# Vera Sós on mathematicians she knew

In an interview Vera Sós gave in Budapest in July 2000 she spoke about mathematicians who had played a large part in her life. The interview was conducted by Gyula Staar and is available in Hungarian on 'Matematika Professzor Asszonya',

*Természet Világa folyóirat*. We present a version of her comments below.**1. Paul Erdős**

Erdős never felt that he was intellectually superior to anyone. He was always direct, friendly and considered himself an equal partner to the young people he talked to.

**2. Tibor Gallai**

You may be surprised that I do not start with him as a mathematician, but rather about his human qualities. Gallai was an infinitely pure man. He stood for the highest of moral standards, morality, human integrity, of which there are very few examples. Even now, years after his death, he is often referred to at conferences: Gallai was the first to prove this point, but he never published it. There are several such items that have since been named after others. He raised his values high, published only his best achievements, his international influence is very significant. Here is a typical story: in 1956, the year of the Great Flood, he received the Kossuth Prize, but the money which came with the prize he gave, as it was, to the victims of the flood. Needless to say, Gallai was never a rich man. As usual,

*Matematikai Lapok*published an article about his award-winning work. Then Pál Turán, one of his best friends, was the editor-in-chief of the journal. Gallai wrote him an official letter in which he complained that the Bolyai János Mathematical Society journal had given such a commendable article about his work that he had, therefore, left the Society in protest.

Here is another image of the man. Gallai moved to the University of Technology in 1948-49, where he became head of the Department of Mathematics. He then resigned and headed to the Mathematical Research Institute. At the age of fifty-five, he left the Institute. He had saved little money, and the mathematician had nothing much to do at that time. For five years, he lived very poorly, in an ascetic manner, without pension or benefits. In fact, no one, not even his closest friends, have ever explained why he had left the Institute. Unfortunately, his wife soon became very ill. For more than ten years, Gallai had been with her from morning to night, doing everything required for such a disease. He had to stop doing mathematics. The exceptions were the short periods when Erdõs was at home. He always went to Gallai and encouraged him to think about mathematics. When his wife died, Gallai was already seventy years old. He picked up the topics he once stopped and wrote some very serious articles. There remained a keen interest and passion for mathematics, even though he had overshadowed it for many years.

**3. Alfréd Rényi**

Rényi was a man of different habits. In a few words: lightweight, direct, versatile, colourful, full of joy, incredibly active. Many have stated that Rényi's main field of research was probability theory. In fact, he was important in many topics in mathematics. He played a central role in Hungarian mathematical life, including education, and high-level dissemination of knowledge. Given that he has lived for less than 50 years, his versatile productivity and its impact are almost unprecedented. He was burning the candle at both ends.

**4. Rózsa Péter**

People either loved or did not like Rózsa

**very much. I was one of the former. Despite the great age difference, our relationship was very close. Rózsa Péter was strict in every way. Expecting others to follow the path she imagined, she kept that in mind in her teaching. If she didn't like something, she quarrelled and yelled. She fought for the truth by all means and with perseverance.**

**5. Lipót Fejér and Frigese Riesz**

They were both friends and rivals, as is often the case with such major figures. They were leading figures in mathematics, and their careers went in close parallel. They were locked together by history for many years in a common room at the university. They were mathematicians of very different statuses, and their little humorous quarrels were the result. Riesz was a theoretician, a more abstract mathematician, Fejér more classic. They had a different style of presentation, a different attitude to people, to life. They both lived as bachelors. Riesz seemed more lonely, withdrawn, aloof. Fejér was a more open, sociable, helpful individual. He was a pianist, he was a friend of poets, he loved life. Géza Ottlik, who was a student of Fejér, wrote: "He was a giant. Eternal consolation a mere being. Whoever did not know, knows nothing about his world and will never know."

**6. Paul Turán**

He taught me at university, and after I graduated, we were lucky enough to get fall in love and get married. My husband also did a lot of mathematics in the humiliating days of labour service. I recorded the lines that appeared in the Journal of Graph Theory after his death: "The joy of starting an unusual problem, the beauty of the problem, the gradual approach to the solution, and the final solution made these days unforgettable. The sense of spiritual freedom and the fact that it cannot be suppressed to a certain extent, all contributed to ecstasy." The Turán extreme graph theorem was born there, first outlined in his head at the top of the pylon while he was at work. He didn't need paper and pencils to think about it.

He was a good mathematician, first of all, because his life was mathematics. He was incredibly intrigued, interested, and on several occasions used mathematics for spiritual survival. This is a great gift. He sought the essence, the cause of the phenomena, and was able to grasp it. Many people know that the Riemann conjecture worried him ... but lifting that weight can help you fight in many ways. Some people put their whole life into it and get stuck. And there are people like him who have been strengthened by this effort. He liked to see deeply into things. He refused to accept a proof until he understood it in its full depth and detail. He was an analyst, and most of his results included the technique of analysis, its method.

The qualities which led him to him being successful were: power of proof, incredible depth of understanding and insight, intuition, stubborn perseverance and never-ending interest in and passion for mathematics. It burned into his soul until the last moment of his life.

We did some work together but our subjects were different, and our mathematical character was different. A painting can be recognised by its style, technique, theme, who painted it, and so it is with mathematics. But we did undertake some joint work. We have a very old joint article on graphs. The problem that we have formulated here is still an open and is a much studied question, and today what we have proved then is often referred to. Do not misunderstand, not because our results are so profound, but the problem is very difficult. Then we have some articles with Paul Erdős and a Canadian mathematician. We applied the generalisations of the graph theory method and the Turán extreme graph theorem to potential theory, geometry, distance distribution. The history of graph theory and of combinatorics in Hungary and abroad is a separate story. It was not a Hungarian specialty so it was very difficult for combinatorics to be properly valued. Paul Erdős was terribly annoyed about that. There was a great deal of awareness, power, and determination to fight such misconceptions. This also contributed to the writing of these articles.

Last Updated April 2020