Personal reminiscences and remarks on the mathematical work of Tibor Gallai

Abstract

Tibor Gallai is my oldest friend . We met more than 52 years ago, and we had our first long mathematical discussion in the summer of 1930 . Our friendship and collaboration started then, and no doubt will last until one of us "leaves" . I still remember that I learned from him at this occasion the beautiful proof of Jacob Steiner for the isoperimetric property of the circle . He pointed out to me that the proof is not quite accurate since Steiner only proves that if the maximum exists then it must be the circle . About two years later I proved that Steiner's proof can easily be repaired since one can show that it can be made to converge. Soon after, I found that Caratheodory found the same proof in 1909 and published it in the Mathematische Annalen . I knew of Gallai's existence many years before we met, since we both were diligent and successful solvers of the problem section of the Hungarian Mathematical Journal for High Schools . We both and in fact most of the Hungarian mathematicians (Gallai on the whole was better at it than I, but Hajos and later Vazsonyi were the real stars) of our generation owe a great deal to this journal and its illustrious editor Andor Farago, who by the way studied mathematics with my parents and who was murdered together with his children by the Fascists in 1945 . Gallai's parents were not very well off. Thus he often had to tutor students and rarely could devote himself completely to mathematics . As a Jew, he faced immediately a serious hurdle ; by a law passed in 1920 only 5% of the university students could be Jewish . Thus it was essential that he should win the mathematical competition for high school students held in June since the victor was automatically admitted to university. I am fairly sure Gallai would have easily won the competition but due to the ill will of some of his teachers he was not allowed to take part . He at first tried to get in to the technological university to become an engineer . I very much disapproved of this since I wanted him to study mathematics . "Fortunately" he was not admitted and after he won the Eotvos competition* held in the early autumn of 1930, he was admitted to the University and started his brilliant career as a mathematician .