# Géza Grünwald

### Biography

**Géza Grünwald**was the son of Ármin Grünwald (1881-1943) and Katalin Sommer who were Jewish. Géza had a brother Gyula Grünwald, born in Pestszenterzsebet, a suburb of Budapest, in 1912. Ármin Grünwald was a house painter who tried hard to educate his sons but struggled to bring in a sufficient income. He did, however, send his two sons to an excellent school. Géza attended the St Stephen's Gymnasium in Budapest where he was taught mathematics by Lajos Erdős, the father of Paul Erdős. One of the pupils at St Stephen's Gymnasium was Paul Erdős and the two, both with a passion for mathematics, quickly became friends. Lajos Erdős realised that his pupil Géza was very talented and he also realised that his family were not really able to financially support their son's education at this school. Lajos supported Géza both with encouragement and with financial support.

Before we go any further we need to clear up a potential difficulty. There were two mathematicians in Budapest in the 1930s who were both named Grünwald, namely Tibor Grünwald and Géza Grünwald, the subject of this biography, but they were not related. Both published papers in the 1930s, both even have joint papers with Paul Erdős, and they were both members of the same group of young Jewish mathematicians meeting together in Budapest. Our archive also contains a biography of Tibor Grünwald but he is listed under the name Tibor Gallai which he adopted during World War II.

Géza Grünwald and Paul Erdős, who was about 30 months younger than Géza, used to walk a great deal in Városliget public park surrounding Hero's Square close to the city centre of Budapest. It was, and still is, one of the city's most popular public parks where many people go to relax and enjoy the sun. It contained a zoo and botanical gardens but Géza and Paul spent most of the time they were in the park trying to outdo each other in mental challenges and trying to beat each other in chess. Grünwald was an exceptionally talented chess player.

While still at the High School in 1927, Grünwald contracted tuberculosis. This was a serious disease and in the 1920s around 50% of those who entered sanatoria with the disease died within five years of contracting it. There was a large difference, however, depending on the sanatorium that the patient went to, with those having a much better chance of a complete cure if it was an expensive sanatorium which offered top quality care and medical attention. Grünwald's parents were not in a financial position to give him this type of sanatorium but Lajos Erdős offered the necessary financial support and Grünwald spent a whole year in a sanatorium, making a complete recovery.

Grünwald should have taken his final school examinations in 1928 but, of course, his illness and the year spent in the sanatorium meant this was not possible. After his recovery he sat his final school examinations in 1929 but, because of the disruption to his schooling, he did not gain one of the top places as would have been expected had his schooling been unaffected. Since Grünwald was Jewish, the fact that his school examinations were not outstanding meant big problems in obtaining a university place. We should explain why being Jewish led to this problem. In 1919 there was a Communist take-over of Hungary. A right wing government took over in 1920 and there was a rise of anti-Semitism with Jews attacked in the streets. In fact the anti-Semitism was written into law in 1920 with universities only allowed to have 5% of their students being Jewish. Grünwald's examination results were not good enough for him to obtain a university place in Hungary with these severe restrictions.

If he could not have a university education in Hungary, then he thought he might be able to gain admission to an Italian university. There were financial problems to this idea which had no easy solution. Again it was Lajos Erdős who came to the rescue. He approached Alfréd Haar who was the professor of mathematics at the University of Szeged and explained to Haar that Grünwald was an outstanding mathematician yet unable to gain admission to university. Let us spend a moment explaining how the University of Szeged had been created not long before this time.

Haar had been appointed to the Franz Josef Royal Hungarian University in Kolozsvár in 1912 and become a full professor there in 1917. Austro-Hungary was aligned to the Central Powers and during the first three years of World War I. In 1921 the Treaty of Trianon was signed which treated Hungary very severely. Its territory was reduced to only one third of its previous size. The terms of the Treaty meant that Kolozsvár was no longer in Hungary (it became part of Romania), so the University there had to move within Hungarian borders. At first it was sited in Budapest for a temporary period of two years before it moved to Szeged, where there had previously been no university. The Department of Mathematics, consisting of the Mathematical Seminary and the Institute of Descriptive Geometry, began operating in Szeged. The department consisted of Frigyes Riesz, Alfréd Haar, Rudolf Ortvay (who held the Chair of Mathematical Physics), and Tibor Radó who had been appointed as Haar's assistant. Following Lajos Erdős's recommendation, Haar invited Grünwald for an interview which went very well and he was accepted into the University of Szeged's mathematics programme.

Alexander Soifer writes in [2]:-

In the early 1930s Budapest, a group of young Jewish students regularly met in a park or took excursions to the countryside to discuss mathematics. ... the regular members of this remarkable group [were]: Paul (Pal) Erdős, Tibor Grünwald (later Gallai), Gergőr (Géza) Grünwald, Ester Klein, György (George) Szekeres, Lily Székely (later Sag), Paul (Pal) Turán, Endre Vázsonyi, and Marta Wachsberger (later Sved).This group met at the Anonymous Statue and called themselves the 'Anonymous Circle'. The mathematical discussions which went on within this Circle were perhaps more significant in Grünwald's mathematical training than his studies at Szeged. Paul Turán writes [6]:-

Grünwald's mathematical interests were wide-ranging. He used to talk about his experiences in Szeged to his friends in Budapest with much enthusiasm. ... Our group of young researchers in Budapest learned of and studied approximation theory through the works of Leopold Fejér. Grünwald regularly attended our weekly meetings which we held near the statue of Anonymous in the city park. There was no equivalent opportunity in Szeged so that it was natural that Grünwald became interested in issues discussed in our group.Grünwald's career at Szeged was highly successful. Beginning with his second year, he won a university prize in each of four consecutive years. In his final undergraduate year he did a project on interpolation and this earned him a university prize. He continued to undertake research on interpolation, advised by Frigyes Riesz, and submitted his doctoral thesis entitled

*Divergence phenomena of Lagrange interpolating polynomials*(Hungarian). He defended his thesis on 4 December 1935 and was awarded a doctorate. The 22-page thesis was published in 1935 in Hungarian. He published two papers in German, namely

*Über Divergenzerscheinungen der Lagrangeschen Interpolationspolynome*Ⓣ (1935) and

*Über Divergenzerscheinungen der Lagrangeschen Interpolationspolynome stetiger Funktionen*Ⓣ (1936). He remained at Szeged to gain a teaching qualification and he was awarded a diploma to teach mathematics and physics in September 1936.

Zoltán Lajos Bay (1900-1992) was appointed professor of theoretical physics at the University of Szeged in 1930. He was a physicist and engineer who developed various technologies. As well as being professor of theoretical physics at Szeged, Zoltán Bay took over the role of head of the research laboratory of the Egyesült Izzó (United Incandescent Lamp and Electricity Co.) factory in 1936. The research laboratory of this electricity company was in Budapest and in September 1937 Grünwald was employed by Zoltán Bay as a mathematician in the research laboratory.

On 22 May 1938 Grünwald married Anna Szilágyi who had been born in Miskolc, Hungary, in 1911. Anna, who had been a school friend of Grünwald's, was the daughter of Adolf Szilágyi and Ilona Kálmán. They lived at Szondi utca 95, Budapest, very close to the entrance to the Városliget public park. Anna and Géza Grünwald had one child, a daughter Eva Grünwald born in Budapest in 1939. Eva and her mother Anna are both listed in [2] as Holocaust Survivors while Géza Grünwald and his brother Gyula did not survive.

Grünwald published 18 papers in his short life before he was murdered in 1942 or 1943. His papers are in Hungarian, German and English. We list these papers at THIS LINK.

Today Grünwald is best known for the Grünwald-Marcinkiewicz Theorem. Lásló Szili and Péter Véeresi write in the Preface to [5]:-

In 1910, exactly hundred years ago, two outstanding mathematicians were born: (in alphabetical order) the Hungarian Géza Grünwald and the Polish Józef Marcinkiewicz. But we must note some other similarities. They proved in the same year (1935) the first version of their famous result (as today called) the Grünwald-Marcinkiewicz Theorem (G-M Theorem, for short). Both improved this first version and got the final form already in the next year; the theorem was a part of their PhD dissertations. And, finally, both were killed during the second world war: Géza Grünwald became a holocaust victim in 1942 while Józef Marcinkiewicz died in 1940 in the Katyn massacre.The Grünwald-Marcinkiewicz Theorem shows that Lagrange interpolation based at the zeros of Chebyshev polynomials can diverge everywhere even for continuous functions.

Now we come to Grünwald's death and must say straight away that its date is unclear. The above quote give 1942, other sources give 1943, but we will look below at the evidence and explain why we have given 16 September 1942. Here is Paul Turán's account [6] (see also [4]):-

I [Paul Turán] began writing about Géza Grünwald in 1943, a little while after I found out that he had died. It was hard to believe that it was at the April 1942, meeting of the Bolyai Mathematical Society when we last met. At the end of that meeting, Géza told me that he was called up for active military duty in the Labour Service Battalions. Young people are shocked when facing death, they can hardly believe in it. I felt just like that and kept hoping that there must have been an error or a misunderstanding, and, in the end, I stopped writing. During the liberation of Budapest in 1945, we all became personally acquainted with death. As time went by, the facts started to come out. We learned that the Hungarian Labour Service Battalion he served in was in fact a "death unit" made up of completely innocent "politically unreliable" people as punishment for an act of sabotage in the city of Györ. Within a few months the entire Battalion was executed except for five lucky survivors, among whom was Mr István Kossa who was a good friend of Grünwald and who stayed with him until his execution According to Kossa and the official paperwork, Grünwald died on 7 September 1943, at the age of 31.István Kossa (1904-1965) was elected Secretary General of the Hungarian Social Democratic Party in 1933 and served as secretary to the United Incandescent Lamp and Electricity Company where Grünwald worked. Kossa was drafted into the same Labour Service Battalion as Grünwald and describes his experiences in [1] where he writes:-

Dr Géza Grünwald, a mathematician at the United Bulb, a good comrade who kept close contact with us but has a weak physique.After World War II, István Kossa became a Hungarian politician and twice served as Minister of Finance.

An István Kossa biography states he escaped the Service Battalion in January 1943 which contradicts the statement that he was with Grünwald until his death on 7 September 1943. The date we have given for Grünwald's death is 16 September 1942 and this is the date given in the Holocaust Survivors and Victims Database [3]. The Database states that he was buried on the same day. We note that the Database also shows that Grünwald's brother Gyula also died after being drafted into a Hungarian Labour Service Battalion after being captured. The Database gives "Date Missing: January 1943."

The János Bolyai Mathematical Society established the Géza Grünwald Memorial Prize in 1951. It is awarded annually to exceptional young mathematicians (up to a maximum of four per year) who have made successful starts to their research careers. See [8] for details. Some sources state that it was first awarded in 1953 by we have found that Lajos Takács won the second Géza Grünwald Memorial Prize in 1952 for his paper

*Investigation of waiting time problems by reduction to Markov processes*.

### References (show)

- I Kossa,
*Dunától a Donig*(Szépirodalmi, Budapest, 1945). - A Soifer,
*The Colorado Mathematical Olympiad: The Third Decade and Further Explorations: From the Mountains of Colorado to the Peaks of Mathematics*(Springer Science & Business Media, 2017). - Holocaust Survivors and Victims Database,
*United Stated Holocaust Memorial Museum*. https://www.ushmm.org/online/hsv/person_advance_search.php - P N, The life and mathematics of Géza Grünwald, as told by Paul Turán at the 1 April 1955, meeting of the Bolyai Mathematics Society in Budapest,
*History of Approximation Theory, Department of Mathematics, Technion Israel Institute of Technology*. https://www.math.technion.ac.il/hat/people/obits/grunwald.html - L Szili and P Véeresi, On the theorem of Géza Grünwald and Józef Marcinkiewicz,
*Marcinkiewicz Centenary Volume, Banach Centre Publications***95**(Institute of Mathematics, Polish Academy of Sciences, Warsaw, 2011), 251-259. - P Turán, Grünwald Géza élete és matematikai munkássaga,
*Matematikai Lapok***6**(1955), 6-26. - P Turán, Géza Grünwald Memorial Prize,
*Matematikai**Lapok***4**(1953), 221-222.

### Additional Resources (show)

Other pages about Géza Grünwald:

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### Cross-references (show)

Written by J J O'Connor and E F Robertson

Last Update April 2020

Last Update April 2020