózsa was unable to find a permanent position, so she took jobs tutoring students privately and teaching in high schools. At the same time, she began her graduate studies, initially focusing on number theory. Rózsa became disheartened when she found that her results had already been proven by someone else. For a while, she turned her interests elsewhere, including to writing poetry, before her friend Kalmár convinced her to resume mathematical endeavour. He encouraged her to look at the work of Kurt Gödel, the Austrian-American mathematician, on the subject of incompleteness.

#### A new field

Rózsa focused on Gödel’s studies of recursive functions. She made her own, different proofs and, in 1932, she presented a paper at the International Congress of Mathematicians in Zurich, Switzerland. For this research, Rózsa was awarded her PhD summa cum laude in 1935. The work also helped to found the modern field of recursive function theory as a separate area of mathematical research and her later book, Recursive Functions (1951) was the first book devoted exclusively to the topic. History has largely overlooked this contribution, however, and Rózsa has been denied the recognition she deserves.

#### Triumph through adversity

In her own lifetime, Rózsa did gain some of the respect she warranted. In 1937, she was appointed as contributing editor of the *Journal of Symbolic Logic*. Just as her career was beginning to take off, a setback materialised in the form of politics. In 1939, Hungary’s pro-Nazi government passed anti-Jewish laws that forbade Rózsa from teaching and which led to her being briefl y confined to a Budapest ghetto. Undeterred, Rózsa continued her research work throughout the Second World War. It was during this period that she wrote her work *Playing* *with infinity*, which discussed the fields of number theory and logic in terms accessible to the lay reader.

#### Aunt Rózsa

When the war ended in 1945, Rózsa was granted her first full-time teaching position when she joined the faculty of the Budapest Teachers’ Training College. In 1952, she was the first Hungarian woman to be made an Academic Doctor of Mathematics. She taught at the college for a decade, until it closed in 1955, at which point she was made a full professor at Eötvös Loránd University. A popular lecturer, she was known as ‘Aunt Rózsa’ to her students and carried on teaching until the age of 70.

Even after her retirement, Rózsa continued her mathematical work, and her final book *Recursive functions in computer theory* was published in 1976, the year before her death.

### Scientific achievements

Rózsa Péter was passionate about mathematics and equally fervent about passing on her love of the subject. She was active in promoting the teaching of mathematics in schools, particularly for girls and young women, and gave lectures on how “mathematics is beautiful”.

Her own research work in the field of recursive function theory broke new ground and helped to establish it as a separate mathematical field. Although largely forgotten since her death, Rózsa was feted in her own lifetime. Amongst the prizes awarded to her were the Kossuth Prize, given by the Hungarian government in 1951 for her work* Recursive Functions*; the Mano Beke Prize from the Janos Bolyai Mathematical Society in 1953; and the State Prize, Silver Degree (1970) and Gold Degree (1973). In 1973, she was also elected the first female mathematician to become a member of the Hungarian Academy of Sciences.

Péter also found success with some of her published works, most notably *Playing with infinity* (1943), which was translated into at least 14 languages, and *Recursive functions in computer theory* (1976), which was only the second Hungarian mathematical book to be published in the Soviet Union – its subject matter is considered indispensable to the theory of computers.