Stefan Banach: who was founder of modern functional analysis - and best quotes as Google Doodle celebrates him

The date is significant as it marks the day that the self taught Polish mathematician officially became a professor

Today, the iconic Google Doodle pays tribute to Stefan Banach, an original member of the Lwów School of Mathematics and founder of modern functional analysis.

Google has decided to remember Banach today, 22 July, as it was on this date in 1922 that the Polish mathematician officially became a professor.

This is everything you need to know about Banach, who is widely regarded as one of the most influential mathematicians of the 20th century.

Who was Stefan Banach?

Banach was born on 30 March 1892 in Kraków, to father Stefan Greczek and mother Katarzyna Banach.

His father was a private in the Austro-Hungarian Army and was unable to marry due to military regulations - with his mother too poor to support the child herself, it was decided that Banach would be sent to the city to be raised by family and friends.

When Banach was 10 years old, in 1902, he enrolled in school where he and his friend,  Witold Wiłkosz, also a future mathematician, would spend their time working on mathematical problems.

Stefan Banach is being remembered in 2022 with his own Google Doodle (Photo: Instytut De Republica)
Stefan Banach is being remembered in 2022 with his own Google Doodle (Photo: Instytut De Republica)
Stefan Banach is being remembered in 2022 with his own Google Doodle (Photo: Instytut De Republica)

Later in his life, Banach would reportedly credit Dr Kamil Kraft, the mathematics and physics teacher at the school, with sparking his initial interest in mathematics.

When he was 18, he moved to Lwów, which today is known as Lviv, to study engineering at the Lwów Polytechnic. At some point he also attended Jagiellonian University as well.

When World War I occurred, Banach was excused from military service due to the fact that he was left handed and had bad eyesight. During this time he instead taught in local schools.

When did he meet Hugo Steinhaus?

Banach’s life changed substantially after meeting Professor Hugo Steinhaus, a renowned mathematician of the time.

The two met in 1916, in Kraków’s Planty park when Steinhaus overheard Banach talking about Lebesgue integration, which at the time was a pretty new idea in mathematics.

Steinhaus became interested in Banach, who was a self-taught mathematician, and shortly afterwards he invited him to work on some problems that had proven to be difficult. Banach solved them within the week.

Stefan Banach’s life changed when he met Hugo Steinhaus (Photo: Instytut De Republica)
Stefan Banach’s life changed when he met Hugo Steinhaus (Photo: Instytut De Republica)
Stefan Banach’s life changed when he met Hugo Steinhaus (Photo: Instytut De Republica)

Steinhaus has been quoted as saying that Banach was his “greatest scientific discovery”.

It was through Steinhaus that Banach was introduced to different academic circles and in 1918, he obtained an assistantship at Lwów Polytechnic.

On 2 April 1919, Banach, Steinhaus and a number of other Kraków mathematicians founded a mathematical society which would go on to become the Polish Mathematical Society.

With Steinhaus’ help, Banach also received a doctorate from the university and in 1922 he published his doctoral thesis which featured the basics of functional analysis, something that would soon become a whole new branch of mathematics.

A statue of the Otto Nikodym and Stefan Banach Memorial Bench, both mathematicians,  sculpted by Stefan Dousa in Krakow, Poland (Photo: Adobe Stock)
A statue of the Otto Nikodym and Stefan Banach Memorial Bench, both mathematicians,  sculpted by Stefan Dousa in Krakow, Poland (Photo: Adobe Stock)
A statue of the Otto Nikodym and Stefan Banach Memorial Bench, both mathematicians, sculpted by Stefan Dousa in Krakow, Poland (Photo: Adobe Stock)

Following the publication of his thesis, Banach was hired as a professor at Lwów Polytechnic. In the following years, Banach went on to become accepted as a member of the Polish Academy of Learning and also headed the second Chair of Mathematics at University of Lwów.

Banach and his fellow mathematicians later founded the Lwów School of Mathematics and in 1929, the group started publishing its own journal, called Studia Mathematica, which was largely devoted to Banach’s specialism of functional analysis.

What happened in World War II?

When World War II broke out, following the invasion of Poland by Nazi Germany and the Soviet Union, Lwów came under the control of the Soviet Union for almost two years.

In 1941, after Lwów was taken over by Germany, all universities were closed, and Banach, as well as his colleagues, were employed as lice feeders at Professor Rudolf Weigl’s Typhus Research Institute.

The Weigl Institute provided employment for a number of university professors and associates during WWII, and it protected them from random arrests and from being deported to concentration camps.

What is he known for?

Over the course of his career, Banach had his name associated with a number of theorems and mathematical concepts, including:

  • Banach-Tarski paradox
  • Banach-Steinhaus theorem
  • Banach-Alaoglu theorem
  • Banach-Stone theorem
  • Banach-Schauder theorem
  • Banach-Hahn theorem 
  • Banach fixed-point theorem
  • Banach spaces
  • Banach algebras
  • Banach measures

When did he die?

In January 1945, Banach was diagnosed with lung cancer. He passed away on 31 August later that year, at the age of 53.

The mathematician passed away when he was 53 (Photo: Instytut De Republica)
The mathematician passed away when he was 53 (Photo: Instytut De Republica)
The mathematician passed away when he was 53 (Photo: Instytut De Republica)

In 1992, the Polish Academy of Sciences established the Stefan Banach Medal in honour of the mathematician. The medal is awarded by the Presidium of the academy for outstanding achievements in mathematical sciences.

Was he married - did he have a son?

Banach married his wife Łucja Braus in September 1920 after they met when Braus was working as a secretary to a cousin of Steinhaus’.

They welcomed their son, Stefan Jr, into the world in 1922. He then went on to become a neurosurgeon and doctor of medicine.

In an interview, when asked if Banach tried to get his son interested in mathematics, Stefan Jr said of his father: “Yes, he tried, but I was more interested in humanities and the natural sciences.

“In any case, the more I learned and understood mathematics in high school the more I came to realise that I could never attain my father’s level.

“And so, quite early on, a desire crystallised in me to study medicine, and my father did not try to stop me. He believed that everyone should earn a living through his hobby.”

Stefan Jr added that while his father was a busy man, he “always had plenty of time” for his son.

He said: “Sundays belonged to me. Every second Sunday we went to see football matches that were played by "Pogonia", a Lvov team.

“On alternate Sundays, when the team was playing away, we would go to the cinema to see cowboy films.”

Stefan Banach quotes

Here are some of Banach’s best quotes to remember the mathematician:

“Mathematics is the most beautiful and most powerful creation of the human spirit. Mathematics is as old as Man.”

“A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies.”

“Mathematics is the most beautiful and most powerful creation of the human spirit.”