Remembering Professor Michał Życzkowski

A great teacher and scientist who reshaped Cracow University of Technology

And became the unsurpassed Master for his students


In 1954 Professor Michał Życzkowski graduated from the Cracow University of Technology, and this date exactly coincided with my graduation at Nowodworski High School in Krakow and with the commencement of my freshman year at the Krakow Polytechnics, now known as Cracow University of Technology (CUT). It was not until my sophomore or junior year at the Polytechnics that my life path crossed with that of Professor Życzkowski’s. At that time the young doctor Życzkowski (who after the WWII was the first PhD at the Polytechnics at tender age of 25) was in charge of the recitations with our section in Mechanics of Materials.

            At first the subject matter was Strength of Materials to be followed later by the Theory of Elasticity. Both subjects were taught by Professor Janusz Walczak, an excellent lecturer. His two-hour lectures were delivered in a large lecture hall destined for a large audience. The sessions were rather formal and in ex cathedra style, leaving little room for questions or comments from students. However, at the recitation sessions lead by the young doctor Życzkowski things looked different. Dr. Życzkowski was an Assistant in Professor Walczak’s Chair of Mechanics of Materials. During the recitation classes with Dr. Życzkowski the students had plenty of opportunity to plunge deep into the core of the problems and to ask all kinds of questions. Dr. Życzkowski was well prepared and ready to oblige and to explain the problem at hand in great detail. He radiated an unbounded energy of life combined with an unusual kindness and willingness to help. In short time it became clear that Dr. Życzkowski is not just a dry introverted scientist, but rather an extraordinary teacher and a warm human being. Somebody you would like to have as a friend. His ability to make complex problems look like a simple matter, and at times almost easy, was uncanny. He never hesitated to go an extra mile to explain certain mathematical intricate details necessary to solve a given problem. Only later in life I understood that such a character trait is a rare trait indeed. It was a rare gift extremely valuable for the young teacher.

            Subjects taught to us were not easy, and they often required a good deal of concentration and solid knowledge of the underlying mathematical techniques. It was my first encounter with the Laplace and Poisson equations, the Fourier series and boundary value problems studied by Dirichlet and Neumann. The favorite subject of Dr. Życzkowski was, I think, the Calculus of Variations and various numerical methods inspired by this Calculus. His through knowledge of the field far surpassed and exceeded standard university level. He was also fluent in other branches of Mathematics, sometimes only remotely related to the courses taught at the university. Till this day it remains a mystery how he acquired such truly nontrivial knowledge of the mathematical methods needed to put a theory to work in the area of engineering. He dazzled us with his virtuoso erudition not only in Mechanics and Mathematics, but also in foreign languages (he spoke German, Russian and English) and in humanities. All these talents seemed to fit well with his ever so optimistic personality. They supplemented his inborn didactic talents. If you observed Dr. Życzkowski stating and then proceeding to solve a mathematical problem, you had no choice but to admire him. And wonder how it is possible for one man to master so perfectly so many subjects. When he lectured, we were struck by awe. Even complex arithmetic Dr. Życzkowski was able to handle using his memory alone, yet he was always willing to stop and to explain to a puzzled listener how the trick was done. His “computing machine”, the state-of-the-art at that time, an object of impressive dimensions, became famous at the Polytechnics. I believe he brought the machine from the Imperial College in London, where after completion of his doctoral thesis in Poland he studied as a post-doc in the period of 1957 and 1958. He also made a number of friends in Russia, and to this day I remember his vivid account of his travels in this country. He read and used in his research a lot of sources then available for pennies – all in the original Russian language. The same goes for the sources in German and in English. A number of Professor Życzkowski’s own doctoral students have completed their graduate or doctoral studies in Russia. Of course, without Życzkowski’s direct involvement and help they would have never been able to do this. From my learned colleagues in the United States I have found out that mere mention of the name “Życzkowski” opened the doors of the most prestigious universities on this continent. One of his best friends in the USA was very amiable Nicholas Hoff, a distinguished Professor at Stanford University.

            During my senior year at the Polytechnics, while majoring in Mechanical Engineering I attended the weekly seminars arranged by Professor Życzkowski. My notes gathered during these regular Tuesday meetings turned out to be of greater value than many prestigious textbooks that I posses. Years later I met with Professor Życzkowski in the United States at the University of Amherst in Massachusetts – again as his student, although at this time I myself was an Assistant Professor at an American university. I remember that his wife Teresa was also present at the series of his excellent lectures given at Amherst. In more recent years Professor Życzkowski and I have met several times at various international conferences. First it was in California in 1968 at the IUTAM Conference hosted by Stanford University, then in Germany, and once at the Spa in Busko, Poland. There Professor Życzkowski found a welcomed retreat from the noise of everyday life. There, I would guess, he was able to “recharge his batteries” so needed for his exacting mental performance. His schedule at the Polytechnics was extremely busy and I often wondered how was he able to find time for completion of all these tasks required of him. It looked like he was able to perform multi-tasking long before this term was even invented.

            Since these words written here are of informal nature, I will take a liberty at quoting some stories which are more anecdotal than historical. One such story begins during a certain Tuesday seminar attended not only by graduate students but also by the faculty from the other departments in the College of Engineering. Specifically, I am referring here to the presence of Professor Barański of the Department of Mathematics. Professor Barański did not think much about engineers’ talents applied to handle Math, and he usually assumed a priori that most of what we did was either wrong or – at best – could not be proved to be correct. Not from the mathematical point of view, even if the common sense and the intuition indicated otherwise.

            At this particular seminar Professor Barański arrived late and did not have sufficient time to read all the equations that appeared on the blackboard. Thus he did not notice the restrictions on the radius of variable “r” which appeared under the logarithm symbol in the equations for stresses present in the classic Lame problem in the Theory of Elasticity. Suddenly a thought occurred to him; he stood up interrupting the lecture and in a rather indignant voice stated that the equation was “obviously wrong”. It was meaningless – he claimed – “when the variable r was approaching zero, as then the logarithm is not defined.” When he finished, Professor Życzkowski took the floor and responded “you are looking for something that is not there”. Then he went on to explain that the radius “r” used in the formula written on the board could never be less than the finite entity “a”, the inner radius of the cylinder. At “r” equal to “a” the logarithmic function approached zero and it made perfect sense, as expected in real life. Professor Barański stopped his monologue and slightly nodding his head in a gesture of surrender withdrew from the discussion. He sat down and remained silent for the rest of the presentation.

            In 1959, when I began my first paid job as an Assistant in the Department of Physics at the Krakow Polytechnics, I also had my very first technical paper published. Of course, it was entirely inspired and co-authored by Professor Życzkowski. On some earlier occasion I came up with the modification of calculations of the moment of inertia. Although I was rather enthusiastic about it, the idea was discarded by Professor Życzkowski, who has shown to Professor Walczak (his boss) and to myself (his student) that the idea could be reduced to just another interpretation of the known process of iteration of a double integral and thus it was not worthy of publication. My second thought, though, was a lucky one and it was approved by the Master. This time the idea had to do with the analogy between post-critical buckling of a beam (a nonlinear problem) and the mathematical pendulum subject to the initial conditions involving large angular amplitude. The formula I proposed was based on Puwein’s approximation of the elliptic integral of the second kind; and this time it worked. Actually it was better than any formula proposed in the literature. The idea was my own, but I owe it entirely to Professor Życzkowski, without whom I would have never noticed the hidden analogy. We published the results as joint paper. Later we did publish jointly a number of papers, but it was the first one, about which I felt most proud.

            It was just the beginning of my professional life in science. Within two years, from 1960 to 1962 I completed my doctoral thesis. The work was inspired and supervised from the beginning to the end by Professor Życzkowski. Michał Życzkowski used to teach us, his students and advisees, that all things – meaning calculations – needed to be done at least twice. When the news was announced that the twins were born by Życzkowski’s wife Teresa, someone commented that this fact agreed with the rule “to get it right, do everything twice”. The “rule of two” was from now on referred as “Życzkowski’s rule”. I remember that his boys, Karol and Adam, at a very early age knew from their father how to raise number two to an arbitrary power and how to convert any given number from the decimal to binary base. I also know that Życzkowski’s son Karol received his name after the Polish Pope John Paul II, who happened to be a personal friend with Życzkowskis’ family. Now Karol Życzkowski is a famous physicist in his own right.

            Some elements of my doctoral thesis caught an eye of several prominent scientists at the Polish Academy of Sciences in Warsaw. Of special interest appeared my approach to estimation of the upper and lower bounds for the limit loads in the Theory of Plasticity. Again, the Calculus of Variations, a favorite branch of Mathematics I have learned from Michał Życzkowski, came in very handy. The pertinent functionals were formulated in my thesis and the extremes were found. Both my reviewers, one from Warsaw and one from Moscow, were definitely impressed and my PhD Thesis was defended magna cum laude in the fall of 1962. Soon after this I was promoted in the Department of Physics to the post of “Adjunct”, which is just one notch below “Assistant Professor”.

            This was the most memorable time in my professional life, filled with scientific work and numerous presentations of my original results at the national and international meetings and conferences. One “very important person” in Mechanics, Professor Wacław Olszak from Warsaw, father of the Theoretical and Applied Mechanics in post-war Poland, commented on my presentation. Turning his head toward my advisor and with a broad smile on his face Professor Olszak said to Życzkowski “you have got a Great grandson”. Here a play of words takes place, since my name in Polish means “grandson”. This was truly an unexpected and a great compliment for me.

            My textbook on “Introduction to Fracture Mechanics” was printed twice at the Mining Academy in Krakow and recently, in January 2009, it appeared in a book form, published by “Akapit”, a publisher associated with the Mining Academy in Krakow. Professor Zenon Mróz of the Polish Academy of Sciences in Warsaw wrote these words about the book “After reading the syllabus and the outline of the contents of this text, I can state that this work presents a valuable addition to the existing literature in the subject. It will help lectures and the practitioners in the field related to Mechanics of Fracture. The author is a recognized specialist in his field and his original contributions are known world wide.” This is just an excerpt from the review of the book. Have I never met Professor Michał Życzkowski in my life, there would be no book written and there would be no review coming from Warsaw.

            Many other events would not have taken place. One of which – again – is of anecdotal nature. In the sixties I was asked to do a presentation summarizing the results of my doctoral research during a seminar at the Warsaw Institute of Mechanics, which is a part of the Polish Academy of Sciences. While speaking to the distinguished audience in Warsaw, I stopped and looked at my wrist watch, so the story goes. Then I said “I have to quit now, otherwise I shall miss my plane to Krakow”. Then I added “There is no problem. My colleague Życzkowski knows the subject and he will continue the lecture”. With these words I handed the chalk to Professor Życzkowski and left the amazed audience. Today, it is virtually impossible to tell how much of this is true, but I must say in retrospect that, if it is true, then I should be ashamed of myself.

            For the conclusion I choose the quote taken from my superior in the Department of Physics. Professor Michał Halaunbrenner respected and admired Michał Życzkowski. One day Professor Halaunbrenner came up with the following descriptive nickname for Professor Życzkowski – “Michał the Wonderful”. I am convinced that Professor Życzkowski truly deserves this gracious nickname. He was a wonderful man in every sense of the word.


I feel obliged to thank Professor Antoni Gajewski, my friend and former Head of the Institute of Physics at the Cracow University of Technology for his encouragement during this work and for the editorial help that he has extended to me in editing the final version of the text. His advice is gratefully acknowledged.


Prof. Miłosz Wnuk