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Home , Andrzej Mostowski, Helena Rasiowa, Karol Borsuk, Roman Sikorski, Wanda Szmielew

Wiktor Bartol

HELENA RASIOWA AND CECYLIA RAUSZER - TWO GENERATIONS IN

Helena Rasiowa was born on June 23, 1917 in , where her father, Wies law B¸aczalski, worked as a high-ranking railway specialist. In 1918, when regained its independent existence as a sovereign state, the B¸aczalski family settled in . The father was offered an important position in the railway administration, which allowed him to ensure good conditions for his daughter’s development. The young Helena completed her secondary education in a renowned school in Warsaw while learning the piano at a music college. Her first decision was to study management and she persisted in it for about one semester. Eventually, her mathematical interest prevailed. At the beginning of the academic year 1938/39 Helena, already mar- ried, became a student of at the Faculty of Mathematics and Natural Sciences at the Warsaw University. Among her new colleagues there were and , who, together with Ra- siowa, would greatly contribute to the development of Polish mathemat- ics after 1945. The list of lecturers at the Faculty included such promi- nent names as those of Wac law Sierpi´nski,, Jan Lukasiewicz and . The year 1939 brought these studies to a stop. The entire family was evacuated to Lvov. However, after one year in exile, they decided to return to Warsaw. Here the 23-year old Helena Rasiowa reestablished contact with her teachers (and also with , one of the founders of the Polish School of Mathematics in the twenties); she renewed her studies in the clandestine university. By July 1944 she had passed all the necessary examinations and pre- pared her Master’s thesis in under the supervision of Jan Lukasiewicz and Boles law Soboci´nski. Unfortunately, in the destruction of Warsaw which followed the Nazi suppression of the Warsaw uprising, the thesis was turned to ashes, whereas Helena survived the end of the uprising

120 with her mother in a cellar buried under the ruins of a destroyed house. Af- ter having managed to leave Warsaw safely, both women subsisted thanks to the help of the family. Immediately after the war Rasiowa worked at school, where she was discovered by . She re-wrote her Master’s thesis and thus graduated from the Warsaw University as Master of Science in 1946. She stayed at the University as an assistant and started to work on her PhD thesis under the guidance of Andrzej Mostowski. Her first publications appeared in 1947: Axiomatization d’un syst`eme partiel de la th´eorie de la d´eduction and Sur certaines matrices logiques. Three years later, in 1950, Helena Rasiowa was granted the PhD de- gree for her thesis Algebraic treatment of the functional calculi of Lewis and Heyting. In 1956 she obtained the highest scientific degree available in Poland, the habilitation, after having presented a treatise consisting of two parts: Algebraic models of axiomatic theories and Constructive theories. By that time she was author or co-author of 20 publications, among them joint papers with Roman Sikorski, Andrzej Mostowski, Andrzej Bia lynicki- Birula, JerzyLo´s. Her professional links with the Warsaw University, initiated by her assuming the position of assistant at the Chair of the Philosophy of Math- ematics in 1946, lasted till her very last days. In 1950 she became associate professor, in 1952 – a deputy professor (a position which disappeared few years later), in 1954 she was already docent, to become permanent profes- sor in 1957 and full professor ten years later. Simultaneously, she held the positions of docent and later professor at the Institute of Mathematics of the Polish Academy of Sciences between 1954 and 1963. Very active in research, she did not restrict her activities to that field. She never rejected any duties at the university. So, she was head of the Chair of Mathematical Logic for nearly thirty years from 1964 to 1993. She was Dean of the Faculty of Mathematics and Physics in the years 1958–1960 and 1962–1966. Then, she re-assumed the same charge in 1968 and remained Dean first of the Faculty of Mathematics and Mechanics and then of the Faculty of Mathematics, Computer Science and Mechanics. Obviously, the Faculty did not change. It was the name that changed to reflect the changes in the scope of areas being taught and investigated. In the Polish Mathematical Society Helena Rasiowa was secretary (1955–1956), President of the Warsaw branch of the Society (1957–1958), Vice-President of the Society (1958) and then again President of the War-

121 saw branch in 1963–1964. In 1987 she was awarded the honorary member- ship of the Polish Mathematical Society. In the Association of Symbolic Logic Rasiowa was Council member in 1958–1960 and member of the Executive Committee for European Affairs in 1972–1977, while in the Division of Logic, Methodology and Philosophy of Science of the International Union of History and Philosophy of Sciences she was Alternate Assessor (1972–1975) and Assessor (1975–1979). Member of the Committee for Mathematical Sciences of the Polish Academy of Sciences since 1961, she was its secretary between 1961 and 1968. In 1972 she was invited to preside the Scientific Council of the Insti- tute of Computer Science of the PAS, which she did until 1983. Moreover, Helena Rasiowa was member of various committees and boards related to the teaching of mathematics or the organization of higher education. Much of her energy was devoted to editorial work. Her persistence was essential for the creation of Fundamenta Informaticae in 1977. Since then, until her demise, she was Editor in Chief of the journal, which in the meantime grew from the initial four yearly issues to twelve in 1995 and sixteen issues in 1996. Since 1974 she was in the Editorial Board of Studia Logica. In 1986 she established editorial cooperation with the Journal of Approximate Reasoning. It seems incredible that in spite of all these duties in very different areas of professional life Rasiowa managed to publish over 100 research pub- lications in the period 1947–1994. These include the classic monographs: The Mathematics of Metamathematics (with R.Sikorski) first published in 1963, and An Algebraic Approach to Non-Classical which appeared in 1974. In the last months of her life she was writing a new book, of which she completed eight chapters. Last but not least, the description of her outcome would not be complete without mentioning one of the most used textbooks in the teaching of mathematics at the universities, the In- troduction to modern mathematics, translated into several languages and thus known to students in many countries. Professor Helena Rasiowa’s achievements and contribution to mathe- matics, and mathematical logic in particular, was well appreciated by the world mathematical community. She was being invited to many universi- ties all around the world, either to give a single lecture or to stay for a longer period as a visiting professor. In the latter form she spent some time at 14 universities: in Argentina, Brazil, Canada, Italy, Mexico and U.S.A. (Princeton, Florida, North Carolina, Case Western Reserve Univer-

122 sity at Cleveland, Tulane University, Chicago, University of California at Berkeley). She gave lectures on the results of her research at 46 scientific institutions in 12 countries. For some years now Polish mathematicians award a yearly prize in the form of an invitation to deliver a Sierpi´nskilecture; the invitation is accompanied by a medal bearing the portrait of W ladyslaw Sierpi´nski, one of the most eminent Polish mathematicians. In 1987 the invitation was extended to Helena Rasiowa to honour her entire outcome in the field of mathematical logic. This award can be seen as the culmination of a long list of prizes she had been receiving in the previous years: prizes of the Polish Mathematical Society (1953), of the Minister of Education (1965, 1974, 1987), of the Polish Academy of Sciences (1972) and the very prestigious State Prize (1984). Rasiowa supervised about 20 , among them that of Ce- cylia Rauszer. Some of her doctoral students are now working abroad, like Michael Bleicher (University of Madison), Vladimir Kirin (University of Za- greb), Dymitr Vakarelov (University of Sofia), Nguyen Cat Ho (University of Hanoi) or Andrzej Salwicki (University of Pau). It seems to be hard to overestimate the influence of Helena Rasiowa in mathematical logic. General algebraic methods applicable to the investiga- tion of both classic and non-classic logics which she developed have become one of the major tools in mathematical logic. Many a logician has been formed by her books and lectures. She was a living example of devotion to mathematics and a caring guide into the field for many.

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When Cecylia Rauszer passed away on May 13, 1994, after a long period of illness, she was only 51 years old. She was born on November 28, 1942, in Grzegorzewice, a small village surrounded by forests and, as it seemed, a perfect hideout in the times of Nazi occupation. Unfortunately, there could be no perfect hideout at that epoch. Cecylia’s mother was shot to death in one of the meanders of this terrible war, she herself, an infant, miraculously survived. After the war the family (the second wife of Cecylia’s father became a real caring mother to the girl) settled in Warsaw, where Cecylia com-

123 pleted her primary and secondary education. In 1960 she became student of mathematics at the Faculty of Mathematics and Physics of the Warsaw University. This was to be the beginning of her lifetime links with the Uni- versity. She graduated in 1964 with very good marks. Her Master’s thesis, supervised by Prof. Stefan Rolewicz, was on Two-sided closed ideals in the ring of operators over Banach spaces containing lp. In 1964 Cecylia Rauszer was admitted to the Warsaw University as assistant in the Chair of the Foundations of Mathematics. Seven years later she made her doctor’s degree under the guidance of Prof. Helena Rasiowa. Her doctoral thesis Semi-boolean structures and their applica- tion to intuitionistic logic with dual functors contained a development of algebraic methods in logic. In 1977 she made her habilitation, the highest scientific degree available in Poland, presenting the work An algebraic and Kripke approach to certain extensions of intuitionistic logic, published in Dissertationes Mathematicae 157 (1980). In 1978 she was offered the position of docent at the Institute of Math- ematics of the Warsaw University and in 1991 she became permanent pro- fessor. In parallel with her employment in the University, she was member of the staff of the Mathematical Institute of the Polish Academy of Sciences in 1975–1976 and 1991–1992. She was visiting professor at the Kentucky State University in Lexington, U.S.A., from 1985 to 1987. Often invited by various universities, Rauszer had also lectured in Brazil, Bulgaria, Canada, France, Germany, Israel, Japan, The Netherlands and Norway. In many cases the cooperation went much further than a single lecture. Her courses and seminars at the Warsaw University covered the area of mathematical logic and its applications in computer science. She knew how to make the subject attractive to students. Over 50 students asked for her supervision over their Master’s theses; she successfully guided 3 PhD theses. Being a “grandchild” of the Polish School of Logic (Helena Rasiowa, who guided her PhD thesis, was an ex-student of JanLukasiewicz), she quickly realized the importance of research in applied logic or, more pre- cisely, in the applications of logic in computer science. Very active in research, she published over 50 papers, a great many of them in computer science. In mathematical logic she focused her interest on non-classical logics, working on their semantic and syntactic aspects. Having become interested in problems related to computer science, she worked on the log- ics of relational databases and later also on nonmonotonic logics, particu-

124 larly on autoepistemic ones. Several papers were concerned with knowledge representation systems, again from a logical point of view. Since the emergence of the Polish School of Mathematics in the twen- ties, Polish mathematicians are well aware that the development of math- ematics requires more than just teaching and research. This accounts for their intense activities in other domains significant for the science. Cecylia Rauszer followed the tradition. Besides being secretary of the Polish Math- ematical Society in 1978 and President of its Warsaw branch in 1991–1993, she was also President of the Foundation for the Development of Polish Mathematics as well as of the Foundation for Mathematics in Computer Science, co-organizer of the Polish Society for Logic and Philosophy of Sci- ence and Vice-President of its Scientific Council. Her hard work in the Group for the Teaching of Mathematics in the Ministry of Higher Educa- tion was highly appreciated. In 1988 she had a great share in the organization of the international conference Open Days in and Set Theory, in 1988 her partic- ipation in the organization of the XXXVIII semester on Algebraic Methods in Logic and their Computer Science applications in the International Ste- fan Banach Mathematical Centre as vice-chairperson of the Organizational Committee was essential for the success of the event. Cecylia translated her affection for mathematics into articles written for the journal M lody Technik, popular among young people interested in modern technology and technological sciences. For that purpose she used the pseudonym of Aleph 0. After some years she collected her articles into a book Mathematical Miscellanies. Being aware of the dangers implied by her illness, she featured ad- mirable tenacity and sprightliness. During her short but frequent stays at the hospital she never stopped working. Quite often her hospital room resembled an office rather than a place for rest. She was admired by all.

Institute of Mathematics, Warsaw University Banacha 2, 02-097 Warsaw, Poland e-mail: [email protected]

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