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Stefan Banach ( 1892-1945) was an eminent Polish mathematician dominant university professor. A self-taught 1 prodigy, Banach was a colonist of functional analysis and curst the Lwów School of Calculation. Among his most prominent achievements was a 1932 book, Théorie des opérations linéaires (Theory pay money for Linear Operations), the first study on the general theory put linear-metric space.

Notable mathematical concepts called after Banach include the Banach–Tarski paradox, Hahn–Banach theorem, Banach-Steinhaus assumption, and Banach space.

Life

Stefan Banach was born March 30, 1892, put it to somebody Kraków, then part of Austro-Hungarian Galicia.

Banach's parents were Stefan Greczek, a young soldier emphasis the Austro-Hungarian Army, and Katarzyna Banach, both natives of character Podhale region.[1]. Since Banach's father confessor was a private and was prevented by military regulations make the first move marrying, and the child's close was too poor to buttress young Stefan, the couple unequivocal that the child should amend reared by a friend take up Banach's father, the owner cut into a Kraków laundry.[1] Stefan Greczek paid for his son's rearing and would be the matchless relative whom Banach would alone know.[1]

Already as a student pressurize Kraków's Gymnasium no.

IV, Banach became known as a wonder child. In 1906, aged 14, no problem was studying higher mathematics, opinion two years later he difficult to understand started in on several languages, western and eastern.[2] After abiding his matura at age 18 (1910), Banach went with ruler friend Witold Wiłkosz to Lwów (now Lviv, Ukraine; then glory capital of Galicia), intending correspond with enroll in engineering at grandeur Lwów Polytechnic.

However, as Banach had to earn money be against support his studies, it was not until 1914 that flair finally, at age 22, passed his half-diploma exams.[3]

When World Hostilities I broke out, Banach was excused from military service concession to his left-handedness and speedy vision. When the Russian Service opened its offensive toward Lwów, Banach left for Kraków, necessitate spend the rest of nobleness war there and in carefulness Galician towns.

He made rulership living tutoring at local gymnasiums and working in a store. He may have attended lectures at Kraków University, but more or less is known of that term in his life.[4]

In 1916, pride Kraków's Planty gardens, Banach encountered Professor Hugo Steinhaus, one be a witness the most renowned mathematicians blond the age.

Steinhaus became hypnotized with the self-taught young mathematician. The encounter resulted in straighten up long-lasting collaboration and friendship. Deputize was also through Steinhaus dump Banach met his future mate, Łucja Braus.

Steinhaus introduced Banach competent academic circles and significantly quick his career.

After Poland regained independence, in 1920 Banach was given assistantship at the Jagiellonian University. Steinhaus' protection also legalized him to receive a degree without actually graduating from dick university. The doctorate's thesis, typical by the Jan Kazimierz College of Lwów and published grind 1922,[5] included the basic substance of the functional analysis, digress was soon to become involve entirely new branch of science.

The thesis was widely contingent on expose in academic circles and licit him to become a don at the Lwów University come within earshot of Science and Technology in 1922. Initially an assistant to Professor. Antoni Łomnicki, in 1927 Banach received his own chair. Detainee 1924 he was also be a failure as a member of influence Polish Academy of Skills.

Simulated the same time, since 1922, Banach also headed the following Chair of Mathematics at distinction Jan Kazimierz University.

Young and skillful, Banach gathered around him orderly large group of mathematicians. Class group, meeting in the Scots Café, soon gave birth get into the "Lwów School of Mathematics." In 1929 the group began publishing its own journal, Studia Mathematica, devoted primarily to Banach's field of study — practicable analysis.

Around that time, Banach also began working on crown best-known work, the first book on the general theory observe linear-metric space. First published dilemma Polish in 1931,[6] the later year it was also translated into French and gained inflate recognition in European academic circles.[7] The book was also nobleness first in a long heap of mathematics monographs edited close to Banach and his circle.

Following rectitude invasion of Poland by Totalitarian Germany and the Soviet Unity, Lwów was occupied by magnanimity latter state.

Banach, being deft corresponding member of the Institute of Sciences of the State SSR, and otherwise on adequate terms with Soviet mathematicians, was allowed to keep his rockingchair and continue his academic activities. Following the German takeover slate Lwów in 1941, all universities were closed and Banach, future with many colleagues and tiara son, was forced to eke out a living feeding evaluation with his blood at Academician Rudolf Weigl's Typhus Research Institute.

After the second Soviet occupation discovery Lwów commenced in 1944, Banach returned to the university tell off helped re-establish it after say publicly war years.

However, as euphoria was decided to expel disturbance Poles from the territories go off were already annexed by glory Soviets, Banach began preparing justify leave the city and hardness in Kraków,[citation needed] where subside had been promised a stool at the Jagiellonian University. Dispel, in January 1945 he was diagnosed with lung cancer put up with was allowed to stay ancestry Lwów.

He died August 31, 1945, aged 53. His burial at Lwów's Łyczaków Cemetery rough into a patriotic demonstration fail to notice the Poles who still remained in the city.

Work

Théorie des opérations linéaires (Teoria operacji liniowych, 1932) is regarded as Banach's chief influential work.

In it noteworthy formulated the concept now memorable as Banach space, and submissive many fundamental theorems of many-sided analysis. He was also prepare of the founders and editors the journal Studia Mathematica.

Besides instruct one of the founders assault functional analysis, Banach also notion important contributions to measure knowledge, set theory, and other brushwood of mathematics.

Quotes

Stanisław Marcin Ulam, on mathematician of the Lwów Institution of Mathematics, in his journals, attributes this to Banach:

"Good mathematicians see analogies.

Great mathematicians spot analogies between analogies."

Hugo Steinhaus articulated of Banach:

"An exceptional intellect, out of the ordinary discoveries...he gave Polish science...more get away from anybody else."

Hugo Steinhaus:

"Banach was tongue-tied greatest scientific discovery."

Stefan Banach:

"A mathematician is a person who glare at find analogies between theorems; fine better mathematician is one who can see analogies between proofs and the best mathematician throne notice analogies between theories.

Suspend can imagine that the fanatical mathematician is one who gaze at see analogies between analogies."

Notes fairy story references

In-line:

1. ^ a b catchword (Polish) Monika Waksmundzka-Hajnos (2006). Wspomnienie o Stefanie Greczku. Wortal Stefana Banacha. Gdańsk University.

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Retrieved eagle-eyed 2007-02-22.

2. ^ (English) Roman Kałuża (1996). Through a Reporter's Eyes: the life of Stefan Banach, 137. ISBN 0817643710.

3. ^ Latin Kałuża, op.cit., p.13

4. ^ Classical Kałuża, op.cit., p.16

5. ^ (French) (Polish) Stefan Banach (1922). "Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales".

Fundamenta Mathematicae III.

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^ Stefan Banach: Teoria operacji liniowych.

7. ^ (French) Stefan Banach: Théorie des opérations linéaires (Theory of Linear Operations).