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My experiences with Paul Erdos

- Prof Herbert Fleischner

Paul Erdos who `left' (as he would have phrased it) last September, was one of the greatest mathematicians of our time. No doubt. The obituaries have expounded on that, and they also made some remarks on his personality such as his attitude towards owning property (`it's a nuisance'), etc. He was described as an eccentric --- which is true if one considers imposed norms as `center'.

How can one describe a human being like Erdos to people who have never met this extraordinary man? Was he unreachable? Was he so preoccupied with writing papers (roughly 1500 and more) that he didn't know anything about the non-mathematical world? I think the best way to describe a human being to someone who has never met him, is to describe encounters with such a person, rather than to try to give a general `overall picture' of the person.

Well, am I one of the lucky few who have met Erdos? Nonsense! I am one of the lucky many who have met `Uncle Paul'! This is how we would address him during the last so and so many years - "hello, Uncle Paul!", "Excuse me, Uncle Paul,....". He didn't care about being called `Professor Erdos'. This `Uncle Paul' was an expression of our respect for this great man, and of our love for him.

I am one of the lucky many...because he was constantly on the move, spending a few weeks here and there, at this or that conference, at this or that university. His homes were with the people he met. He would stay with colleagues whenever possible; only during the last years did he stay in an apartment given to him by the Hungarian Academy of Sciences, whenever he was in native Hungary. But most of the time he was not in Hungary. An anecdote says that many years ago, when he had to fill out a visa application for a trip to the USA, he answered the question: 'Country of Residence' by filling in -- 'Hungary, USA, Canada, Israel, Australia' -- and this was not a lie! These were the countries where he could be contacted at the time. Until the 1970's it was his mother who would know at any given time where Erdos could be 'found'; after she died, Ron Graham of Bell Labs (USA) who took over this function (and managed his finances, etc.). 'Uncle Paul' was a true cosmopolitan...

I first saw Erdos when I was a student in Vienna in the 1960s. He had been invited to give a one-hour lecture. In his talk he spoke about various results proved by himself or others, and posed a number of problems. Depending on the difficulty of a problem, he would attach a symbolic prize to it. Being a student in my first semesters, I got lost after a few minutes, and spent the rest of the lecture just watching this slim little man who seemed to be so far away...Would I ever be able to solve one of his problems, albeit one with the smallest prize? I was just dreaming. So I had seen Erdos once or twice during my years as a student in Vienna. I had seen him, but not yet met him...

In the summer of 1969, shortly after graduating from the University of Vienna, I attended a combinatorics conference in Oberwolfach (Germany). Paul was there, of course. It was my first conference. I was just a little duckling in mathematical research --- no great results yet. Somehow he was interested in talking to me (he was always interested in the newcomers). He asked me: 'Do you have a boss?' I thought he meant the professor whose assistant I was at the Technical University of Vienna. In fact, he meant to ask whether I was married or engaged. He had his special (humorous) terminology or phrases. So, in a family the wife is the 'boss', the husband is the 'slave', and the children are the 'epsilons' (referring to the epsilon in analysis -- the arbitrarily small real number). If a couple got divorced, Erdos would say 'the husband has been liberated'; if a man married a second time, Erdos would say 'he has been recaptured'. This sounds rather male-chauvinistic, and seems to portray him as having been hostile towards families.

However, this was not the case. True, he was a staunch single, but he was friendly with female colleagues and wives of male colleagues. He was extremely nice to colleagues' children, buying them sweets and being tender towards them. Apparently he didn't want to have responsibilities towards a partner or children. He was married to mathematics.... nonetheless, he would be concerned about his colleagues' well-being. Having seen my son in 1977 when he was only three years old, Erdos asked me many years later how he was doing in school, etc. Which proves that 'Uncle Paul' also had a fantastic memory.

His terminology embraced alcohol which he would call 'poison' (implying that he was a staunch anti-alcoholic as well); 'Uncle Sam' would stand for the USA, whereas 'Uncle Joe' meant the Soviet Union. If a person had reached the age of 60 (or was it 70? I don't remember), he would call this person an 'archeological discovery'. For various ages he had similar terms, e.g. 'legally dead', 'living dead', etc. Himself he would call p.g.o.m., that is 'poor grand old man'.

I also recall that he was quite a good ping-pong player. In 1969 at the Oberwolfach meeting (quoted above) and later at a meeting at Memphis State University, we played ping-pong. It was not easy to score against him for, due to the way he held the paddle, he could give the ball a heavy spin...

In the summer of 1975 (or was it 1977?) Gert Sabidussi organised a combinatorics workshop at the University of Montreal. Quite a few Hungarian colleagues, including Erdos, attended this workshop. On one of the weekends we had a picnic at a nearby lake. When we had finished our lunch, the other Hungarian colleagues strolled away and kept at a safe distance (they knew why). So, when he suddenly said 'Who is going to have a little hike with me?', I found myself as being the only person standing next to him. There was no escape! On the other hand, what harm could it do to walk onto one of the nearby hills with p.g.o.m.?

So we went onto that hill, using a dried up creek's bed as the path to reach the hilltop. It was not only a hot day, it was steaming hot along our route because the bushes formed a sort of a roof over the creek. Furthermore they have these vicious animals in Canada who bite you at any time, at every step --- the black flies. They are faster than mosquitos, and you stand no chance against them. So, while walking up the hill, we discussed superpower contention between 'Uncle Sam' and 'Uncle Joe', the Chinese experiences, and some mathematics. I had to concentrate on our discussion and on the stones along the route. By the time we came back to join the other workshop participants, my arms, neck and face were covered with itching pimples from the bites of the blackflies. However, 'Uncle Paul' apparently had had no problems with them; I couldn't detect a single pimple in his face!

'Uncle Paul' has left, but he bequeathed to us a huge pile of problems which still have to be solved. It will take generations to solve or disprove his conjectures... and I am one of the lucky many who have met this wonderful man, chatted with him, discussed mathematics with him - and hiked with him onto a hilltop in Canada while being eaten up by black flies.

Herbert Fleischner is an Austrian professor of graph theory who has solved one of Paul's US$100 problems and written international textbooks. He joined the UZ staff in March 1997, after a couple of stints as visiting professor.

Here are some more obituaries of Paul --- if you know any others, please let us know.

Paul is also listed in the St Andrew's Archives.

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