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AN INTERVIEW WITH SIBE MARDESIC
James Keesling, University of Florida, USA
Sibe Mardesic is a mathematician who has had a considerable influence on research in topology in the course of his career. It is my pleasure not only to know his mathematics, but also to know him personally. His manner is just as attractive as his mathematics. He is personable, gracious and unassuming. We have a joint paper together and he is the ideal collaborator. His clear mathematical mind and congenial manner made working together a very gratifying experience for me. When we began our work he had a clear idea what results could be expected and what tools would be useful. He also knew that the devil was in the details and was never satisfied until every step of each proof was absolutely clear.
Sibe has attained preeminent stature, but that was not the sort of thing that he set his sights on. His focus was always on mathematics itself and the beauty he saw in it. As he says in our interview, Some questions would just attract my imagination and I would follow that trail persistently and for an extended period of time. By hard work and good results he showed that certain areas of mathematics were fruitful. In so doing he prepared the way for others to follow. Those who did have much to be grateful for.
At the end of the interview there is a biographical sketch which includes Sibe's major accomplishments and some of the recognition that he has been accorded. Please do not think that this is the final chapter in the life of Sibe Mardesic. He is still active and there is more to come.
Sibe, tell us about your family.
The family on both, my father's side (Mardesic) and my mother's side (Karaman), is from Dalmatia, the coastal region of Croatia. Presence of the Mardesices in Komiza on the island is documented since 1539. They fished sardine and cultivated grapevine. My grandfather Sibe spent 30 years as lighthouse keeper on remote islands of the Adriatic. My father Pavao was a naval architect and a mechanical engineer. My mother Anka comes from a family of merchants from the coast town of Split and its hinterland.
I understand that your family spent time in different countries while you were growing up. Tell us about this experience.
My father studied at the well-known Technical University in Vienna. The period from 1923 to 1929 my parents spent in Hamburg, where I was born on June 20, 1927 in Bergedorf, a suburb of Hamburg. In 1929 we moved to Chile, where my father worked in a factory near Antofagasta. We returned to Split in 1930 and this concludes my childhood traveling. My parents, beside their mother tongue Croatian, spoke fluently Italian, German, French, English and Spanish. This gave me a good start and enabled me to get pretty good in these languages and Russian.
Sibe Mardešić as a child. Source [PDF].
When were you first attracted to mathematics? Did your parents or other family members play any role in encouraging this pursuit?
My father wanted me to become an engineer and paid particular attention to my school grades in mathematics. Towards the end of the Second World War I joined the Yugoslav Navy, where I worked in the Meteorology Service. There I met a student of mathematics of the University of Zagreb, Mr. B. Makjanic, who later became a known meteorologist. He introduced me to mathematics beyond the school level. I was fascinated by what he told me about sets and their cardinal numbers and I made the decision to study mathematics as soon as I got released from the Navy.
Sibe Mardešić in 1948. Source [PDF].
Who were the teachers and others that had the most influence on you in choosing the direction of your studies?
I enrolled at the University of Zagreb in 1946/47. At that time there were few professors at the Mathematics Department. I was attracted to set theory by Prof. Dj. Kurepa and to geometry by Prof. R. Cesarec.
How did you happen to go into topology? What influenced the direction of your research in this field?
Shortly after obtaining my B.Sci. in 1950, I became assistant to Prof. Zeljko Markovic. In his youth he spent a year in Paris and was fascinated by the work of H. PoincarĂŠin celestial mechanics. He wanted me to become interested in dynamical systems, and it was clear to him that to do global analysis one needs a good understanding of topology. Therefore, he suggested that I first study "Lehrbuch der Topologie" by H. Seifert and W. Threlfall. This turned out to be very good advice. I read the book in great detail and fell in love with (algebraic) topology. In my Ph. D. thesis I considered some problems of K. Borsuk concerning homology of function spaces. In the process of writing the thesis I corresponded with S. Lefschetz, who at some point suggested that I visit the Institute for Advanced Study in Princeton. With letters of recommendation by Borsuk, Eilenberg and Kuratowski, I was accepted to the Institute, where I spent the years 1957/58 and 1958/59. In Princeton I attended lectures by R. H. Fox, J. Milnor, J. Moore, N. Steenrod and G. Whitehead and I became a topologist.
Sibe Mardešić in front of the The Institute for Advanced Study in Princeton,
New Jersey, USA. Source [PDF].
You are not alone in your family as a mathematician. Your wife Vera is also a mathematician. How did the two of you meet? You have had a long and happy marriage. Did your common interests in mathematics help contribute to this?
It was most fortunate for me that I met Vera. This happened in 1948/49, when I was a junior and she was a freshman. Throughout my life I always had her full support. She understood how important my work was to me and she provided a happy and secure environment for me. The fact that she is herself a mathematician enabled her to follow my work and accompany me on many of my mathematical trips. She did most of her work under the guidance of Prof. Victor Klee.
I understand that your son Pavao is also a mathematician. What field is he in? Did your daughter Milica also pursue mathematics?
My son Pavao is indeed a mathematician. He has a B. Sci. and a M. Sci. from Zagreb and a Ph. D. from UniversitĂŠde Bourgogne, Dijon, France, where he now has a position. His area is dynamical systems, in particular, singularities of polynomial vector fields in the plane. My daughter Milica has a Ph. D. in linguistics from Zagreb. We have five grandchildren, from 10 to 3 years old, which give us a lot of joy and pleasure.
What do you see as the highlights of your career in research? What contributions would you like to be most remembered?
It appears that my most successful result is the factorization theorem in dimension theory, which is quoted in most books on dimension theory. I like my work on continuous images of ordered continua. I believe that I will be remembered for my contributions to shape theory and strong homology. My shape theory book with Jack Segal has been well received. I have a new book on strong shape and Steenrod homology which is in preparation. I am hoping that it will be received as well as the shape theory book has. I also like my work with L. Rubin and T. Watanabe on approximate inverse systems. I always wanted to be an algebraic topologist, but did not quite succeed. Therefore, I like my recent results concerning higher derived limits of homological progroups.
You have had a tremendous influence in building the Mathematics Department at Zagreb. There are no doubt many young mathematicians who are in departments that are building. As one who has been very successful at this, what advice would you give?
Sibe Mardešić with Pavel S. Aleksandrov, distinguished Russian mathematician.
I have been very devoted and faithful to Mathematics in Zagreb. I dedicated approximately equal shares of my time and energy to research, teaching and organization. I tried to transfer to Zagreb good things that I saw at other more developed places. I paid particular attention to teaching at the graduate level.
Several of our graduate students at the University of Florida have come from Zagreb. They were deeply influenced by your teaching. Do you have a special philosophy or methodology in your teaching? Many of us envy the profound influence you have had as a teacher. Could you help us with some practical insights?
I first try to understand the material properly. Then I try to present it clearly, giving the necessary background. Enthusiasm of the teacher and an honest, respectful and friendly approach to students are essential features of successful teaching.
I am sure that there are many young students and mathematicians contemplating their futures right now who would like to know what direction to go. Do you have any thoughts about the future of topology and mathematics in general that might be helpful to them?
I never thought very much about the direction in which I was going. Some questions would just attract my imagination and I would follow that trail persistently and for an extended period of time. The internal beauty and consistency of a result is what always mattered to me.
We have all been saddened by the events in the former Yugoslavia. As you know my step-father's family came from Croatia, so I also have a sense of personal distress in what has happened. Are there steps that the mathematical community can take to help bring stability? What can we do to help mathematics prosper in this region?
I was deeply shaken by these events. Fortunately, unlike many others, my own family was spared from personal tragedies. I hope that the situation in my country will gradually stabilize. It is now important that we resume the excellent ties which we had before with our colleagues abroad. Let us be in touch through mail, visits and common programs. It would be nice if we could together revive the Dubrovnik topology meetings. I wonder if there would be a way to help us fill up the gaps in our library which occurred during the war.
Sibe, as one who has admired your work for many years, it was a privilege for me to interview you for Topology Atlas on the web. Thank you for the interview and for your continuing contributions to topology.
Sibe Mardesic - Biography
Elementary and high school in Split (Croatia). B. Sci. in Mathematics 1950 (Faculty of Natural Sciences and Mathematics, Zagreb), Ph. D. in Mathematical Sciences 1957 (University of Zagreb). Ph. D. Thesis: Homology properties of some function spaces. Habilitation (Faculty of Natural Sciences and Mathematics, Zagreb) 1960. Habilitation Thesis: On covering dimension and inverse limits, Illinois J. Math. 4 (1960), 278-291.
Sibe Mardešić is a member of Academia Europaea (The Academy of Europe)
Faculty of Natural Sciences and Mathematics, Zagreb: Asst. 1951, Asst. Prof. 1960, Associate Professor 1962, Professor 1966. Retired 1991. Chairman of the Mathematics Department, Faculty of Natural Sciences and Mathematics, Zagreb, 1961/62; Vicedean, Faculty of Natural Sciences and Mathematics, Zagreb, 1964/65; President of the Council of Faculty of Natural Sciences and Mathematics, Zagreb, 1966/67; Dean of Faculty of Natural Sciences and Mathematics, Zagreb 1974/75 and 1975/76; Dean of the Mathematics Department of Faculty of Natural Sciences and Mathematics, Zagreb 1983/84; Head of the Chair for Topology of the Mathematics Department of Faculty of Natural Sciences and Mathematics, Zagreb, from 1978 to 1982. Head of the Graduate School for Mathematics of the University of Zagreb from 1960 to 1971; Editor in chief of the journal Glasnik matematicki from 1963 to 1976; Member of the Advisory boardof the journal Topology and its Applications since 1971. President of the Croatian Society of Mathematicians and Physicists 1971-1974. Organizer of several international conferences and schools (Dubrovnik 1976, 1981, 1986).
Visiting Member of the Institute for Advanced Study, Princeton, N.J., 1957/58 and 1958/59; Visiting Lecturer, University of Washington, Seattle 1965/66. Visiting Professor, University of Heidelberg, 1971/72; Visiting Professor, University of Pittsburgh, Fall Semester 1972/73; Visiting Professor, University of Utah, Salt Lake City, Fall Semester 1977/78; Visiting Professor, University of Kentucky, Lexington, Spring Semester 1977/78; Visiting Professor, University of Washington, Seattle, Spring Semester 1987/88 and Fall semester 1988/89; Research programs and series of lectures in the duration of one month approximately at the following universities: L'Aquila (1979), Tsukuba (1981), Perugia (1985 and 1990), Oklahoma (1987), Milano (1993).
Areas of primary interest: Topology, in particular, inverse systems, dimension theory, shape theory and homology theory. 124 published research papers, 19 professional papers and 3 books. Papers published in various journals including: Topology and its Applications, Topology, Fundamenta Mathematicae, Transactions of the American Mathematical Society, Proceedings of the American Mathematical Society, Bulletin of the American Mathematical Society, Comptes Rendus de l'Academie Paris, Doklady Akademii Nauk SSSR, Michigan Mathematical Journal, Illinois Mathematical Journal, Pacific Mathematical Journal, Rocky Mountains Mathematical Journal, Bulletin of the Polish Academy of Sciences, Uspehi Matemativ ceskih Nauk, Tsukuba Journal of Mathematics, Mathematica Japonica.
Sibe Mardešić. Source [PDF].
Reviews and Lectures
Almost 500 reviews for international reviewing journals (Mathematical reviews and Zentralblatt fĂźr Mathematik). Over 260 lectures at conferences and universities in 20 countries. Undergraduate courses in Mathematical Analysis and Topology. 13 different Graduate courses in Topology.
Societies and Recognition
Associated Member of the Yugoslav (Croatian) Academy of Sciences and Arts 1975; Member of the Yugoslav (Croatian) Academy of Sciences and Arts JAZU (HAZU) 1988; Member of Academia Europaea 1990. Member of the American Mathematical Society since 1958; Member emeritus of the American Mathematical Society since 1992. Professor emeritus of the University of Zagreb, 1996. Award for Scientific achievements of the Republic of Croatia Rudjer Bošković 1964, Work Medal with Golden Wreath 1975, Award of the City of Zagreb 1978, Award for Life Achievements of the Republic of Croatia 1990.
Interview from Volume 1, #3 of TopCom
Source at.yorku.ca; published in 1996.
Many thanks to Professor James Keesling for his kind permission to publish his interview for the readers of the CROWN. D.Ž.
The interview has been translated into Croatian by Dr. Željko Hanjš, University of Zagreb:
James Keesling: Intervju s akademikom Sibom Mardešićem [PDF], Matematičko-fizički list, Zagreb, 2008.-2009., str. 156-158.
Many thanks to Branimir Dakić, prof., Zagreb, for kind permission to reproduce some of the photos from his article [PDF] published in Matematika i škola no. 41, 2007.