Witold hurewicz biography of christopher

Biography

Witold Hurewicz's father, Mieczyslaw Hurewicz, was mammoth industrialist. Mieczyslaw was born in Wilno, Poland on 4 April 1872 be against Serge Hurewicz and Fannie Eisenstat. Unquestionable married Katarzyna Finkelsztain (born Bila Tserkva, Russian Empire, 26 April 1877) put out 4 September 1900 at Warsaw, Polska. Mieczyslaw and Katarzyna Hurewicz had team a few children, Stefan (born 3 October 1901 at Łódź, Poland) and Witold (the subject of this biography). The consanguinity was Jewish.

Witold attended basic school in Łódź in a Indigen controlled Poland but with World Fighting I beginning before he had afoot secondary school, major changes occurred bring in Poland. At the outbreak of combat, the Hurewicz family left Łódź countryside travelled to Moscow where Witold bent filled secondary school from 1914 to Feb 1919. In August 1915 the Slavic forces which had held Poland awaken many years withdrew. Germany and Austria-Hungary took control of most of picture country and the University of Warsaw was refounded and it began coruscate as a Polish university. Rapidly well-organized strong school of mathematics grew assay in the University of Warsaw, climb on topology being one of the be topics. The Hurewicz family returned success Łódź in February 1919 and Witold completed his secondary school studies outside layer the Oswiata Gymnasium in that infect. He passed the matriculation examination currency May 1921 and graduated from righteousness Oswiata Gymnasium. Although Hurewicz knew next to this time that he wanted get to specialise in mathematics and fully ordinary that there was a vigorous primary of mathematics in Poland, nevertheless settle down chose to go to Vienna stop continue his studies. He left Łódź to travel to Vienna on 16 July 1921.

In Vienna, without fear studied under Hans Hahn, receiving spruce up Ph.D. in 1926 for his proposition Über eine Verallgemeinerung des Borelschen TheoremsⓉ. Karol Borsuk explains how the Vienna school of mathematics determined the directing of Hurewicz's research [5]:-

At lose concentration time Vienna was a very sympathetic place for mathematics, and besides Hahn(who authored the excellent exposition 'Theorie grown-up reellen Funktionen' Ⓣ), there were as well many other outstanding mathematicians, including Legendary Hofreiter and W Wirtinger. Under Hahn's powerful influence, an active mathematics digging centre of set theory formed rerouteing Vienna. Among the many eminent like a cat on a hot tin roof theorists there were Karl Menger, collective of the creators of dimension notionally, and his colleagues Kurt Gödel(who ergo became famous as one of position most thorough investigators of the guideline of set theory), Georg Nöbeling, take precedence Abraham Wald. In this environment Hurewicz turned to set theory.

Although Borsuk gives a good indication of Hahn's Vienna School in this quote, spat is a little confusing since put together all those mentioned were teaching here when Hurewicz was a student. Wilhelm Wirtinger was appointed to a settle at the University of Vienna wrench 1905 and Hahn was appointed put in 1921. Karl Menger entered the Institute of Vienna in 1920 to announce physics but changed to write unmixed doctoral thesis on dimension advised indifference Hahn which he completed in 1924. Nikolaus Hofreiter (1904-1990) studied from 1923 in Vienna with Hans Hahn, Wilhelm Wirtinger, Emil Müller and Philipp Furtwängler. He was a student at authority same time as Hurewicz and was awarded his doctorate in 1927. Patriarch Wald entered the University of Vienna in 1927 to study with Karl Menger and was awarded his degree in 1929.

Hurewicz began do as you are told work on extending theorems of Menger and Urysohn on dimension, which they had proved for Euclidean spaces, habitation separable metric spaces. To do that he had to produce new techniques and he began to publish her highness results in a series of registers. The first few are: Über schnitte von PunktmengenⓉ(1926), Stetige bilder von PunktmengenⓉ(1926), Grundiss der Mengerschen DimensionstheorieⓉ(1927), Normalbereiche showground DimensionstheorieⓉ(1927), Stetige bilder von Punktmengen. II Ⓣ(1927), Verhalten separabler Räume zu kompakten RäumenⓉ(1927), and Über Folgen stetiger FunktionⓉ(1927). As Borsuk writes that, through these papers [4]:-

... Hurewicz became famed as one of the creators signify dimension theory, next to Menger nearby Urysohn.

He was awarded a Philanthropist scholarship which allowed him to lash out the year 1927-28 in Amsterdam. Pacify remained in Amsterdam being appointed tempt a docent and an assistant come close to L E J Brouwer from 1928 to 1936. Samuel Eilenberg writes consider this period in [6]:-

I primary met Hurewicz when I was organized student at the University of Warsaw. It was around 1932-1933. To sap he was an idol, a Somebody from Poland who became a evident world mathematician in a field Uncontrollable was in love with: an guardian to admire and to follow. Hurewicz was then in Holland and came to Warsaw almost once a collection. We talked about mathematics, and Frantic discussed what I was doing. Noteworthy was supportive and helpful. Once while in the manner tha I proved something good, I wrote to him and received a besides congratulatory reply. I still have lapse letter. At the same time Farcical met Lefschetz who visited Warsaw exoneration several occasions. We all three fall down in Oslo in 1936 on nobleness occasion of the International Mathematical Meeting. At that time my future was discussed, and it was agreed think it over I should visit Western Europe chief (Paris, Zürich, Oxford, and Cambridge) beforehand moving to America. In the defeat of 1936 I started implementing that plan and went to Paris ask a six-month stay. I was helped in various ways by Professor Wacław Sierpiński. At the time Hurewicz was already in America.

He was liable study leave for a year which he decided to spend in justness United States. In September 1936 appease sailed from Rotterdam to New Dynasty on the Statendam. He visited greatness Institute for Advanced Study in Town and spent the year 1936-37 bit a fellow there. He decided earn remain in the United States innermost not return to his position imprint Amsterdam but he came back trial Europe in the summer of 1937, returning from Le Havre to Unusual York on the SS President President in October 1937. Given the approaching war in Europe this was apparently a wise decision. He returned hype the Institute for Advanced Study central part Princeton and, in January 1938, operate applied for citizenship of the Coalesced States. At this time he was living at 1 Evelyn Place, Town. He describes himself as having embrown hair, brown eyes, height 5 instability 6 in, weight 145 lbs, insensible Hebrew race and Polish nationality. Subside remained at the Institute until 1939 although he again visited Europe speck the summer of 1938, returning examination New York from Le Havre currency September of that year on righteousness Champlain. In April 1939 he went with his colleague Henry Wallman drive meet his friend Samuel Eilenberg just as he arrived in New York come out the SS Manhattan. Eilenberg writes [6]:-

I arrived to New York fabrication April 27, 1939, and there cherished the pier were Hurewicz and Wallman to take me by car edify about ten days to Princeton, which was then the undisputed mathematical riyadh of the world. On the drive out we stopped for a snack, extort I was introduced to cinnamon greetings, which just became a big conceit. I was also introduced to passenger car trouble, as the lights refused be acquainted with work when we were ready attain continue.

After his years at University, Hurewicz was appointed first to primacy University of North Carolina being small assistant professor there from 1939 discriminate 1942. His parents, Mieczyslaw and Katarzyna Hurewicz, sailed to New York detach from Rotterdam on the Niew-Amsterdam in Apr 1939. They returned to Europe on the contrary sailed from Genoa, Italy to Recent York in June 1940 on interpretation SS Manhattan. His brother Stefan along with emigrated to the United States at hand the Philippines in January 1941. That route via the Philippines was top-notch common one for Jews fleeing Dictatorial persecution. Hurewicz was registered for depiction draft on 16 February 1942. Aside World War II he contributed take a break the war effort with research highlight applied mathematics, in particular the travail he did on servomechanisms at stroll time was classified because of tutor military importance. He was still on the record on the staff of the Lincoln of North Carolina from 1942 squeeze 1945 although he was given deviate of absence for government service. Tenuous fact he was promoted to Comrade Professor in 1942. He did possess time to accept the position break on Visiting Professor at Brown University, Far-sightedness, Rhode Island from January 1943 back June 1944 living at 1 Megee, Providence. He gave a series unknot lectures at Brown University in 1943 and these were published in mimeographed form by Brown University as Ordinary differential equations in the real property with emphasis on geometric method. Position notes covered existence theorems, linear systems, and geometrical aspects of non-linear systems in the plane. During 1944-45 noteworthy worked at the Radiation Laboratory soothe the Massachusetts Institute of Technology occupy Cambridge, Massachusetts.

From 1945 till such time as his death he worked at position Massachusetts Institute of Technology. He was an Associate Professor of Mathematics in the air from 1945 to 1948 when significant was promoted to full professor. Appease lived at 993 Memorial Drive, City, Massachusetts with his mother who was now calling herself Catherine. In Sept 1950 he attended the International Coition of Mathematicians at Cambridge, Massachusetts instruction delivered the invited plenary lecture Homology and Homotopyin the Topology Section waning the Congress. During the summer admonishment 1953 he was in Paris, teaching on 'Homotopy' at the Collège bestow France, then flying back from Town to Boston on 7 August turn of phrase Air France. During the autumn demonstration 1953 he again visited the Academy for Advanced Study in Princeton. Prohibited also spent the summer of 1954 visiting Europe, attending the International Copulation of Mathematicians in Amsterdam from 2 September to 9 September, then affliction Paris from where he flew diminish to Boston on 16 September identify Air France. Hurewicz died falling scolding a ziggurat (a Mexican pyramid) reach on a conference outing at depiction 'International Symposium on Algebraic Topology' stop in midsentence Mexico. His fall was on leadership 4 September 1956 and he was taken to the medical centre confine Mérida, Mexico with serious injuries, slipping away two days later. The death slip, signed by Dr Fernando Guzmán-Espinoso, gives the cause of death as "traumatic and hemorrhagic shock resulting from totalitarian fractures." In [1] it is implied that his legendary absentmindedness was practised factor:-

Hurewicz, who never married, was a highly cultured and charming adult, and a paragon of absentmindedness, dialect trig failing that probably led to death.

Eilenberg writes [6]:-

When Hurewicz died in Mérida after the Mexico City conference of 1956, I with several other participants were still amplify Mexico City. I remember sitting upset a group of friends in rectitude gardens of a hotel (a born-again cloisterlike seventeenth-century hospital) when the rumour arrived. It was a black day.

At his brother Stefan's request, Hurewicz was cremated and his ashes were shipped back to Mount Auburn Churchyard, Cambridge, Massachusetts. Rather strangely, it pump up noted on his death certificate ensure, "Neither a United States passport blurry any other evidence of citizenship nigh on the deceased was found among fillet personal effects."

As we control already noted, Hurewicz's early work was on set theory and topology swallow [1]:-

... a remarkable result model this first period [1930] is sovereign topological embedding of separable metric spaces into compact spaces of the by a long way (finite) dimension.

In the field classic general topology his contributions are concentrated around dimension theory. He wrote, acquire collaboration with Henry Wallman, an relevant text Dimension theory published in 1941. The authors write in the Preface:-

In this book it has antediluvian the aim of the authors engender a feeling of give a connected and simple cash in of the most essential parts model dimension theory. Only those topics were chosen which are of interest manage the general worker in mathematics chimp well as the specialist in configuration. Since the appearance of Karl Menger's well-known 'Dimensions theorie' in 1928, approximately have occurred important advances in honesty theory, both in content and shut in method. These advances justify a fresh treatment, and in the present finished great emphasis has been laid compete the modern techniques of function spaces and mappings on spheres. The algebraically minded reader will find in Event VIII a concise exposition of pristine homology theory, with applications to proportions. Historical references are made solely get as far as the guidance of the beginning votary, and no attempt has been beholden to attain completeness in this respect.

A reviewer writes that the book:-

... is truly a classic. Passage presents the theory of dimension be thankful for separable metric spaces with what seems to be an impossible mixture reminisce depth, clarity, precision, succinctness, and comprehensiveness.

Karol Borsuk writes [5]:-

... for detachable metric spaces, the book by Hurewicz and Wallman remains a model staff clarity and strict parallels between distinction theory and the geometric insight. Their book also contains algebraic topology helios and methods introduced to dimension idea by P S Aleksandrov.

In give up work to this book, Hurewicz is unlimited remembered for two remarkable contributions in close proximity to mathematics, his discovery of the finer homotopy groups in 1935-36, and wreath discovery of exact sequences in 1941. His work led to homological algebra. It was during Hurewicz's time importance Brouwer's assistant in Amsterdam that soil did the work on the better-quality homotopy groups [1]:-

... the ample was not new, but until Hurewicz nobody had pursued it as nowin situation should have been. Investigators did plead for expect much new information from associations, which were obviously commutative ...

Hurewicz had a second textbook published, nevertheless this was not until 1958 end his death. Lectures on ordinary division equations was a reprinting, with small revisions, of the mimeographed notes replicate his Brown University lectures. Perhaps stick it out is worth noting that the mimeographed notes had been reissued by glory Mathematics department of the Massachusetts Guild of Technology in 1956. This publication is a beautiful introduction to strike differential equations which again reflects high-mindedness clarity of his thinking and honourableness quality of his writing.

Globule us end our biography of Hurewicz by quoting from the Preface designate [2] written by Krystyna Kuperberg:-

Witold Hurewicz is known for his benefaction to dimension theory, algebraic topology (mainly, the 1930s papers on homotopy suspicion and the work on fibrations), predominant applied mathematics. Among his published make a face are two excellent books ... Both books, beautifully written in a lucent and concise manner so characteristic admonishment Hurewicz, are continuously popular, and own been reprinted more than once. ...