At the University of Lwów, Stark was taught by Stefan Banach, Hugo Steinhaus and other leading Polish mathematicians. In his second year of study Kazimierz Kuratowski was appointed as a professor at the university. Not only did Lwów have an impressive collection of lecturers but perhaps even more remarkable is the list of outstanding students who studied with Stark over the following few years including Juliusz Schauder, Mark Kac, Stanisław Ulam, Władysław Orlicz, Wilhelm Birnbaum, Henryk Auerbach, Ludwik Sternbach, Stanisław Mazur and Julian Schreier. Birnbaum spoke about this group of talented students:-
Mathematics in that group of infatuated young people was kind of a fever. We would get together at all times of day and night, talking incessantly mathematics.In 1929, while still an undergraduate, Stark was appointed as a junior assistant to Banach, who held the chair of mathematics, at the Mathematical Institute. Stark graduated from the Faculty of Mathematics and Natural Sciences in Lwów in 1933 and continued to work at the Mathematical Institute. Mark Kac got to know Stark when he attended a proseminar on algebra and number theory. Stark was very ready to help everyone and, in particular, he assisted Kac in many ways including translating his first serious mathematical note into English - the note was published in 1934.
On 1 September 1939 Germany attacked Poland and World War II began. Stark was in Warsaw when the city fell to the Germans before the end of September when those defending the city were forced to surrender through lack of supplies. About 30% of the inhabitants of Warsaw were Jewish and, after the Germans took control of the city, they constructed a ghetto in the Jewish district where this 30% were forced to live in an area of less than 3% of the city. Stark was one of the half million confined to the ghetto were he lived for a while. The Germans never intended the Warsaw ghetto to be permanent, rather they saw it as a holding area until they had decided what to do with those confined there. In the summer of 1942 they began to transfer the inhabitants of the ghetto who had survived (many had died of starvation and disease in the confined space) to concentration camps.
Stark survived the Warsaw ghetto and was transferred to several concentration camps. He spent time in four different camps, Majdanek, Plaszów, Ravensbrück and Sachsenhausen. Majdanek, on the outskirts of Lublin, Poland, was a forced labour camp where exterminations were not carried out but, nevertheless, many thousands of the inhabitants died. Plaszów, close to Kraków, was also a forced labour camp but those unfit to work were killed. Ravensbrück, in northern Germany, was a concentration camp mainly for women but some men, such as Stark, were also kept there. Less than one fifth of those sent to Ravensbrück survived. Sachsenhausen was a concentration camp in Oranienburg, Germany. Remarkably, against all the odds, Stark survived this horrific experience and, after the defeat of Germany in 1945, was able to return to Poland.
In 1946 Stark was appointed as a teaching associate at the University of Wrocław. In 1948 he published On a functional equation and, in the following year, the paper On a ratio test of Frink in which he gives an extension of Raabe's test for convergence. In 1948 he produced a set of mimeographed notes, in Polish, of the course on algebra that he was giving at the University of Wrocław. He was appointed as a research associate at the State Institute of Mathematics in 1949, one of the first appointments following the founding of the Institute on 20 November 1948. Kazimierz Kuratowski was appointed to head the Institute in 1949. Stark continued to work for the Institute, which became part of the Polish Academy of Sciences following its foundation in 1952. After the Academy was set up, the Institute was known as the Mathematics Institute of the Polish Academy of Sciences, and Stark worked at the Institute for the rest of his life. His position at the University of Wrocław ended in 1950 and, in 1954, he was promoted from research associate at the Mathematics Institute to assistant professor and given the title of docent.
Stark published several textbooks which were very popular in Poland and some were translated into other languages. He published the 629-page textbook Analytic Geometry (Polish) in 1951. An indication of its popularity is the fact that further editions were published in 1958, 1967, 1970 (enlarged), 1972 and 1974. V Hlavaty writes in a review:-
This textbook deals with metric, affine and projective geometry of linear and quadratic varieties in the plane as well as in the three-space. The author does not confine himself only to real plane (real space) but considers also the complex plane (complex space). Besides items usually dealt with in textbooks of elementary analytic geometry the reader finds here the introduction to synthetic projective geometry, to the theory of matrices (and determinants) with the usual applications and to the (three-dimensional) elementary vector calculus.All the rest of Stark's textbooks were written in collaboration with Andrzej Mostowski who had been appointed head of the division for the foundations of mathematics at the Mathematics Institute in the year the Institute was set up. Their first joint publication was the book Higher algebra (Polish) published in three volumes; Volume 1 appeared in 1953, Volume 2 in 1954 and Volume 3 also in 1954. All three volumes were reviewed by Antoni Zygmund who begins a review of the first volume as follows:-
This is primarily a university textbook beginning with the material for first year students. The style is clear, proofs given in great detail and the didactic aspect of the presentation receives considerable attention. In line with this the presentation in the first half of the book follows the classical pattern and the more abstract methods are postponed to the second half.For the second volume, Zygmund writes:-
The present volume contains the theory of polynomials with numerical coefficients, and together with the first volume contains all the material to be covered during the first year of the university. Abstract methods are avoided; elements of abstract algebra are to be given in volume three.Zygmund's review of the third volume begins:-
It is intended as an introduction to Modern Algebra, is written, as are the preceding volumes, with great care and attention to didactic aspects, and contains a large number of examples and problems.A second edition was published in 1959 and a third edition in 1967. The two authors collaborated on two further textbooks. Linear algebra (Polish) was first published in 1958 with further editions in 1966, 1968, and 1973. J W Andrushkiw writes in a review:-
The presentation may be said to be "classical'': the discussion confines itself to the real and complex number fields and the concept of the group is not used. However, a very clear presentation, a careful attention to didactic aspects, instructive examples and satisfactory number of problems make this volume a valuable textbook for an introductory course in linear algebra.The final collaboration between Stark and Mostowski led to The elements of higher algebra (Polish) which was essentially a rewrite of the first two volumes of their earlier Higher Algebra textbook although it certainly did not replace the earlier work as further editions of the earlier work continued to be produced after Elements of higher algebra was published. The first edition of Elements of higher algebra appeared in 1958 with further editions in 1963, 1965, 1968, 1970, and 1972. An English translation was published in 1964. Reviewing the original 1958 Polish edition, M Fiedler writes:-
The book is written clearly, with great stress on didactic principles of the presentation.Stark concentrated much of his efforts in the later part of his career on publishing. He was head of the publishing department of the Polish Mathematical Society, managing editor (later editorial secretary) of Studia Mathematica and, from 1958, editorial secretary of Acta Arithmetica :-
He had great knowledge and experience in publishing matters and his editorial services were also sought by other journals ('Colloquium Mathematicum', 'Dissertationes Mathematicae').Also, he was an editor for the Works of Juliusz Pawel Schauder, which was not published until 1978, four years after Stark's death, and an editor of the Selected Works of Wacław Sierpiński published in three volumes between 1974 and 1976.
There were other roles that Stark took in addition to these relating to publishing. He was secretary of the Mathematics Committee of the Polish Academy of Sciences and, between 1962 and 1967, he was Deputy Director of the Mathematics Institute of the Polish Academy of Sciences.
Over the last few years of his life he battled against health problems, particularly a painful heart disease. Despite these years of ill health, his final death was sudden and unexpected.
Article by: J J O'Connor and E F Robertson
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