Stefan Banach was one of the world's most important mathematicians of the 20th Century. Whilst you might not have heard of him, he led a fascinating and important life.

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In the following article, we'll briefly highlight why he was important and look into some of his most important contributions to mathematics.

## Who is Stefan Banach?

Stefan Banach was one of the world's most important mathematicians and scientists of the 20th Century. He established the field of modern functional analysis, which as an entirely new branch of mathematics at the time.

Stefan also helped develop the theory of topological vector spaces. Much of his work is widely used in mathematics today from Banach space, Banach algebra, Banach manifold, Banach measure, Banach integral, Banach limit, and Banach bundle.

## What did Stefan Banach discover?

Stefan Banach discovered many important mathematical concepts but is best known for his work on functional analysis. Functional analysis, according to Wikipedia is:

"[A] branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g., inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense."

Crystal clear right? The following video will help you understand the concept a little better.

## Some Interesting facts about Stefan Banach

Here are some interesting facts about the great mathematician Stefan Banach.

## 1. Stefan Banach never knew his mother

Stefan never knew his mother. His father Stefan Greczek and his biological mother never married.

Whilst his name is construction of his father's first name and declared mother's surname, she left his father when he was just **4 days** old.

Nothing more is known about her and Stefan's father told Stefan he was sworn to secrecy about her identity. According to his birth certificate, her name was Katarzyna Banach, but this is thought to be false by many historians.

## 2. Stefan's father didn't really look after him either

Not long after his mother left, he was raised by his grandmother in Ostrowsko. But she soon fell ill, and Stefan's father sent him to be raised by Franciszka Plowa who lived in Kraków with her daughter Maria.

His father didn't support Stefan much throughout his childhood and school studies and openly told him he was on his own once he left school.

## 3. Stefan liked to do most of his work at Cafe's

Stefan was certainly an interesting character it seems. According to his friends and peers, he preferred to do most of his work in cafes throughout Lvov (Lviv).

According to Stan Ulam (a notable mathematician in his own right and one of his friends) :

"It was difficult to outlast or outdrink Banach during these sessions. We discussed problems proposed right there, often with no solution evident even after several hours of thinking. The next day Banach was likely to appear with several small sheets of paper containing outlines of proofs he had completed."

## 4. Banach spent the war feeding lice

During the outbreak of WW2, Banach was working as the Dean of the Faculty of Science at Ivan Franko University. But this all changed when National Socialist Forces occupied Lvov (now Lviv, Ukraine) in 1941.

He was often arrested under various charges but avoided being executed like many other academics in Poland. Throughout most of the occupation, he was forced to take up less academical challenging work that involved feeding lice in a German Institute for the research of infectious diseases.

As soon as Lvov was liberated by Soviet forces in 1944, he was reinstated to his former position.

## 5. The Banach-Tarski paradox will make your head hurt

In 1926, Banach worked with another mathematician, Alfred Tarski, to publish an interesting paradox. It apparently proved that a ball, or any object, can be divided up into subsets.

Nothing strange there, but they went on to show that these pieces could then be reassembled to form two new identical objects of the same dimensions as the first.

Their worked caused a bit of a stir in the mathematical community. They used, in part, a highly respected axiom called the Axiom of Choice, for their paradox.

Since the results are clearly can't be true, it caused many of their peers to begin to question the basic premise of the axiom.