Wacław Sierpiński The Warsaw School of Mathematics and the Present State of Mathematics in Poland

The lecture which we give below was delivered by Wacław Sierpiński on 15 April 1959 at the Polish Institute of Arts and Sciences in America.

In order to understand the origins of Polish mathematical research it would be helpful to know something of its state before World War I. There were, at that time, only two Polish Universities, and at each of these were only two professors of mathematics: Kazimierz Zórawski and Stanislaw Zaremba in Krakow, Jozef Puzyna and myself in Lwów. In addition several Polish mathematicians occupied chairs in foreign universities and polytechnics. Among these were Ptaszycki, Sochocki and Staniewicz in St Petersburg, Młodziejewski in Moscow, Przeborski in Kharkov and Lichtenstein in Leipzig. Warsaw did not have a Polish university but a Polish centre of mathematics did exist: the Mathematics and Physics Circle, established in 1905 and directed by Samuel Dickstein, a man who rendered great services to Polish science and especially to Polish mathematics. He founded and edited the first two Polish mathematical periodicals, in 1887, Prace matematyczno-fizyczne (Mathematical-Physical Studies) and in 1897, Wiadomosci matematyczne (Mathematical News). Both these publications exist to this day and are now issued by the Institute of Mathematics of the Polish Academy of Sciences, the former under the title Prace matematyczne (Mathematical Studies) since physicists now have their own publication.

The Warsaw Mathematics-Physics Circle consisted mainly of Polish mathematics school teachers; however, at its sessions also scientific problems were discussed. But the number of mathematicians doing scholarly work in the so-called Congress Poland could be counted on one's fingers. In 1906 there was founded in Warsaw the Society of Scientific Courses which was a substitute for a Polish University. The first chairman of the Scientific Council of these Courses, or the rector of this institution, was Dickstein. Fifty-three years ago I taught higher mathematics at these courses for two years, until the time I transferred to the University of Lwów.

In 1907 the Warsaw Scientific Society was established. Most on its founders were former professors and alumni of the so-called Warsaw Main School, i.e. the Polish University, which had been closed by the Russians after the January Insurrection of 1863. Dickstein was one of the mathematicians among them and he became the vice-president of the Society's first board of directors. When the first members of this society were elected in January 1907, I had the honour of being chosen a member.

Before World War I there was no mathematical society covering the three sectors of partitioned Poland and there were no conventions of Polish mathematicians. There existed only a mathematics section at the conventions of Polish naturalists and physicians. At such a meeting which took place in 1911 in Krakow, the four mathematics professors who were then teaching at the Polish universities, and Dickstein from Warsaw, presented their papers. Apart from the formal meeting, we held friendly discussions about everything except mathematics because each of us was working in a different field. Zórawski was interested in geometry, Zaremba in differential equations, Puzyna in analytical functions, Dickstein in the history of mathematics, and I in the theory of sets and the theory of numbers. Thus, at that time, we had no common problems which would interest us as a group.

One must note that contemporary mathematics is divided into several dozen branches of which each has its own problems and research methods. These branches are so broad and each has such a voluminous literature that a single individual after several years of work is able to command one or, at most, two.

After the meeting in Krakow I came to the conclusion that the conditions then prevailing among us, each of our mathematicians working in a different branch, were not the best. There was no cooperation or mutual control. Though there were then Polish mathematicians whose names were known abroad, there was no Polish mathematics. I decided that it would be more fruitful to have a greater number of our mathematicians working in some single field of research.

In 1913 Stefan Mazurkiewicz came to Lwów to prepare for his doctorate under my direction. The subject of his doctoral work was the solution of a difficult problem posed by me in the theory of sets of points. In this same year I offered an assistantship at the Mathematical Seminar of Lwów University to Zygmunt Janiszewski, a doctor of the University of Paris, whose work was in the field of topology.

In 1919, the three of us met as the first professors of mathematics in the re-born Polish University at Warsaw. There we decided to found a periodical dedicated to the theory of sets, topology, the theory of functions of a real variable and mathematical logic, which would publish studies in French, English, German and Italian. It was thus that Fundamenta Mathematicae, whose 46th volume is at present in print, was born.

Up to 1909 the theory of sets was not offered as a separate subject anywhere. I gave the first lectures titled, "The Theory of Sets" at the University of Lwów in the autumn of 1909. There still exist the transcripts of these lectures that had been published by the students and it was upon these transcripts that I later based my book Zarys teorii mnogosci (Outline of the Theory of Sets), which was published in 1912 by the Joseph Mianowski Fund in Warsaw. This institution, named after the last rector of the Warsaw Main School, during the sixty-odd years of its activity contributed greatly to the development of Polish scholarship in the former Congress Poland, publishing many books and studies by Polish scholars, including also a number of mathematical works. The Mianowski Fund published a second edition of my book in 1923 and in 1928 an enlarged edition in two sections (altogether 469 pages), the second section being devoted to general topology. After World War II, certain expanded sections of these books appeared in English: In 1952 Toronto University Press in Canada published my 290 page General Topology. My 480 page Cardinal and Ordinal Numbers appeared in 1958 in Warsaw as volume 34 of Mathematical Monographs, which are now published by the Mathematical Institute of the Polish Academy of Sciences.

In 1951 there appeared Algèbre des ensembles (202 pp.) as volume 23 of Mathematical Monographs, and in 1957 there came out in New York an enlarged edition of my Hypothèse du continu (214 pp.). These four books can be regarded as the continuation and the development of my lectures on the theory of sets which I began half a century ago in Lwów.

When in 1919 Stefan Mazurkiewicz, Zygmunt Janiszewski and I were appointed professors of mathematics at the University of Warsaw, each of us, in addition to teaching other branches of mathematics, offered courses or seminars on the theory of sets, topology and the theory of functions of a real variable. Among the students of those days many were very capable, and some later became noted mathematicians. Among these were Kuratowski, Saks, Tarski, Knaster, Zygmund, Lindenbaum, Szpilrajn-Marczewski, Borsuk, Zarankiewicz, Eilenberg, Popruzenko, Aronszajn, Mostowski, Charzynski and others. Some became professors or docents of our University and together we formed the Warsaw School of Mathematics.

One occasionally hears the reproach that during the inter-war period mathematical research in Poland was one-sided. This is not quite correct since in Warsaw the members of our school worked in such various fields as the theory of sets, topology, the theory of functions of a real variable and mathematical logic. Apart from our school Prof Zórawski and his pupils were occupied with geometry, and Prof Dickstein with the history of mathematics. In Krakow, Prof Zaremba and his students devoted themselves to classical analysis, while the Lwów School of Mathematics, with Stefan Banach at its head, practiced functional analysis, while Professor Hugo Steinhaus was concerned with the theory of probability and applied mathematics. In Wilno, Professor Zygmund and his pupils worked on the theory of trigonometric series. It is true that some branches of mathematics were not practiced in Poland during the inter-war period, but this does not justify the statement that Polish mathematical research of that time was one-sided.

One must take into consideration that in the period between the two wars there were in Poland not more than thirty professors of mathematics and theoretical mechanics at the six universities, two polytechnics and the Mining School. Contemporary mathematics branches out into several fields and if at least one of the Polish mathematicians of that time had worked in each of these, the situation would have been similar to that which existed before World War I - there would have been no cooperation among mathematicians; there would have been no Polish mathematics, but only several individually working Polish mathematicians.

Thanks to the fact that many of our scholars were working in specific fields of our science, we have obtained results which are highly regarded by mathematicians of other countries. When the twenty-fifth volume of our periodical, Fundamenta Mathematicae appeared in 1935, J D Tamarkin, then professor at Brown University in Providence, wrote in the Bulletin of the American Mathematical Society that the history of our periodical was, at the same time, the history of contemporary theory of functions of a real variable.

During the inter-war period, there appeared 32 volumes of Fundamenta Mathematicae, which contained 972 studies by 216 authors from all over the world, among them almost all of the distinguished specialists in the field to which Fundamenta is dedicated. In 1947, L'lntermédiaire des Recherches Mathématiques which appears in Paris, reprinted all problems (in the section "Problemes") which had been posed in the thirty-two volumes of Fundamenta, with the explanation that "this publication specialising in the theory of sets, has greatly aided the development of contemporary mathematics." Since the first volume of Fundamenta Mathematicae was out of print, it was reprinted in 1937. This, in the case of a Polish scientific publication, was an exceptional event. During the war and afterwards, several other of the out-of-print volumes of Fundamenta were reprinted in the U.S.A. by a photomechanical process.

In 1932 there began to appear Monografie matematyczne (Mathematical Monographs), a series of volumes in French, English and German, in which our mathematicians treated specific branches of mathematics in an original manner. The first volumes of this series received great recognition abroad. Today, there is no major mathematical library in the world which does not have a set of Mathematical Monographs. An indication of their importance is the fact that during the war the out-of-print volumes of this series were reproduced in the United States. Before the war there were seventeen volumes of the Monographs. At present there are about forty. They are now published by the Institute of Mathematics of the Polish Academy of Sciences. From the very beginning the Editorial Committee has been headed by Professor Kazimierz Kuratowski. The committee is composed of seven Polish mathematicians, among them one from America, Professor Anthony Zygmund. The first volume of the Monographs consisted of the book Operations linéaires by Stefan Banach, undoubtedly the most distinguished mathematician Poland has produced.

Stefan Banach, born in 1892, was a student of the Polytechnic in Lwów. After some time he abandoned his studies and tutored privately in Krakow. One evening in 1916 in the "Planty" park he sat down on a bench occupied by three mathematicians: Hugo Steinhaus, then a docent at Lwów University; Otton Nikodym, a former pupil of mine from Lwów; and the late Witold Wilkosz. They were discussing some mathematical problem which had not been solved at that time. Banach eavesdropped, introduced himself into their conversation and offered his opinion as to how it could be solved. Steinhaus and Nikodym became interested and suggested future meetings. They also recommended some books. Soon Banach began to solve difficult problems and publish his scientific work. I accepted one of his first studies in 1920 for the first volume of Fundamenta Mathematicae. We decided that Banach's work was sufficient for a doctor's degree, but, because he had not gone through the prescribed university studies, it was necessary to obtain a dispensation from the Ministry of Education in order to permit him to take the doctoral examinations. These he passed with honours. Then began his lightning scientific career. A year after he obtained his doctorate, he wrote a new work solving problems which had puzzled the greatest mathematicians, and was made docent of mathematics at the John Casimir University in Lwów. Less than a year later, having published new work, he was appointed associate professor and the following year, at my instance, chosen as a corresponding member of the Polish Academy of Arts and Sciences. In 1927 he became Professor and in 1928, together with Hugo Steinhaus, began to edit the periodical Studia Mathematica in Lwów, which presented research in the fields of analysis and the theory of probability, in French, English and German. In 1930, Banach received the first Prize in Science offered by the City of Lwów and immediately before the war he received the High Scientific Award of the Polish Academy of Arts and Sciences. Unfortunately, Banach died in Lwów in 1945 at the height of his career, after an illness of several months. To honour his memory the city of Wrocław, whose university is in a way a continuation of the John Casimir University of Lwów, renamed one of its streets after Stefan Banach. Banach left about sixty mathematical works and studies of which several were written in collaboration with others. In addition, he wrote several handbooks on arithmetic, algebra and geometry for elementary schools and high schools either himself or in collaboration with Włodzimierz Stozek and myself.

In order to evaluate Banach's influence on the development of contemporary mathematics it is sufficient to glance at current mathematical publications, American, for example. We find the name of Banach mentioned very often. It is cited even in titles. Most often it is a case of the so-called "Banach Space." The paradox is that this man who always lacked money had his own space - but only in the realm of mathematical abstraction. It would be difficult to explain simply what these Banach spaces are. I shall mention one more easily understood proposition, formulated by Banach and Tarski thirty-five years ago. They proved that each sphere K can be divided into a few parts so that after certain moves and revolutions of each of these parts one can obtain two full spheres. Each of these spheres will be of the same size as sphere K. In short, by proper division into several sections one can obtain two spheres of the same size. It is easy to imagine what revolution there would be in contemporary physics and in the everyday life of the individual if this proposition could be realised. Unfortunately, the proof of this paradoxical proposition is a pure proof of existence and does not offer any possibility of even approximate realisation. Kurt Gödel proved later, however, that this proposition never leads to contradiction with generally accepted axioms so that all efforts to disprove Banach's and Tarski's proposition were from the beginning doomed to be unsuccessful.

During the last war some Polish mathematicians found themselves abroad and almost all occupied posts at American universities.

Anthony Zygmund, an alumnus and later docent at the University of Warsaw, then professor at the Stefan Batory University in Wilno, is now a professor at the University of Chicago.

Alfred Tarski, alumnus and docent of the University of Warsaw, is at present a professor at the University of California (Berkeley). He was chairman of the American Society of Symbolic Logic and later President of the International Union of Philosophy of Science.

Samuel Eilenberg, alumnus and doctor of the University of Warsaw, is now professor at Columbia University in New York.

Nachman Aronszajn, alumnus of the University of Warsaw, is now professor at the University of Kansas at Lawrence.

Jerzy Spława-Neyman, doctor and docent of the University of Warsaw, is now professor of statistics at the University of California (Berkeley).

Mark Kac, alumnus and doctor of the John Casimir University in Lwów, is now professor at Cornell University in Ithaca.

Stanisław Ulam, alumnus and docent at the University of Lwów, is now Senior Scientist in the University of California Laboratory at Los Alamos.

Otto Nikodym, before the war docent at Warsaw University is now professor at Kenyon College, Gambia, Ohio.

Wacław Kozakiewicz, alumnus and docent at the University of Warsaw, was, until his recent untimely death, professor at the University of Saskatchewan.

The former docent at the Jagellonian University, Alfred Rosenblatt, was for many years professor at the University of Lima where he died after the war.

Zbigniew Lepecki, alumnus of the University of Warsaw, was professor at the University of Parana in Brazil where he died after the war. The fact that such a large number of Polish mathematicians found positions in some of America's most important universities, is a sufficient testimony to the high level of mathematics in the pre-war Polish universities.

I would also like to mention that in addition to those who came out of the Polish school of mathematics, two other Poles are holding teaching positions in mathematics in the U.S.A.: Stefan Bergman who is professor at Stanford University, and Matthew M Fryde who has been appointed visiting professor of the history of mathematics at Yeshiva University in New York.

World War II caused heavy and irreparable losses to Polish mathematics. About fifty percent of our mathematics professors perished, among them many eminent scholars. In addition, over thirty younger mathematicians and scientific workers were lost. Twenty of our mathematicians died in circumstances which are difficult to believe. Some were tortured in concentration camps, others were murdered by the Gestapo and still others died in gas chambers.

The Mathematical Seminar of the University of Warsaw was demolished by a bomb and burned down on 1 September 1942, together with the Mathematics Library which adjoined it.

All of the Warsaw mathematicians lost their private libraries, their collections of reprints and their archives. In October 1944, at the collapse of the Warsaw Insurrection, the Germans expelled the inhabitants from the city, and the Brandkommando burned it down systematically block by block. The manuscripts of Warsaw scholars, containing the results of their work between 1939 and 1944, also went up in flames. When in 1945 I informed my colleague, Professor Paul Montel of the Sorbonne, of this, he read my letter to the Academy of Sciences in Paris and the Academy voted to publish it. It was unique that a message of this sort should appear in the Academy's Comptes rendus.

As a result of the war our country lost about sixty percent of its mathematicians. When after the war Professors Julius Rudnicki of Torun, Kazimierz Zórawski of Warsaw and Zygmund Krygowski of Poznan, died, I became the senior mathematician of Poland.

Even before World War II Polish mathematicians had intended to create a National Institute of Mathematics. The Mathematics Committee of the Council of Exact and Applied Sciences had initiated the necessary moves. Unfortunately, the war prevented the realisation of this project and it was not until 1948 that there was established in Warsaw, the State Institute of Mathematics. Its aim apart from cultivating the various branches of mathematics which had reached a high level before the war, (the theory of sets, topology, functional analysis, the theory of real functions and foundation of mathematics) was to encourage development of research in analysis, algebra, the theory of probability, and to initiate research in the application of mathematics to technology, physics, industry and the national economy.

When the Polish Academy of Sciences was established, the State Mathematical Institute became one of its scientific institutes. From its very beginning, more than ten years ago, the director of the Institute has been Kazimierz Kuratowski. His deputies in scientific matters are at present Professor Karol Borsuk and Andrzej Mostowski. The latter is this year lecturing at the University of California at Berkeley. The Scientific Council of the Institute, of which I have the honour to be the chairman, is composed of twenty-seven professors, of whom ten are from outside of Warsaw.

The Mathematics Institute has in Warsaw, Wrocław, Krakow, Poznan, Torun and Lublin fifteen sections: Algebra, Functional Analysis, Mathematical Analysis, Numerical and Graphic Analysis, Analytical Functions, Functions of a Real Variable, Differential Geometry, Theoretical Mechanics, Foundations of Mathematics, Differential Equations, Integral Equations, Statistical Quality Control, Mathematical Statistics, Topology, and the fifteenth and last section, Application to Science and Economics.

Until recently the Institute of Mathematics also had a mathematical computers unit attached to it. For various reasons it was separated and made a part of the Technical Sciences Section of the Academy of Sciences. Since modern electronic computers and their servicing are very expensive, allocations to the mathematical computers unit took up the greater part of the budget of the whole Institute. These electronic machines must first be designed and then constructed and for this, the close cooperation of engineers and mathematicians is necessary. The computers are of two kinds:

Those which give only approximate graphic solutions of various equations: ordinary or differential; and the so-called digital computers which accurately perform arithmetical operations on integers having hundreds or thousands of digits. The machines of the first kind, which we already have in Warsaw, are necessary for the practical application of mathematics. Pure mathematicians, however, are interested in machines of the second sort. The construction of such a machine has now begun. In the United States and in some European countries there exist enormous electronic computers which have already given science answers to various interesting questions relating to prime numbers. These machines have solved problems which, because of their length, could not have been solved by the best calculators within the period of a lifetime. With the help of an electronic computer it was possible in Sweden to find the largest prime number known, composed of 969 digits.

The Mathematical Institute of the Polish Academy of Sciences currently employs about 150 scientists from all over Poland, among whom are 80 professors or docents, the remainder having at least a master's degree.

The Mathematics Institute of the Polish Academy of Sciences is at present conducting in Warsaw and in other cities a series of seminars, lectures and discussions which are headed by professors or docents. Their aim is to educate a younger generation of scientists. In the last academic year there were forty-four such lectures or seminars in various fields of mathematics. The Institute also supports several fellows who already have a master's degree and are aspiring to the doctorate.

The Scientific Council of the Mathematics Institute conducts examinations for doctorates and confers the degree of doctor, as well as the title of docent and professor. It may seem strange that an institution which is not a university or another academic school has the right of conferring degrees and scientific titles. I feel, however, that in the case of the Mathematics Institute this is entirely justified and that the scientific degrees conferred by the Mathematics Institute have even greater weight than those which are conferred by the Councils of academic schools. After all, the Councils are composed, at most, of only a few mathematicians from a single centre plus specialists in other studies, (Physics, Astronomy etc.) who cannot evaluate properly the scientific abilities of candidates from the field of mathematics. These members vote according to the evaluation of the few specialists on the Council. The Scientific Council of the Mathematics Institute, however, is composed of about thirty of the most distinguished mathematicians of the country.

The Mathematics Institute of the Polish Academy of Sciences currently publishes the following scientific periodicals:

Fundamenta Mathematicae, a periodical appearing since 1920 in foreign languages dedicated to the theory of sets and its application, already discussed in detail. The editor-in-chief is Professor Kazimierz Kuratowski. So far forty-five volumes have appeared.
Studia Mathematica, which presents, in foreign languages, works in the field of analysis and theory of probability. So far sixteen volumes have appeared. The editor-in-chief is Professor Hugo Steinhaus in Wrocław.
Annales Polonici Mathematici (since 1954). This is a continuation of Annales de la Société Polonaise des Mathématiques, which now has twenty-live volumes. It publishes in the languages of international Congresses, works dedicated to mathematical analysis, geometry, and the theory of numbers. The editor-in-chief is Professor Franciszek Leja in Krakow.
Colloqium Mathematicum contains reports in foreign languages about research and results and a journal of events which are of interest to mathematicians. The editor-in-chief if Professor Edward Marczewski in Wrocław.
Prace matematyczne (Mathematical Studies). This is a continuation of the periodical, Mathematical and Physical Studies founded in 1887 by Samuel Dickstein. Thus far it has forty-nine volumes. The editor-in-chief is Professor Władysław Orlicz in Poznan.
Wiadomosci matematyczne (Mathematical News), a continuation of the periodical founded under that name in 1897 by S Dickstein. The editor-in-chief is docent Marcel Stark in Warsaw.
Zastosowania matematyki (Applications of Mathematics). The editor-in-chief is Professor Hugo Steinhaus in Wrocław.
Rozprawy matematyczne (Mathematical Proceedings) containing dissertations and researches on special problems. The editor-in-chief is Professor Karol Borsuk in Warsaw.
Monografie matematyczne (Mathematical Monographs) appearing since 1932, which has been explained in detail.
Acta Arithmetica, a periodical of an international character, dedicated to the theory of numbers. Before the war it was edited by Arnold Walfisz and Salomon Lubelski. The fourth volume appeared last year under my editorship. This periodical prints works in foreign languages and is headed by an Editorial Committee, made up of the world's greatest specialists in the theory of numbers.

In addition, the Bulletin of the Polish Academy of Sciences publishes mathematical results in foreign languages.

That Fundamenta Mathematicae, Studia Mathematica and Acta Arithmetica are well received abroad is evident from the number of foreign studies submitted to them for publication.

The second volume of the new series of Mathematical News, which appeared last year has a bibliography of works published by mathematicians living in Poland during the period from l944 to 1954. This bibliography consists of 1,716 titles by Polish scientists printed in Poland and abroad, (monographs, university handbooks, and original works). It does not list works in the field of teaching elementary mathematics, problems, reports or reviews. This bibliography is divided into eleven sections; for example, (I) The foundations of mathematics (including the theory of sets and mathematical logic); (II) topology, (III) functional analysis, etc. Every section is preceded by a description of the problems and the chief scientific results and each contains conclusions relating to future development of the field in Poland.

In return for our mathematical periodicals published in foreign languages, we receive mathematical periodicals from all over the world. Therefore the library of the Mathematical Institute is well equipped with current mathematical publications.

The Mathematical Institute maintains contacts abroad. Last year several of our scholars went abroad to Congresses or less important meetings, for lectures and in the case of the younger ones, for study. Several of our mathematicians have been invited for one or two semester lectures by various American universities. For example, Professor Roman Sikorski has been lecturing in New Orleans; Professor Andrzej Mostowski has been lecturing for several months at Berkeley; Docent Wanda Szmielew spent all of last year lecturing at the same school; Professor Helen Rasiowa, last year lectured in Argentina and Brazil and this year is the Dean of the Mathematics and Physics Faculty of Warsaw University. Next year, she will again lecture abroad. It is worthwhile noting that in relation to me this is already the fourth generation of Polish mathematicians. Professor Rasiowa was awarded her doctor's degree by Professor Mostowski; Professor Mostowski by Professor Kuratowski, and Professor Kuratowski by myself.

Many foreign mathematicians have come to us for guest lectures and some of the younger ones for studies. In the last few years several of the alumni of the University of Warsaw, presently professors at American universities, have visited us: Professors Anthony Zygmund, Alfred Tarski, Jerzy Spława-Neyman and Nachman Aronszajn. We are expecting others.

Since the last war there have been five Polish mathematical congresses. The first of these, the Fourth Polish Mathematical Congress, took place in December 1946, in Wrocław. It was attended by fifteen mathematicians from Wrocław, twenty-nine from other Polish cities and three from foreign countries. The next, the Fifth Polish Mathematical Congress, met in Krakow at the end of 1947. It was attended by more than fifty mathematicians from Poland and eight from other countries. In September 1948 the Sixth Polish Mathematical Congress was held in Warsaw and this brought together one hundred and ten mathematicians of whom ten were from abroad. The Eighth Congress was held in Prague, together with the Third Czechoslovak Mathematical Congress. There were about a hundred and twenty participants, among them fifty Poles, sixty Czechs, six Hungarians, and one Frenchman. The Ninth Congress was held in Warsaw in September 1953 and was attended by two hundred Poles and forty mathematicians from fourteen foreign countries.

Since 1953 there has not been a Congress in Poland devoted to the whole of mathematics. However, there have been meetings or conferences devoted to specific fields of mathematics with the participation of guests from abroad. These were dedicated to the discussion of particular fields of mathematics. Holding congresses which are attended by several hundred mathematicians in various fields, many of whom come from abroad, presents many problems. Especially serious is the difficulty in providing living quarters for them. Therefore we have begun holding meetings which are limited to fields. In the autumn of this year there will take place in Warsaw under the sponsorship of UNESCO a conference, dedicated to the foundations of mathematics, at which we expect several score specialists from abroad.

The last International Mathematical Congress which took place in September of last year at Edinburgh, Scotland, and which was attended by two thousand participants from all over the world, included more than 20 mathematicians from Poland and 10 Polish mathematicians now living abroad. Each of our mathematicians read a paper presenting his latest findings.

In ending this survey of Polish mathematics I should like to mention the so-called "Mathematical Olympics" which, beginning with 1950, have been held each year by the Polish Mathematical Society. These are contests in which students in the higher classes of secondary schools participate. The rules of the Olympics provide for three contest levels, based on the solution of problems posed by the head committee of the Olympics. The first degree involves the solution of a series of problems at the rate of four problems per month for a period of three months. The answers are returned in writing to the district committees of the Olympics. These district committees located in major cities such as Warsaw, Krakow, Wrocław, Gdansk, etc., study the solutions and pick the candidates for the second stage of the contest. This consists of solving within two days, six problems presented by the head committee. The work is supervised in the six cities where the district committees are located. The solutions are then studied by the head committee which chooses the candidates for the third stage of the contest This takes place in Warsaw and again consists in the solution in writing of six problems under supervision. The head committee studies the solutions and awards the prizes and honours. The winners of the contests after graduating from secondary school, are admitted to science and technical departments in the schools of higher education without competitive examinations. The state also offers them special scholarships.

Many of our best alumni were drawn from among the winners of these mathematical Olympics. One of these, Andrzej Schinzel from Sandomierz, was the winner of the first mathematical Olympics while still very young with two years of intermediate school to finish. Today, at 22, with a master's degree in mathematics, he published 33 works in the most serious periodicals in Poland, France, Italy, Switzerland, Belgium, Czechoslovakia, Hungary, India and China. He is perhaps the only Polish mathematician whose work has been published in Chinese. The success of these mathematical Olympics has encouraged the specialists from other fields to organise similar events. We already have a Physics Olympics.

If I compare the present state of mathematics in Poland with that of 55 years ago, when I began my scientific career, I must say that despite the enormous losses occasioned by World War II, the present situation cannot even be compared with that which existed several years ago. There is no doubt in my mind that at the present time Polish mathematics are in a flourishing state.

Last Updated September 2025