Janos Aczel (1924-2020)

by Orr Shalit

I was saddened to find out that Janos Aczel passed away earlier this month. In my early days, after Boris Paneah got me hooked on functional equations, Aczel’s books caught my eye. Since then I am a fan of his. In particular, I was drawn by a small booklet by him whose title I am not able to reconstruct, and his two larger books “Lectures on Functional Equations and Their Applications” (1966) and “Functional Equations in Several Variables” (1987, co-authored with, Dhombres), which for a couple of years were to me among the most interesting and useful books I knew.

I have two stories two tell about Janos.

When I came to do a postdoc at the University of Waterloo in 2009, I was already working in operator algebras, and my supervisor was Ken Davidson. However, I remembered my functional equations origins, and I was happy to find out that Janos Aczel is an Emeritus Professor there. I was invited to give a talk at the Analysis Seminar, and my plan was to talk about the triumph of my PhD work. However, my talk was planned quite badly, or maybe I was just too excited, and my talk was over before half an hour. For a young mathematician in a new department, fresh out of his PhD, this is a disaster. The seminar leader asked if there were any questions or comments, and there was a brief and awkward silence. But then Janos raised his hand, and when he got permission to make his comment he said: “a good talk should have a good beginning, a good end, and the two should be close to one another“, and when he said the word “close” he held his hands open with palms facing each other, indicating a very small distance. To this everyone laughed, and I was somehow less perplexed, and we all went to have the after-the-seminar-beer, half an hour earlier than usual. That was a beautiful act of kindness, that I will always remember.

Speaking of beautiful acts of kindness, this brings me to the second story. Janos and I met several times to discuss functional equations. In one of our meetings he brought up the fact that his wife is Jewish. Janos was a student in Budapest during World War II. He told me that during World War II, the Jews in Hungary at a certain age were sent to forced labor camps. Hungary was an ally of Germany, and had several anti-semitic laws and measures (a number of Jews were deported to Poland where they were murdered) but Jews were not closed in ghettos and for the most part were not sent to concentration camps, until Germany invaded Hungary, in 1944.

Janos told me that some of the Jewish students had to go to forced labor, but then some were released and allowed to go back to university. (About three fourth of the forced laborers did not survive). But they missed a year of classes! So some top students, and Janos was among them, volunteered to teach the returning Jewish students the material that they missed. This might sound like a light anecdote, missing classes! You have to remember Janos acted in a deeply anti-semitic country, and even though there were no deportations to concentration camps yet, there were quotas of how many Jews could work in certain jobs, and there were also “spontaneous” mass executions, before the Germans invaded. I consider this a beautiful act of solidarity and resistance.

One of the students that Janos tutored was Susan, they fell in love, and she later became his wife. I don’t remember if he told me how exactly Susan survived the horrible years to come (did she hide her identity, hide herself, or did she flee). She survived, and they lived together until Susan passed away in 2010.

I am sorry that I did not interrogate Janos for more details at the time and write them down, but I thought I should write down what I remember. I added some historical details using this Wikipedia article (and also the corresponding one in Hebrew).