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Márk Antal
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Devecser, Veszprém County, Hungary
Cluj-Napoca, Romania
Biography
Márk Antal was the son of Simon Kohn and Mária Preis. The family were Jewish and the first explanation we have to give is about his name being Antal while his father's name was Kohn. In fact when Márk was born he was given the name Márk Kohn. He was brought up and attended schools as Márk Kohn and only changed his name to Márk Antal in 1898 when he was 18 years old. Many Hungarians with German names changed their name to make himself more Hungarian. This was standard practice carried out at that time to show solidarity with Hungarian culture. We do not know why he chose Antal, but it is both a common Hungarian given name and family name derived from the Latin Antonius. It must be a coincidence that the young man with a passion for mathematics chose Antal which means 'number' in Swedish. The other comment worth making at this point is that in Hungary the family name comes before the given name, so in Hungarian references his name will be given as Antal Márk.Two famous Hungarian mathematicians were born in the same year as Márk Antal, namely Lipót Fejér and Frigyes Riesz. In fact Antal and Fejér both studied at the Pécs Secondary School where they were taught mathematics by Zsigmond Maksay (1850-1896). Let us note that when at the school in Pécs, Antal was known by the name of Kohn while Fejér was known by the name Weisz. Maksay (19 December 1850 - 21 October 1896) played an important role in making both Antal and Fejér enthusiastic about mathematics and, in particular, about problem solving. He had studied at the universities in Cluj and Budapest before becoming a mathematics teacher at the Nagykálló Secondary School. In 1882 he moved to the secondary school of Pécs where he became one of the most enthusiastic supporters of the Secondary School Mathematical Journals (Középiskolai Matematikai Lapoknak, known as KöMaL) from its very beginning in 1893. He contributed to KöMaL and also encouraged his pupils to contribute. As an example, he published Determining the radius of the sphere that can be inscribed around the tetrahedron. Antal became an regular contributor, under the name Kohn Márkus, when Dániel Arany, the founder of the journal, was editor. Maksay also encouraged his pupils to enter the yearly Eötvös competition which was held for the first time in the autumn of 1894. Antal was praised for his performance in the 1898 Eötvös competition.
After graduating from the Pécs Secondary School in 1897, Antal entered the Polytechnic University of Budapest where he studied mathematics and physics. After graduating from the University in 1901 with a secondary school teacher's diploma in mathematics and physics, Antal taught at various secondary schools in Budapest. He was a middle school teacher in Budapest (1901-1908), taught at a higher commercial school in the VIII district of Budapest (1908-1910), and was a regular teacher at the IV district of Budapest girls' high school (1910-1914). He had continued his interest in KöMaL during his years as a university student and published regularly in the journal. As a secondary school teacher in Budapest, he contributed many articles, in fact over 30 articles between 1900 and 1914. Between 1907 and 1914, together with László Rátz, he edited the journal. Filep László writes in [12]:-
In his articles, Márk Antal covered many areas of high school mathematics in a way that was understandable to students. He gave simpler proofs of several theorems than those known, mainly in combinatorics and analysis. In his five-part series of articles on geometric constructions, he generalised an important result of József Kürschák. He showed in Part V that geometric constructions can also be performed with a parallel-edged ruler.To give an example from the November 1913 edition of KöMaL, we note that he contributed the paper Relationship of a geometric theorem with the Simson line. In 1914 he published the combinatorics book Kapcsolástan. Kombinatorika.
In 1993 Vera Oláh interviewed Albert Korodi (1898-1995), who had a career as an engineer and physicist, and asked him, "How and when did you become acquainted with the High School Mathematics Journals?" He spoke about Antal in his reply [13]:-
From 1908 to 1916 I attended the Markó Street Real School. My mathematics teacher was Károly Fröhlich, and György Pólya taught alongside him as a trainee teacher for a year. I read the Secondary School Mathematics Journals (KöMaL), diligently submitting my solutions. The co-editor of the journal at that time, Márk Antal, taught at the Váci Street Girls' Gymnasium, where my sister attended. I asked her to introduce me to her teacher, who welcomed me very kindly, asked me what parts of mathematics interested me, recommended literature, and encouraged me to pursue mathematics. So, as I gained practice in solving problems, after my high school graduation I entered the national mathematics student competition and came first in mathematics, winning the Eötvös Prize.During the years when Antal was teaching in Budapest he married Szeréna Winternitz (born 22 December 1882), daughter of the physician Antal Winternitz and has wife Fanni Friedmann, in Budapest on 6 July 1905. Márk and Szeréna Antal had two sons, János Antal (1907-1943) and István Antal (1909-1978). We give some details of János Antal (born in Budapest on 17 October 1907) and István Antal (born in Budapest on 27 January 1909) below.
The publication of KöMaL was suspended from September 1914 due to the outbreak of World War I and Antal's work as an editor of the famous journal ended. His teaching career was also interrupted when he entered military service in the Austro-Hungarian Army. During World War I, Hungarian troops fought on all major fronts in Serbia, Russia and Italy suffering heavy losses. Antal served in the military for four years, during which he was posted to the most difficult places. He began his service as an artillery sergeant and eventually retired as a captain, earning numerous decorations, including the most prestigious ones.
The end of World War I marked the beginning of a chaotic political period for Hungary. The Austro-Hungarian Empire dissolved and in October 1918 Hungary declared independence and the First Hungarian Republic was set up under the leadership of the liberal Mihály Károlyi. At this stage Antal, back in Budapest from military duty, took care of his wife Szeréna and his two young sons János and István. He also gave private tuition and it is conjectured in [12] that he may have taught a very young Pál Erdös at this time. From the end of 1918, he was one of the vice-presidents of the Hungarian teachers' union. In December 1918, the National Association of Municipal Employees set up an 11-member School Reform Committee, headed by a four-member board. One of its members was Márk Antal, who was in charge of the secondary schools. The committee produced a report about a new curriculum and Antal wrote the section on the purpose of teaching mathematics. It began by stating:-
Introducing students to an exact way of thinking is the primary duty of mathematics education. This goal can be achieved mainly by educating students to work independently. The teacher should only teach as much as is absolutely necessary; he should see the greatest success of his work in making them think.The countries surrounding Hungary demanded more territory from an already much reduced Hungary and Mihály Károlyi resigned. The Communists took control and on 22 March 1919 announced the establishment of the Hungarian Soviet Republic led by Béla Kun. Antal, who was known as a Communist supporter, became a group leader in the People's Commissariat for Public Education on 24 April 1919. On 24 June the People's Commissariat for Public Education was split into three parts with Antal in charge of the group with jurisdiction over all schools and colleges. Antal's group began to put together proposals for the reform of education and he proposed giving a series of university lectures in the following semester under the title The School of Communist Society. This, however, never happened since the Hungarian Soviet Republic fell in August 1919 and, after a chaotic few weeks, Romanian troops entered Budapest. There followed a campaign of violence against Communists and Jews resulting in many being executed. Antal was briefly imprisoned but when he was released, fearing for his life, he fled with his family to Vienna.
The Antal family were only in Vienna for a short while before they decided to move to Cluj-Napoca which had been part of Hungary but was by this time in Romania. When Cluj had been Hungarian, Jews were educated in the standard school system and there were no specialist Jewish schools. When Cluj formally became Romanian with the Treaty of Trianon in June 1920 the situation for the Jews of Cluj changed and they asked Antal if he would organise a Cluj Jewish Secondary School. Quite how he went about this we do not know, but by the autumn of 1920 a Cluj Jewish Boys' School and a Cluj Jewish Girls' School had been set up.
The Cluj Jewish schools were set up with a board of trustees and they approached Antal and offered him the position of principal of both the Cluj Jewish Boys' School and the Cluj Jewish Girls' School. He was pleased to accept but there were problems. Antal did not speak Romanian but the trustees required all teaching in the schools to be in Romanian. It was not too much of a problem, however, all it meant was that he was not allowed to teach classes. His approach, therefore, was to attend classes to see how they were being taught, then give sample lessons to his teachers showing them his ideas on teaching but also allowing plenty of opportunity for discussion. Now we are fortunate to have details since the minutes of one of these sessions with the school teachers is preserved in the Memorial Book [16]. Filep László tells us more details from the Memorial Book in the article [12]:-
The minutes also reveal Márk Antal's child-centred and education-centred pedagogical principles. He worked with his students on his free Saturdays in an informal manner, introducing them not only to mathematics, but also to the masterpieces of Hungarian and world literature. In his apartment, he began his private university activities in 1920, primarily for young people who did not know Romanian but were interested in higher mathematics. He also gave lectures on Marxism to interested intellectuals. The authorities did not look favourably on the survival of the Hungarian language and culture in the school.In 1927, together with other schools which the Romanian authorities thought were aiming to restore Cluj to Hungary, both the Cluj Jewish Boys' School and the Cluj Jewish Girls' School were closed.
Now from as early as 1920 Antal had been running what might be considered as a private school/university from his home. When the Jewish school were forced to close in 1927 this had the effect of making him work even harder giving university level courses in mathematics from home, taught in Hungarian. The Memorial Book [16] gives the titles of these courses:-
... Number theory, Set theory, Analysis, Vector theory, Political arithmetic and Insurance mathematics, Analytic plane and 3-dimensional geometry, Differential geometry, the Mathematical foundations of the theory of relativity, the Sociological role of mathematics, and the Mathematical foundations of the theory of knowledge.Students attending his courses were prepared to take the matriculation examination for Budapest universities. After a few years, he also gave higher level lectures at the meetings of the Natural Science Department of the Transylvanian Museum Association. His favourite topics included Einstein's theory of relativity and the work of Farkas Bolyai and his more famous son János Bolyai.
During the 1920s and 1930s various political parties were formed in Cluj and Târgu Mureş representing the Hungarian minority in Transylvania. After 1926 the Hungarian People's Party was the main party supporting the Hungarian people in Transylvania. Antal was active in the cultural committee and the educational department of the Hungarian People's Party [2]:-
He organised Marxist seminars in the second half of the 1920s. ... at the beginning of each of Márk Antal's seminars he said a few words about the Communist Manifesto: "Every seminar should start with this," he said, "it contains the quintessence of Marxism. What a pity that it is not allowed to be taught at the university, and when we come to power, it will be on everyone's lips and will be considered as commonplace."One might wonder how Antal earned a living to support himself and his family after he lost his job as head of the Jewish Schools. In fact, he worked as a mathematician at the Minerva Insurance Company from 1927 to 1940.
The Vienna Awards (so called since they were made in Vienna) were two decisions made by Germany and Italy shortly after the beginning of World War II rewarding Hungary with the return of certain disputed territory. The Second Vienna Award made on 30 August 1940 stated that Hungary was to regain Northern Transylvania from Romania. This meant that Cluj became Hungarian and Antal convinced the Hungarian Minister of Education to approve the reopening of the Jewish Boys' School and the Jewish Girls' School in Cluj. He was again appointed as head of the two schools. With Cluj returning to Hungary, Antal was able to teach in the school as well as be its director. Antal advertised for teachers and of the many applicants chose Dezsö Lázár as a mathematics teacher.
In [15] Júlia Szegő describes Márk Antal as a smiling, direct, helpful man, whom everyone simply called Uncle Antal. She gives other information telling us about his character:-
He had one of his young colleagues bring specialist books from Göttingen at his own expense. He looked everywhere for talented young people and small children. This quality of his was known in Transylvania, so children interested in mathematics were even brought to him from Timisoara. When his house was being tidied up, he noticed a kind of arithmetic example written in chalk on the wall. He discovered that the "culprit" was one of the young masons, who said that he was very interested in mathematics, but his poor parents could not afford to teach him. Márk Antal taught him and then had the young man, Sándor Kun-Kúti, taught at a higher level. He became a university lecturer in Budapest.Antal wrote a book with the title The Basics of Higher Quantitative Analysis but it was never published and only parts of it survived. The first chapter discusses counting, the second chapter discusses congruences, and the third discusses the elements of analysis (series, limits, Dedekind cuts). The next chapter has been lost but probably developed the real numbers using Dedekind cuts. Antal takes a philosophically inspired approach to the number systems:-
If we consider objects outside ourselves as wholes, then each object makes a certain impression on our mind. We can designate each new impression by a sign (I) or by a word. The very knowledge that I have an impression and that there is another one leads to counting, which is nothing more than a way of ordering impressions.He spends time looking at the relationship between ordinal and cardinal numbers. He explains that an axiomatic approach, for example with Peano's axioms, means that the problem of the relationship between ordinal and cardinal numbers goes away. He claims, however, that the axiomatic answer to the question is not satisfactory from either a philosophical or didactic point of view. In fact Antal follows Russell explaining that for ordinal numbers, the ordering obtained during counting can be discovered, while in cardinal numbers, the mathematical operation of correspondence can be discovered. Since the first of these is much simpler, he claims that the concept of ordinal numbers had to develop first.
Antal only had two years back as principal of the Jewish schools when he died suddenly of a heart attack in October 1942. His funeral was well attended but his wife had died earlier and his son János was not able to attend. His son István was the only close family member at his funeral. Let us say a few words about his two sons and explain why János could not be at the funeral.
János Antal was born in Budapest but lived in Cluj from 1920 when the family moved there. As a secondary school pupil in Cluj he contributed to Napkelet, the journal of the Hungarian Literary Society. He wrote activist-futurist poems and, in addition to Napkelet, he contributed to Korunk, a literary journal with a Marxist political stance. He studied in Vienna and Paris before settling in Budapest. He wrote novels and a poetry book. He was a member of the Hungarian Communist Party and was one of the organisers of the People's Front. He was imprisoned for his political views in 1937 and was released in 1942 to go to the Soviet front where he died of typhus.
István Antal was born in Budapest but lived in Cluj from 1920 when the family moved there. He entered the Vienna Academy of Music in 1925 and, after graduating, he went to Berlin where he completed his artistic training as a pianist. In March 1936 he gave his debut concert in the Vigadó Concert Hall in Budapest. From 1945 he was a teacher at the Hungarian National Music Association, and from 1948 at the Liszt Ferenc Academy of Music in Budapest. He gave concerts in many European countries. In 1948 he went to Sweden on a scholarship. Returning to Hungary, he continued his activities as a performer and teacher until his death in 1978. He has recorded a number of popular CDs playing, for example, music by Franz Liszt, Ludwig van Beethoven, Béla Bartók, Robert Schumann, Johannes Brahms and other leading composers.
Let us end with a quote from [8]:-
The teachers and alumni of the Szamos Street Gymnasium in Cluj-Napoca pay tribute to the memory of their excellent teacher Márk Antal with respect and love.
Written by J J O'Connor and E F Robertson
Last Update March 2026
Last Update March 2026