He lived difficult days in Budapest during the second world war and, after being liberated by the Russian soldiers in 1945, he determined that whatever would happen later, he had had the hardest part of his life and it should go differently later. We have certainly witnessed that, as far as mathematics is concerned, it certainly did, since his was one of the most successful careers in mathematics.

... sees theology and music as neighbouring spheres and close of kin; and besides, music has always seemed ... a magic marriage between theology and the so diverting mathematics.

What happened was that she explained the material so well that I didn't understand it.

[Rényi] sat down to talk to me. He asked if I would go to the Soviet Union as an research student. I said I would happily go there. And to Szeged? "Not there," I replied, "because my widowed mother lives in Pest." "How are you happy to go to remote Moscow then?," Rényi asked. With this, it was arranged that I go to Szeged to work with Professor Kalmár as a postgraduate student. I had already seen Kalmár at an academic meeting by then, and he had impressed me very much.

Yet the three years spent in Szeged became perhaps the most pleasant period of my life.

Between 1953 and 1956 ... we regularly had lunch together in the restaurant of the University of Szeged and went afterwards to have coffee in an espresso bar.

Lajos Pukánszky claimed to have named me a rabbit based, he said, on a careful analysis of my individuality. But then Adam Korányi thought everyone was a rabbit, and then we started calling each other bunny rabbits. ... The Szeged Institute of Mathematics at that time was a wonderful place, with three incredibly knowledgeable professors: László Kalmár, Béla Szökefalvi-Nagy and László Rédei at the forefront. Under the spell of mathematics, we lived on a wonderful mountain of magic. Although we knew what was around us, our days were filled with a joy and serenity stemming from self-confidence and inner security. A manifestation of this was the bunny rabbit game and the consequence of our lifelong friendship.

Kalmár knew everything, but by then he was no longer working on mathematical topics. I don't know how that happened to him - even though he wasn't that old; he was 50 years old. He knew everything, he understood everything, he remembered everything, but he didn't have the patience to sit down and think.

The representation distinguishes itself by all the qualities of a scientific representation, e.g. by lucidity, caution, simplicity and completeness.

It is about the deducibility of axiom B8 from the other axioms of Gödel's axiom system of set theory. The present work also describes the development of the axiomatic structure of set theory up to Gödel's axiom system; then, without using axiom B8, it is proven that with an exactly delimited but sufficiently broad predicate concept there is a class for each predicate, the elements of which are those and only those sets for which the predicate is valid. Axiom B8, however, is a special case of this proposition, and it follows from this that Axiom B8 is dispensable. It should be noted that the core of the proof is a purely combinatorial consideration.

This paper is a preliminary report containing the results of the dissertation of the author, submitted in fulfilment of the requirements for the degree of Candidate of Mathematical Sciences. A paper containing the detailed proofs of the results will appear (in English) in the 'Acta Math. Academicae Scientiarum Hungaricae'.

I was hoping that I would get some advice from him on what direction to go to prove the independence of the continuum hypothesis. (This is what Paul Cohen did in 1963). Erdős listened politely and asked, "And are you interested in normal mathematics, too?" It was clear that this was not an insult but an inquiry. He was simply interested in the answer. Luckily, as a result of conversations I had had with Géza Fodor, there was a problem that I could ask him about. He immediately began to guess and prove. The initial results of our first joint paper were worked out that day.

It would be Erdős's first joint paper with Hajnal, bearing on partitions of all finite sets, that would veer closest to central developments of the 1960s in set theory, these being in the investigation of large cardinal hypotheses. Erdős and Hajnal provided the context, spurred the possibilities, and got enticingly close to a transformative result.

Erdős was amazing! I have a hard time explaining what that fantastic young man was like because everyone - who isn't as old as me - only knew him when he was older. He was 43 then. Terribly old! I was only 25. First of all, he could give his undivided attention. Although mathematicians hate to hear other people's ideas (I don't know if you noticed that?), he was able to understand mine down to the smallest detail and move things on right after. And in the meantime, he was already starting to guess new things, ask questions - so it was very good to work together. We got along very well even in the fact that everything remained in his memory - then we went over the results with ten statements, he remembered them, and I remembered them.

American and Hungarian mathematics education are very different. In America the first years of the university, the so-called undergraduate training in mathematics, is essentially a substitute for high school material. Even in lectures given to third-fourth year mathematics students, it is not customary to prove more difficult results. Then in graduate training, which is truly excellent, the Americans catch up. A dissertation written at a good university usually contains significant results.

Hajnal published over 150 research papers during his career. He is well known for his work on set theory and was an Honorary President of the European Set Theory Society. Widely viewed as one of the founders of combinatorial set theory, his ground breaking work in collaboration with Erdős and Richard Rado led to the theory of set mappings and the partition calculus. He was the first to introduce and study relative constructibility, extending the work of Gödel, and his celebrated joint result with Galvin on cardinal exponentiation inspired Shelah to create PCF theory. He also published more than 30 papers on set theoretic topology, and in so doing, played an essential role in the introduction of the tools and methods of modern set theory to problems of general topology. In addition to his work in set theory, he made significant contributions to finite combinatorics as well. Perhaps the best known of these is the Hajnal-Szemerédi theorem on equitable colouring of graphs that proved a conjecture of Erdős. He had 56 joint papers with Erdős, making him Erdős's second-most frequent co-author.

The really big team was when Imre Csiszár played on the first board, I on the second and Ervin Györi on the third.

During the summer of 1999, András Hajnal was diagnosed with lung cancer. In order to provide András with a pleasant weekend in the midst of his treatment, it was decided that an international conference on Set Theory should be organised in his honour. As the scheduled date of the conference drew nearer, there was some concern that it might coincide with András's surgery. But, in the end, the timing could not have been better. A week before, it finally became clear that András's treatment had been successful and the conference turned into a celebration of his complete recovery. (Only one of the participants was heard to complain that if he had known how healthy András was, he would not have come.)

There can have been few conferences which were easier to organise. Because of the respect and deep affection which everybody in Set Theory has for András, there was no difficulty in putting together an outstanding program, which included many of the leaders in the field. The only difficulty concerned the name of the conference. Of course, there could be no question that András fully deserved a conference in his honour. Everybody is aware of his fundamental work in combinatorial set theory, cardinal arithmetic, set theoretic topology, as well as in finite and infinite combinatorics. However, especially before it became clear that he would fully recover his health, it seemed a little indelicate to officially refer to it as the Hajnal Conference. (Somebody made the slightly bizarre suggestion that it should be advertised as a conference to celebrate András's 68th birthday.) But now two years have passed and we can finally openly admit that the conference was held in honour of András and dedicate these Proceedings to him on the occasion of his 70th birthday.