Waclaw Sierpiski and his colleagues are credited with revolutionizing Polish mathematics during the first half of the 20th century. They took a couple of relatively new fields of mathematics and devoted whole journals to them. Although detractors had opined that such an experiment could not succeed, the mathematical heritage of the Polish community between the world wars has left a legacy of results, problems, and personalities, chief among them being Sierpiski.
Sierpiski was born in Warsaw on March 14, 1882. His father was Constantine Sierpiski, a successful physician, and his mother was Louise Lapinska. Sierpiski received his secondary education at the Fifth Grammar School in Warsaw, where he studied under an influential teacher named Wlodarski. From there, he entered the University of Warsaw and began studying number theory under the guidance of G. Voronoi. In 1903, Sierpiski's work in mathematics was recognized by a gold medal from the university, from which he graduated the next year. After graduation, he taught in secondary schools, a standard career path due to the shortage of positions available to Poles under Russian rule. In that capacity, he was involved in the school strike that occurred during the revolution of 1905. Even though the strike was not wholly unsuccessful, Sierpiski resigned his teaching position and moved to Krakow.
In 1906 Sierpiski received his doctorate from the Jagiellonian University in Krakow. Two years later he passed the qualifying examination to earn the right to teach at Jan Kazimierz University in Lwow, to which he had gone at the invitation of one of the faculty. There, Sierpiski offered perhaps the first systematic course in set theory, the subject of his investigations for the next 50 years. In 1912 he gathered his lecture notes and published them as Zarys Teorii Mnogosci ("Outline of Set Theory"). Sierpiski's texts were recognized by prizes from the Academy of Learning in Krakow.
With the outbreak of World War I in 1914, Sierpiski was interned by the Russians, first at Vyatka, then in Moscow. This internment was not particularly severe, for while he was in Moscow, Sierpiski was accorded a cordial reception by the leading Russian mathematicians of the era. In fact, he was able to conduct some joint research with N. Lusin during this period in the field of set-theoretic topology.
The area of set-theoretic topology in which Sierpiski worked depended on a few basic notions. One of these is that of a closed set, or a set that includes its boundary. A simple example is the interval of real numbers between 0 and 1, including both endpoints. Related to the notion of a closed set is that of an open set, one which does not include its boundary. An example of an open set is the interval between 0 and 1, not including either 0 or 1. If one takes that interval and includes 0 but not 1, then the set is neither closed nor open. Much time was spent investigating the results of combining open and closed sets in various infinite combinations. The entrance of infinity is what required the use of methods and ideas from set theory.
When the war ended Sierpiski returned to Lwow, but in the fall of that year he was appointed to a position at Warsaw. He devoted a number of papers to the set-theoretic topics of the continuum hypothesis and the axiom of choice. The continuum hypothesis, which had been known to Georg Cantor, claimed that there were no infinite numbers between the number of integers and the number of real numbers. If the continuum hypothesis is present, it reduces the complexity of the hierarchy of infinite numbers. The axiom of choice had been a matter for much discussion at the turn of the 19th century, allowing for the possibility of making an infinite number of choices simultaneously. Some distinguished French mathematicians like Emile Borel questioned the meaningfulness of such a choice, and one of the early consequences of investigation into the axioms of set theory was the discovery that the axiom of choice was equivalent to a number of other propositions of set theory. Sierpiski took an agnostic position with respect to the axiom, using it in proofs and also trying to eliminate it wherever possible.
It was during the period between the world wars that Sierpiski, in conjunction with several Polish colleagues, created what has since become known as the Polish school of mathematics. The subjects that dominated the Polish school were logic and set theory, topology , and the application of these subjects to questions in analysis. To make certain that there would be an audience for the work in these areas, the journal Fundamenta Mathematicae was founded in 1919. Although by the end of the 20th century a profusion of specialized journals within mathematics had sprung up, Fundamenta was the first of its kind and was greeted with some suspicion about its likelihood for survival. The quality of its papers was high, the contributors were international, and the problems proposed and solved were substantial. As a permanent record of the Polish mathematical school, Fundamenta Mathematicae supplements the reminiscences of those who took part in the work.
Sierpiski often led the Polish delegations to international congresses and conferences of mathematicians. One of the most ambitious projects in which he was involved was a Congress of Mathematicians of Slavic Countries, whose very existence attests to a political consciousness side-by-side with the mathematical one. The event took place in Warsaw in 1929 and was chaired by Sierpiski.
During World War II Sierpiski was in Warsaw, holding classes in whatever secret settings were available. A good deal of the discussion went on in Sierpiski's home, where his wife did her best to make guests feel as comfortable as possible in such troubled times. In 1944, the Nazis took control of Warsaw and Sierpiski was taken by the Germans to a site near Krakow. After the latter city was liberated by the Allies, he held lectures at the Jagiellonian University there before returning to Warsaw.
The period after the war was marked by further honors to Sierpiski as his students dominated the mathematical landscape. He served as vice president of the Polish Academy of Sciences from its inception and was awarded the Scientific Prize (First Class) in 1949, as well as the Grand Cross of the Order of Polonia Restituta in 1958. There were not many mathematicians in any country who approached his publication records of more than 600 papers in set theory and approximately 100 articles about number theory.
Sierpiski died in Warsaw on October 21, 1969. His mathematical textbooks educated an entire generation, and he helped to lay the foundations of the discipline of set-theoretic topology. Sierpiski's legacy was in establishing a Polish mathematical community, a contribution at the same time to mathematics and to national identity.
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