A Beautiful Mind

  • A Beautiful Mind
  • A Beautiful Mind
  • A Beautiful Mind
Issue 123, May 2019.
A Beautiful Mind
Lviv’s Stefan Banach was a mathematician wunderkind – during some of Lviv’s most tumultuous times.
You’d be forgiven for not knowing the name Stefan Banach, a self-taught mathematics prodigy and scientific genius. How many people can name famous mathematicians anyways, even if they were instrumental in the development of topological vector spaces, measure theory, integration, the theory of sets, and orthogonal series? Well, if you can name one, let it be Lviv’s-own Banach, who studied and taught in the city under four different regimes, from 1910-45. Here’s his story.
Polish Beginnings
Banach was born in the Polish city of Ostrowsko, about 50 km south of Krakow. It didn’t start out easy for the future math king – his father couldn’t marry his mother due to military rules, and his mother was too poor to keep him, so she left him when he was just four days old and he was sent to live with relatives. He lived with his grandmother until her death and then moved to Krakow, where he would receive his first formal education from Juliusz Mien, a French intellectual. It was Mien that taught Banach the fundamentals of mathematics. He taught him French, too, just to be sure.
Move to Lviv
He finished his secondary education in Krakow in 1910. According to a colleague, Banach was very good in math and sciences, but graduated without distinction. He chose to study engineering at the Lviv Polytechnic University (1910-16) and while the world was crumbling around him, he spent his time tutoring, building roads, and attending math lectures. It was at one of these lectures at the Jagiellonian University in Krakow that Banach met, by chance, Steinhaus – a mathematician recently employed by Lviv University. Impressed by the young Banach’s talents for math, he shared with him a problem he was working on and couldn’t solve. They solved the question together, published it in 1918, and a lifelong collegial friendship was born. He even introduced Banach to his wife, Lucia Braus, who he married in 1920.
Math Wizard
At the same time, he became an assistant professor of mathematics at the university, where he was doing his doctoral research under the guidance of Lomnicki. By 1922, he was awarded his habilitation (a degree allowing him to teach at university) by Lviv’s Jan Kazimierz University for his thesis on measure theory. He was promoted to a full professor in 1924, spent the next academic year in Paris and later, alongside Steinhaus, founded the Studia Mathematica. And thus, began an extensive career in academic mathematics. He would write dozens of articles for acclaimed academic journals, present his papers at prestigious academic conferences, like the International Congress of Mathematicians, and work with some of the finest minds in the field.
Surviving the War
Banach was elected President of the Polish Mathematical Society in 1939 and was allowed to stay after the Soviets invaded Lviv in 1939. He continued to hold his chair at the university, now named Ivan Franko University, and was named Dean of the Faculty of Science. Famous Soviet mathematicians like Sobolev and Aleksandrov would visit him during this period, and he would attend conferences throughout the USSR. Banach was in Kyiv when the Nazis invaded and was promptly arrested after racing back to Lviv to be with his family. While many prominent scientists were executed – including his advisor Lomnicki – Banach miraculously made it through the war. He spent the remainder of the Nazi occupation feeding lice at Professor Weigel’s Institute in Lviv. After the Red Army recaptured the city in 1944, Banach helped to reestablish the university. He was up for the Minister of Education position in Poland before succumbing to lung cancer in 1945 at age 53. He is buried in Lviv’s Lychakiv cemetery. 
Sobolev remembers his last meeting with Banach, in 1944, like this:
“Despite the grave illness that was undercutting his strength, Banach’s eyes were still lively. He remained the same sociable, cheerful, and extraordinarily well-meaning and charming Stefan Banach whom I had seen in Lviv before the war. That is how he remains in my memory – with a great sense of humour, an energetic human being, a beautiful soul, and a great talent…”.