Read the interview about the life and work of Otakar Borůvka and the activities of the Society responsible for his legacy. Eduard Fuchs, who had been meeting with him for almost 30 years, reminisced about this mathematician.
Let's start with how Otakar Borůvka came to our faculty. Originally, he was a student of civil engineering at the Czech Technical University in Brno. How did it happen that Professor Matyáš Lerch chose him as an assistant professor at the Department of Mathematics of the Faculty of Science of the newly established Masaryk University in Brno in 1921?
Matyáš Lerch was an outstanding world-famous mathematician, but reportedly, he was very unpleasant and demanding as a teacher. Students at the Czech Technical University in Brno avoided him as much as possible, and in the subject Lerch taught, when they could choose from two parallel groups with different teachers, Borůvka was one of the few who deliberately chose Lerch. Thus began the symbiosis of Lerch and Borůvka.
In 1922, Borůvka passed his state exams. He obtained a qualification in mathematics and physics for teaching at secondary schools. What was the study of mathematics like at that time?
At that time, there was no separate specialized study; teacher training in two subjects was pursued. Even when I started at the faculty in 1963, we began compulsory studies in the chosen teaching combination from the 1st year, and only after 2 years could we possibly switch to a specialized study. Until the mid-20th century, primarily trained teachers came from the faculty. However, after completing his studies, Borůvka did not enter secondary school practice and remained at the faculty as an assistant professor.
Please describe the period when after the death of Prof. Lerch, Borůvka was introduced to the study of differential geometry by Prof. Eduard Čech who arranged for him, among other things, a two-year study stay in Paris at the Sorbonne with Prof. Élie Cartan.
Eduard Čech is objectively the most recognized Czech mathematician of the 20th century. When he came to Brno, he, in my opinion, tested Borůvka on differential geometry. The method developed by Élie Cartan in Paris was a new, very difficult mathematical discipline, in which only a few people in the world truly excelled. Čech gave Borůvka an extensive article on a topic that no one in Brno knew anything about. And he said, "Dear colleague, prepare yourself; tomorrow you will tell us about it in the seminar." In my opinion, it was a test, and Borůvka obviously succeeded with Čech, who soon recommended him for foreign internships.
Borůvka already submitted a solution to the fundamental problem of combinatorial optimization in 1926 - the Minimum Spanning Tree Problem (MSTP), which is known in the world literature. This first "graph" algorithm was created at a time when graph theory did not exist de facto. MSTP plays a central role in complexity estimates in computer science, in the construction of computer networks, telecommunications networks, solving transportation problems, finding maximum flows in networks, and in a range of other problems. This work of his is not only widely cited but also a part of basic courses in this area in higher education and various optimization courses around the world. How does this topic relate to the internship with É. Cartan?
Around 1930, during his internship in Paris, Borůvka gave Professor Cartan a choice of several topics he could lecture on in seminars. Surprisingly, Cartan chose the aforementioned problem for Borůvka. Borůvka had a fantastic memory; even after 50 years, he remembered exactly who was at the seminar, where they sat, and what they asked. I do not mean to say that Borůvka did not appreciate this result; after all, it made him most famous in the world. However, for him, it was a local issue, separate from the major theories he later dealt with. Here, in general, he solved an important problem caused by a specific question: How to build an electricity distribution network in southern Moravia?
What did Borůvka focus on as a mathematician?
He was typical in that he gradually worked in a number of mathematical disciplines, approaching them in his own unique way. When you want to start studying a theory you do not know, you usually study everything known in that area. But Borůvka was the opposite extreme - of course, he had to familiarize himself with what the theory was about, but he deliberately did not study the details; he wanted to go his own way. Very soon, from differential geometry and mathematical analysis, which he pursued under Lerch's influence, he moved in the 1930s to modern algebra, and after the war, he switched to differential equations, which was the last major area he focused on. The current or relatively recent mathematical generation that Borůvka influenced thus forms the so-called school of differential equations. It played the most significant role because it was the last theory he devoted the last 40 to 50 years of his life to. It is an immensely rich area with various directions, one of which is the so-called Brno School of Differential Equations.
You studied under Borůvka. What was he like as a teacher?
In his lectures, he repeated and thoroughly discussed the material so that everyone truly understood it. He lectured slowly and very meticulously, methodically perfectly.
You encountered Borůvka for decades. What are your personal memories of him?
I crossed paths with Borůvka for nearly thirty years on a daily basis. When I joined the faculty as a half-time assistant professor in 1963, still during my studies, our offices were next to each other. Soon, I got to know his family as well. We were almost fellow countrymen - he was born in Uherský Ostroh, and I grew up in nearby Bzenec. Borůvka fondly remembered his youth. His daughter, Yvona, whom I befriended, also studied mathematics and was a year below me. We attended Borůvka's elective lectures on algebra together. And in the last years when Prof. Borůvka could not come to the faculty due to health reasons, I often visited him at home. What was he like as a person? He was a “First Republic” gentleman of the old school, kind and empathetic. I never saw him visibly upset or emotionally stirred by anything.
Borůvka was known for organizing a variety of mathematical activities. What were they about?
He was social and cared about the team spirit of the mathematical department. In the 1960s, when our mathematical department was still located in Janáček Square, he introduced Thursday teas. Tea was served in one of the lecture halls at three in the afternoon, and it was obvious that any teacher who was free at that time would at least stop by for a while. Borůvka was always there. He also organized renowned mathematical trips together with Slovak mathematicians. In this regard, he was sociable, but personally, he was rather introverted. I must also mention his long-standing effort to establish the mathematical journal Archivum mathematicum, which is still a hallmark of our department.
Borůvka had strong ties to Slovakia. How did he influence mathematicians there?
Prof. Borůvka was born near the Slovak border. His relationship with Slovakia was cultivated from an early age as something natural. Slovaks greatly appreciated him, even though the generation of direct participants has essentially passed away, their successors continue to acknowledge his influence. After World War II, when Slovak mathematics and science in general needed to reach a higher level, Borůvka travelled to Bratislava for many years and lectured on mathematics week after week. He essentially educated a whole generation of young mathematicians in Bratislava. And he did it, which is almost unimaginable today, in his personal free time and without any claim to reward. He saw it as a moral obligation and hardly ever talked about it. Slovaks were, of course, aware of this. We also met during the mentioned mathematical trips. And when we in Brno were organizing major international summer schools on algebra, with which Borůvka had no professional connection, logically, we collaborated with mathematicians from Bratislava.
What was Borůvka like as a person?
He treated all people without exception very kindly and tolerantly. The people he truly valued and chose as collaborators were those who could reach the appropriate level of professional expertise. He was conservative in the good sense of the word. I already mentioned that he had a photographic memory; he could recall and describe his trips to France in the 1920s in the smallest detail.
He did not always have an easy personal life. He had two children. The older one was his son, whom he was very fixated on, but he emigrated. At that time, it practically meant a cessation of personal contacts. Something like today's video calls or other regular communication options did not exist then, and meetings were not possible. And his daughter Yvona tragically passed away in 1993. Her daughter, Borůvka's granddaughter, was studying with us at that time, and coincidentally, I supervised her thesis.
How could it happen that Borůvka ceased to be a university employee in 1970?
It happened exactly in the style of normalization. In 1969, a communist scoundrel named Hrbek, a professor of medicine from Olomouc, became the Minister of Education. He decided to "cleanse" the education system, and Borůvka received a cyclostyled letter from the minister informing him that his employment at the university was terminated. Fortunately, Borůvka, unlike many others, did not have existential problems and could essentially retire. However, it was possible to arrange for him to transition to a partial position at the Mathematical Institute of the Academy of Sciences. And because at our Department of Mathematics and Statistics there was not a downright scoundrel among us, Borůvka kept his office. He went there for many years, even though he was not technically a university employee. He had his taxi driver who would take him there and bring him back.
How was Borůvka's most frequently published photograph created?
It was taken at the celebration of my first wife's 40th birthday, where Borůvka attended. It was in 1981, and Borůvka was eighty-two at the time. This photo was taken at the celebration, and it turned out very well, so it is widely circulated.
How was the Society of Otakar Borůvka, which participated in the celebrations of his 100th birthday in 1999, established?
Even during Borůvka's lifetime, we wanted his name to be somehow preserved. We agreed with one of Borůvka's most prominent students, František Neuman, who was a professor at the Brno University of Technology, and with Bedřich Půža, who later transferred from our faculty to the Brno University of Technology, to establish a foundation bearing Borůvka's name. This foundation later evolved into the Society of Otakar Borůvka, which continues its work to this day. We advocated for the establishment of a tombstone corresponding to his significance at the honorary burial site in the Brno cemetery. In addition to organizing and hosting celebrations and events, we take care of Borůvka's grave. Thanks to the Society and its guiding spirit, Borůvka's student Ladislav Kaňovský, Borůvka's room has been preserved. Mathematics department originally resided, until 1964, in Kotlářská Street in the building where physics is now. In 1964, it moved to Janáček Square, where Borůvka had his office until the end. Even after his death, the office remained intact. When we moved to Building 8 in Kotlářská Street, we managed to move the furniture from his original office and have it renovated.
And what is on the agenda for the 125th anniversary of Professor Borůvka's birth, which we commemorate in 2024?
Celebrations will take place at several locations. Partially in Uherské Hradiště, because O. Borůvka attended grammar school there, and the Society of Otakar Borůvka has long-standing strong ties with the local grammar school. In Brno, there will be an unveiling of a commemorative plaque on the house in Roubalova Street, where Borůvka lived. We are also organizing meetings with Slovak mathematicians, as Slovaks will naturally attend the celebrations. There will also be a memorial event at the central cemetery. The next day, a commemorative plaque will be unveiled here at the faculty, on the building of the Department of Mathematics and Statistics in Kotlářská Street. The programme will continue with a scientific conference. And there are plans for a cultural and social commemoration of Borůvka, where students from the Uherské Hradiště grammar school will also perform.
Thank you for the interview
Zuzana Jayasundera
On September 24, a group of graduates from the teacher training program in mathematics and physics visited us. They completed their studies in 1970, so we gave them a tour to show how the faculty has changed since then.
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