János Dezső Aczél

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26 December 1924
Budapest, Hungary
1 January 2020
Ottawa, Ontario, Canada

János Aczél was a Hungarian mathematician who spent the second half of his career in Canada. He was a leading expert in functional equations, organised many international conferences on the topic and wrote important books.


János Aczél was known as John Aczél after he came to Canada. He was the son of Deszo Scheibel (1881-1965) and Irenae Adler (1887-1972). Deszo Scheibel worked for a company producing chemical and medical products but after the Treaty of Trianon in 1920 the company became Romanian and Deszo wanted to remain in Hungary so he started his own business in Budapest selling medical equipment produced by various companies. He married Irenae, who had a daughter Maria (born about 1908) from a previous marriage. They ran a boarding house in Bálvány street to make extra income and some time after János was born they moved to Vilmos Császáar street which has been renamed Bajcsy-Zsilinszky street. Their house also contained an elementary school and János attended this school for four years beginning in 1931.

At age ten, János attended an English language school in which all the subjects were taught in English. He said [9]:-
From that time on my parents were insistent on my learning English but not French, because whenever they wanted to leave me out of the discussion they used French between them. So I teamed up with one of my classmates and we took private classes from a teacher of French.
Not only did he learn English and French but also German. This was learnt at home since he had a grandmother living with his family who had been born in Vienna and did not speak Hungarian, only German. János learnt German speaking with his grandmother. He then entered the Magyar Királyi Berzsenyi Dániel Gimnázium, a humanist secondary school in Budapest's 5th district named after a nineteenth-century Hungarian poet. It was an eight year grammar school and he studied there from 1935 to 1943. For a long time he did not know which subject he would study at university. One day his mathematics teacher came into the classroom and said that János Aczél was the only pupil to hand in correct solutions to the mathematics test. He decided immediately that he would study mathematics and so, having successfully graduated from the high school, entered the Pázmány Péter University in 1943 to study that subject. We note that in 1950, the university was renamed to Eötvös Loránd University.

At Pázmány Péter University, Aczél was taught by a number of outstanding mathematicians. Among his mathematics lecturers were Pál Veress (1893-1945) who worked on number theory and topology and had published the textbook 'Real Analysis', Pál Szász who taught an analysis course, and Béla Kerékjártó who taught an analytical geometry course. Aczél explained [9]:-
Pál Szász did a very good job of teaching us the fundamentals but Kerékjártó was different. Although his lectures were held with the charm of a French charmeur, they were often not clear enough and he also made mistakes that he took very lightly.
Germany invaded Poland in September 1939 and World War II began. Italy joined Germany declaring war on Britain and France in June 1940 and in November of that year Hungary signed the Tripartite Pact. Hungary began to recover territory lost through the 1920 Treaty of Trianon and invaded Yugoslavia in April 1941. These events were worrying for Aczél but he was not directly affected and his time at secondary school and his first year at university was not disrupted. Things changed dramatically after Germany invaded Hungary on 19 March 1944. Hitler had feared that Hungary was seeking to negotiate peace with the Allies and as a consequence would turn against Germany. Life now changed completely for Aczél. The Pázmány Péter University closed and, on 15 May 1944 he was called up for labour service.

He was sent to Miskolc to work at the wood mill at the end of the narrow-gauge Lillafüred Forest railway. This railway, opened in 1920, brought wood down from the forests of the Bükk Mountains. The railway still exists today as a tourist attraction and I [EFR] have enjoyed rides on it on two separate visits to Miskolc. It was no tourist attraction when Aczél was made to work at the wood mill and, although he said the work was not too hard, he tried to escape on 5 October. He returned to Budapest but was again forced to do hard labour, this time sent to the village of Fertorákos on the Austrian-Hungarian border where he was made to dig ditches as part of tank defences. There he met up with János Horváth, who had been a fellow mathematics student in Budapest. They had Pál Veress's textbook with them and one day they were caught reading the book when they should have been digging. Asked by the foreman what the book was, they got away with it by saying they were using it as toilet paper. Aczél later told this story to Fejér [9]:-
After the war we told the story to Lipót Fejér who was angry with Pál Veress and so he answered that after all it was not a big lie, actually.
From Fertorákos, Aczél was marched to the Mauthausen concentration camp then to Gunskirchen, one of the sub-camps of the Mauthausen concentration camp. He was lucky that he was liberated by the Americans soon after reaching Gunskirchen. He took quite a while to reach Budapest but when he did he found that both his parents and his half-sister had survived although most of his more distant relations had been killed.

Back in Budapest, Aczél married Zsuzsi on 26 December 1946. She had been born in 1927 and later when they lived in Canada she was known as Susan. At the time they were married, both were still mathematics students. They had two daughters, Catherine (known as Kati) and Julie. János Aczél continued the university course he had been on prior to the German invasion of Hungary. He was, in parallel, doing research for a Ph.D. and studying for a teaching qualification. His thesis advisors were Lipót Fejér and Frigyes Riesz. Aczél wrote [16]:-
Both, but mainly Fejér, were my thesis supervisors. They gave me huge leeway on what I wanted to do and include in my thesis. Another professor who influenced me greatly was Pál Szász. What impressed me most about all three was that they were accessible to a measure unusual for that time and place and gave occasion to me (and other advanced students) to present my results (Szász in seminars, Riesz in his regular classes). From Fejér one learned mostly in informal conversations and informal parts of his lectures. Fejér was not a strict examiner, yet most Hungarian mathematicians were (and are) genuinely his students or his students' students. Personality, accessibility, and genuine caring seem to have more effect than formal teaching.
Aczél graduated with his Ph.D. in 1947 having made up the time he had lost in labour camps. His thesis was Finite differences and functional equations and he had ten papers published in 1947-48. The notion of mean values and A generalization of the notion of convex functions were published in 1947 and the following eight papers in 1948: On mean values; Über eine Klasse von Funktionalgleichungen ; On mean values and operations defined for two variables; (with István Fenyö) On fields of forces in which centres of gravity can be defined; (with István Fenyö) Über die Theorie der Mittelwerte ; Sur une équation fonctionnelle ; Un problème de M L Fejér sur la construction de Leibniz ; and Sur les opérations définies pour nombres réels .

We noted above how Aczél learnt English, French and German. We see that his first mathematics papers were written in these three languages but none in his native Hungarian.

In 1947 Aczél was awarded a Ph.D. and received his teaching qualification but he had no job. He applied for a position as a quality controller and was made to sit a written intelligence test. When asked for the next number in the sequence 1, 4, 9, ... he gave the answer, "Any number is possible." He was not offered the job; it was not for his lack of mathematical skill but rather because he was seen to be "over qualified." He was then employed by a trade union as a statistician, a subject he knew nothing about. He quickly pleased his employer, however, who doubled his salary. This meant that when he was appointed as an assistant lecturer at Szeged University in 1948 he took a large cut in his income.

When Aczél was appointed as an assistant lecturer in mathematics at the Mathematics Department at Szeged University he was joining an impressive staff. The head of the department was László Kalmár and his colleagues included László Rédei, Gyula Szökefalvi-Nagy (1887-1953) and his son Béla Szökefalvi-Nagy (1913-1998) [9]:-
The atmosphere in Szeged was very good, it was great talking to the various people. The hot tempered Kalmár had great theories about maths education. I was impressed by the calm Béla Szökefalvi-Nagy. Zsuzsi thought that the bit strange Rédei was the best lecturer. We had a good relationship with Károly Tandori (1925-2005), who was another assistant lecturer.
In order to make more money, Aczél had a second occupation as a secondary school teacher. He was able to arrange for all his school teaching to be from 8:00 to 10:00 each day, and he then went to the Mathematical Institute.

Aczél left Szeged in 1950 when he was sent to Miskolc University to be the head of the mathematics department. He spent three years there but although there were good times, he found that the quality of the students was getting poorer. He organised conferences on teaching mathematics and applications of mathematics at Miskolc, although there was no international participation. Relations between some colleagues at Miskolc were difficult so when he was sent to Debrecen to be head of the analysis department he was happy to move. He had excellent colleagues there including Tibor Szele, Ottó Varga and Béla Gyires. The atmosphere in Hungary changed, however, in November 1956 when Soviet tanks rolled into the country [9]:-
After the war, the German occupation and the "shoah" we had great hopes in the new system and disillusionment came gradually. Most of the mathematicians were members of the Socialist Party before 1956 and were not after that. We had to persuade each other to enter the Party because it was not advantageous for the Institute if it had no party members. You just started to realise what was going on and were getting disappointed. There were prisoners working at the new university in Miskolc. You just slowly came to accept things you could not believe at first.
In Debrecen he began writing two books, namely Funktionalgleichungen der Theorie der geometrischen Objekte and Vorlesungen über Funktionalgleichungen und ihre Anwendungen which were published in 1960 and 1961 respectively. The first of these was a joint work written in collaboration with Stanislaw Golab who was Head of the Department of Mathematics at the Jagiellonian University in Krakow, Poland. For information about these books, see THIS LINK.

Aczél also collaborated with the Polish mathematician Jan Mikusinski. By 1960 travel outside the Soviet Union became possible for Aczél and in that year he made visits to both East Germany and West Germany. In 1961 he was invited to a geometry meeting at the German research centre in Oberwolfach to be held 12-16 June 1962. Problems obtaining a visa meant that he only arrived just before the meeting closed. The meeting was productive, however, since he was invited to be one of three organisers of a functional equations meeting in Oberwolfach in September 1962. The other two organisers were Otto Haupt and Alexander Markowich Ostrowski. This meeting had been arranged to take place after the International Congress of Mathematicians in Stockholm in August 1962. Berthold Schweizer writes [22]:-
I first met the person behind the name [Aczél] in August of 1962 in Stockholm. We had both come to take part in the International Congress of Mathematicians; we and our spouses took to each other immediately; we began our unending exchange of jokes and stories; and when I pointed out that the fundamental tenet at a crowded smorgasbord was "to each according to his ability", our friendship was sealed.
The Oberwolfach meeting was successful even though there were relatively few participants. Among those attending, in addition to the three organisers, were: Susan Aczél, János Aczél's wife; István Fenyo from Budapest; Einar Hille from New Haven, Connecticut; Olga Taussky-Todd from Pasadena; and Jack Todd, also from Pasadena.

In 1963 Aczél began to have travel problems. He was one of the organisers for the October 1963 functional equations meeting in Oberwolfach, the other two organisers again being Otto Haupt and Alexander Markowich Ostrowski. He was then to go to Florida for a ten month research visit. He said [9]:-
My permission to travel and the visa (for which you could not apply individually but only through the department of foreign relations) arrived 2 months later. I am a precise man, and I wrote a letter to the Ministry that the 10-month holiday they permitted was beginning right then. I had been invited to a longer session, a six-week conference at Stanford University. There I received a telegram asking why I had not returned to Hungary yet. Then I contacted the Hungarian Embassy in Washington, where I was told that the problem had been settled and my holiday ended in September. It was a narrow escape from getting disciplinary measures. My saving grace was that it was all in writing. But I was banned from travelling abroad for a few years.
Berthold Schweizer writes [22]:-
In the fall of 1963, Janos was a Visiting Professor at the University of Florida. I was at the University of Arizona and invited him to come to Tucson to give a series of lectures. I chose Thanksgiving because the weather is ideal then and because the holiday break would give us ample time for sightseeing. And so he arrived on November 23. En route his plane had stopped in Dallas. In his hand he carried a copy of that city's newspaper - its headline screaming out the news of Kennedy's assassination. In the days of apprehension and mourning that followed, we grew much closer to each other.
The difficulties that Hungarians had obtaining permission to travel contributed to Aczél's decision that he would try to emigrate. First he went with his family to Vienna, Austria, then to Cologne, Germany. An invitation to join the faculty of the University of Massachusetts in Amherst, USA, was tempting but Aczél feared that, although he was too right-wing for Hungary at this time, he was probably too left-wing to enjoy spending the rest of his life in the United States. He was working in Cologne, and still considering the American invitation, when he attended another functional equations meeting in Oberwolfach, organised by the same three mathematicians as the previous two, in July 1965. Michel Amedee McKiernan, who had been a student of Karl Menger and was at that time a member of the Functional Equations group at the University of Waterloo in Canada, was one of the participants at Oberwolfach. He invited Aczél to join the faculty of the University of Waterloo. Aczél quickly received a formal invitation, rapidly accepted and by September 1965 he was teaching at the University of Waterloo. He said [9]:-
The university in Waterloo was relatively new. The research council was very happy to see me there, so I received quite a huge grant. I had several doctoral students, but [John Baker, Mark Taylor and Che Tat Ng] are really the most outstanding ones. I became a Canadian citizen in 1971. I often went to conferences and we also went on holiday a lot around the world. The conferences in functional equations and information theory continued.
Shortly after arriving in Waterloo, Aczél wrote the Foreword to the English translation to his 1961 book on functional equations. He wrote in October 1965 [2]:-
The revisions in this new edition are partly based on experiences of further lectures in Debrecen (Hungary), Gainesville (Florida), Giessen and Cologne (Germany), and Waterloo (Ontario). Warmest thanks go to students and colleagues at all these places for their valuable comments.
For further information about this book, including the Publisher's information, the Foreword, and extracts from some reviews, see THIS LINK.

The authors of [8] tell us that soon after arriving at Waterloo:-
... he founded 'Aequationes Mathematicae' and set up an editorial office at Waterloo. ... During his tenure at Waterloo, he brought a continuous stream of scholars to the university. Some of them came to Canada to attend the International Symposium on Functional Equations, some came to Waterloo as visiting scholars for a few months, and some came as faculty members. The lectures they delivered broadened and deepened the subject areas. He wrote a mini-course type survey article on webs and quasigroups. Amongst his doctoral students at Waterloo, Mark Taylor carried that torch. The two of us were more interested in information theory. John Baker specialised in analysis. János always allowed his students to develop naturally.
Aczél was given the title "distinguished professor" in 1969. He retired in 1993 but continued to write excellent papers. He had for many years been interested in the application of functional equations to the behavioral sciences and his last few papers were written on this topic with Duncan Luce, Tony Marley, and Che Tat Ng.

Aczél received many honours for his outstanding mathematical contributions. At a conference on functional equations in Spain in 1988 he received a Santiago Ramón y Cajal Medal from the scientific council. In 1990 he was elected honorary doctor at the university of Karlsruhe, surprisingly in economics, not in mathematics. In 1971 he was elected a member of the Royal Society of Canada and in 1991 he was elected a member of the Hungarian Academy of Sciences. He received honorary doctorates from Graz University in 1995, from the Silesian University of Technology in Katowice in 1996 and from the University of Miskolc in 1999. In 2004 he won the Kampé de Fériet Award of the annual Information Processing and Management of Uncertainty conference [19]:-
... for his pioneering work on the theory of functional equations, with applications in many fields, such as information measures, index numbers, group decision making, aggregation, production functions, laws of science, theory of measurement and utility theory.
In 2008, he was elected an honorary member of the Hamburg Mathematical Society.

Susan Aczél died on 23 May 2010 after a short illness [24]:-
While we all mourn her loss, we will always treasure our memories of her life and recall her gentle, caring attitude and her wisdom. The Aczel family believes that an investment in talented graduate students will result in far-reaching benefits for Canada at home and abroad. To this end, they have established the Susan and Janos Aczel Graduate Scholarship at the University of Waterloo.
János Aczél died peacefully in hospital, following a brief illness, on Wednesday, 1 January 2020, six days after his 95th birthday. He was buried at the Capital Funeral Cemetery in Ottawa on 26 January 2020 and a Celebration of Life was held at the University of Waterloo on 17 April 2020.

References (show)

  1. J Aczél, Vorlesungen über Funktionalgleichungen und ihre Anwendungen (Birkhäuser, 1961).
  2. J Aczél, Lectures on functional equations and their applications (Academic Press, New York, 1966).
  3. J Aczél, On applications and theory of functional equations (Academic Press, New York, 1969).
  4. J Aczél and S Gołab, Funktionalgleichungen der Theorie der geometrischen Objekte (Panstwowe Wydawnictwo Naukowe, Warsaw, 1960).
  5. J Aczél and Z Daróczy, On measures of information and their characterizations (Academic Press, New York, 1975).
  6. W Benz, Einige Worte zum 80. Geburtstag von János Aczél, Aequationes mathematicae 68 (3) (2004), 121-126.
  7. B Ebanks and C Tat Ng, Tribute to a Distinguished Professor János Aczél at 80, Aequationes mathematicae 69 (1-2) (2005), 1-5.
  8. B Ebanks and C Tat Ng, In celebration of the life of Professor János Aczél, Aequationes mathematicae 94 (3) (2020), 401-404.
  9. Z Daróczy, An interview with János Aczél, Aequationes mathematicae 89 (1) (2015), 1-16.
  10. F Hahn, Review: Lectures on functional equations and their applications, by János Aczél, The American Mathematical Monthly 75 (3) (1968), 314.
  11. P C Hammer, Review: Lectures on functional equations and their applications, by János Aczél, Science 155 (10 March 1967).
  12. M Hosszú, Review: Lectures on functional equations and their applications, by János Aczél, Mathematical Reviews MR0208210 (34 #8020).
  13. J Kampé de Férie, Review: On measures of information and their characterizations, by János Aczél and Zoltán Daróczy, Bull. Amer. Math. Soc. 83 (1977), 192-196.
  14. M Kuczma, Review: Vorlesungen über Funktionalgleichungen und ihre Anwendungen, by János Aczél, Mathematical Reviews MR0124647 (23 #A1959).
  15. R D Luce, Personal reflections on an unintentional behavioral scientist, Aequationes mathematicae 58 (1999), 3-15.
  16. A C Michalos (ed.), The best teacher I ever had: personal reports from highly productive scholars (Althouse Press, London, Ontario, 2003).
  17. A Nijenhuis, Review: Funktionalgleichungen der Theorie der geometrischen Objekte, by János Aczél and Stanislaw Gołab, Bull. Amer. Math. Soc. 68 (1962), 552-555.
  18. A Nijenhuis, Review: Funktionalgleichungen der Theorie der geometrischen Objekte, by János Aczél and Stanislaw Gołab, Mathematical Reviews MR0133763 (24 #A3588).
  19. Professor Janos Aczel, Kampé de Fériet Award.
  20. R M Redheffer, Review: Lectures on functional equations and their applications, by János Aczél, Quarterly of Applied Mathematics 27 (4) (1970), 554.
  21. Remembering John Aczel, Ottawa Citizen (11 January 2020).
  22. B Schweizer, János Aczél - A Personal Appreciation on the Occasion of his 60th Birthday, Aequationes mathematicae 28 (1-2) (1985), 1-3.
  23. B Schweizer, János Aczél - A Personal Appreciation on the Occasion of his 60th Birthday, Aequationes mathematicae 28 (3) (1985), 209-211.
  24. Susan Aczel, Waterloo Region Record (5 June 2010).
  25. C Tat Ng, Tribute to a Distinguished Professor János Aczél at 85, Aequationes mathematicae 80 (1-2) (2010), 1-4.
  26. We remember Distinguished Professor Emeritus János Aczél, Pure Mathematics, University of Waterloo (8 January 2020).

Additional Resources (show)

Other pages about János Aczél:

  1. Books by János Aczél

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update September 2023