Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the world's most important and influential 20th-century mathematicians.

Before he could do so, he died in August 1945, having been diagnosed seven months earlier with lung cancer. Some of the notable mathematical concepts that bear Banach's name include Banach spaces, Banach algebras, Banach measures, the Banach–Tarski paradox, the Hahn–Banach theorem, the Banach–Steinhaus theorem, the Banach–Mazur game, the Banach–Alaoglu theorem, and the Banach fixed-point theorem. ==Life== ===Early life=== Stefan Banach was born on 30 March 1892 at St.

Mien taught Banach French and most likely encouraged him in his early mathematical pursuits. In 1902 Banach, aged 10, enrolled in Kraków's IV Gymnasium (also known as the Goetz Gymnasium).

After graduating in 1910, Banach moved to Lwów (today called Lviv) .

While generally Banach was a diligent student he did on occasion receive low grades (he failed Greek during his first semester at the gymnasium) and would later speak critically of the school's math teachers. After obtaining his matura (high school degree) at age 18 in 1910, Banach moved to Lwów (today called Lviv) with the intention of studying at the Lwów Polytechnic.

As Banach had to earn money to support his studies it was not until 1914 that he finally, at age 22, passed his high school graduation exams. When World War I broke out, Banach was excused from military service due to his left-handedness and poor vision.

He attended some lectures at the Jagiellonian University at that time, including those of the famous Polish mathematicians Stanisław Zaremba and Kazimierz Żorawski, but little is known of that period of his life. ===Discovery by Steinhaus=== In 1916, in Kraków's Planty gardens, Banach encountered Professor Hugo Steinhaus, one of the renowned mathematicians of the time.

The theory of what came to be known as Banach spaces had antecedents in the work of the Hungarian mathematician Frigyes Riesz (published in 1916) and contemporaneous contributions from Hans Hahn and Norbert Wiener.

After Poland regained independence in 1918, Banach was given an assistantship at the Lwów Polytechnic.

In 1919, with several other mathematicians, Banach formed a mathematical society.

The society was officially founded on 2 April 1919.

In 1920 he received an assistantship at the Lwów Polytechnic.

The doctoral thesis, accepted by King John II Casimir University of Lwów in 1920 and published in 1922, included the basic ideas of functional analysis, which was soon to become an entirely new branch of mathematics.

His funeral at the Lychakiv Cemetery was attended by hundreds of people. ==Contributions== Banach's dissertation, completed in 1920 and published in 1922, formally axiomatized the concept of a complete normed vector space and laid the foundations for the area of functional analysis.

The doctoral thesis, accepted by King John II Casimir University of Lwów in 1920 and published in 1922, included the basic ideas of functional analysis, which was soon to become an entirely new branch of mathematics.

The thesis was widely discussed in academic circles and allowed him in 1922 to become a professor at the Lwów Polytechnic.

At the same time, from 1922, Banach also headed the second Chair of Mathematics at University of Lwów. Young and talented, Banach gathered around him a large group of mathematicians.

His funeral at the Lychakiv Cemetery was attended by hundreds of people. ==Contributions== Banach's dissertation, completed in 1920 and published in 1922, formally axiomatized the concept of a complete normed vector space and laid the foundations for the area of functional analysis.

In 1924 he was also accepted as a member of the Polish Academy of Learning.

In 17 June 1924 Banach become a correspondence member of the Polish Academy of Sciences and Fine Arts in Kraków. ===World War II=== 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.

Initially an assistant to Professor Antoni Łomnicki, in 1927 Banach received his own chair.

Around 1929 he began writing his Théorie des opérations linéaires. After the outbreak of World War II, in September 1939, Lwów was taken over by the Soviet Union.

In 1929 the group began publishing its own journal, Studia Mathematica, devoted primarily to Banach's field of study—functional analysis.

First published in Polish in 1931, the following year it was also translated into French and gained wider recognition in European academic circles.

His major work was the 1932 book, Théorie des opérations linéaires (Theory of Linear Operations), the first monograph on the general theory of functional analysis. Born in Kraków, Banach attended IV Gymnasium, a secondary school, and worked on mathematics problems with his friend Witold Wilkosz.

In this work Banach called such spaces "class E-spaces", but in his 1932 book, Théorie des opérations linéaires, he changed terminology and referred to them as "spaces of type B", which most likely contributed to the subsequent eponymous naming of these spaces after him.

Around 1929 he began writing his Théorie des opérations linéaires. After the outbreak of World War II, in September 1939, Lwów was taken over by the Soviet Union.

Banach, from 1939 a corresponding member of the Academy of Sciences of Ukraine, and on good terms with Soviet mathematicians, had to promise to learn Ukrainian to be allowed to keep his chair and continue his academic activities.

In 1941, when the Germans took over Lwów, all institutions of higher education were closed to Poles.

Following the German takeover of Lwów in 1941 during Operation Barbarossa, all universities were closed and Banach, along with many colleagues and his son, was employed as lice feeder at Professor Rudolf Weigl's Typhus Research Institute.

When the Soviets recaptured Lwów in 1944, Banach reestablished the University.

Employment in Weigl's Institute provided many unemployed university professors and their associates protection from random arrest and deportation to Nazi concentration camps. After the Red Army recaptured Lviv in the Lvov–Sandomierz Offensive of 1944, Banach returned to the University and helped re-establish it after the war years.

Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the world's most important and influential 20th-century mathematicians.

Before he could do so, he died in August 1945, having been diagnosed seven months earlier with lung cancer. Some of the notable mathematical concepts that bear Banach's name include Banach spaces, Banach algebras, Banach measures, the Banach–Tarski paradox, the Hahn–Banach theorem, the Banach–Steinhaus theorem, the Banach–Mazur game, the Banach–Alaoglu theorem, and the Banach fixed-point theorem. ==Life== ===Early life=== Stefan Banach was born on 30 March 1892 at St.

In January 1945, however, he was diagnosed with lung cancer and was allowed to stay in Lwów.

He died on 31 August 1945, aged 53.

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