Ladies and Gentlemen!

When more than thirty years ago or so, right after getting my doctorate, I found in a journal and read with youthful zeal, a short note by a young American mathematician William A. Kirk, it had hardly occurred to me that I would be standing before you today. I had not expected that I would have the honor of introducing to you an Honorary Doctor of Maria Curie-Skłodowska University, a world-known mathematician, a research leader of a large group of mathematicians from all over the world whose field is the Metric Fixed Point Theory, a theory which draws on the insights I found in the note just mentioned.

I could not have known at that time that I would have the pleasure of introducing to you today my close friend, a friend of our University and a friend of the whole group of Lublin mathematicians, followers of his theory.

I have known our Honorary Doctor, Professor Kirk for over thirty years now (this year is the thirtieth anniversary of his first visit to Lublin), and those many hours we spent engaged in mathematical disputes (and not only on those), don't make it any easier for me to carry out this laudation. For, it is not lofty, dignified words adorned with many modifiers, befitting this occasion, that are coming to my mind. Rather what comes to my mind is our joint work, the joy of the discussions we had, many meetings we took part in in various parts of the world, and a number of things that befell us that are of anecdotal nature and which perhaps should not be told on such a solemn occasion (at least not in its official part).

Who is Professor William Arthur Kirk then? To us, who know him well he is just Art. He is our friend, research leader, often a companion, although this latter phrase may appear too frivolous to some.

If I were to present him to a group of mathematicians I could give a long lecture bristling with specialist jargon, including terms such as the "metric fixed point theory," "nonexpansive" - and "asymptomatically nonexpansive mappings," "Lipshitzian" - and "uniformly Lipshitzian transformations," the "normal structure of convex sets," "weak" and "weak star topologies," "hyper convex spaces," "utra-filter methods," and many others. In one word: I could use specialist jargon to try to argue for the greatness of Art as a mathematician and laud his achievements. Yet, by using such a hermetic text and specialist jargon, would I sound convincing to you?

What special traits, then, distinguish Art from renowned mathematicians and what is
it that has led him to today's ceremony? If I were to answer this question in one
sentence I would say that **Professor William A. Kirk has been fortunate**. Let me try
to prove this theorem.

Firstly, he was fortunate to be able to discover in himself an outstanding talent for mathematics which led him to undertake his studies at the Indiana State University, De Pauw University and to enroll in a doctoral study program at the University of Missouri. Secondly, he was fortunate to have met his mentor and Ph. D. supervisor Leonard M. Blumenthal, a distinguished mathematician, the founder of metric geometry. It is probably under Professor Blumenthal's guidance that Art Kirk started to apply geometrical methods in mathematical analysis, to which he has been faithful ever since.

Around 1964 a very important event happened in Art's life. He discovered and proved a theorem, the references to which I found in the above-mentioned note. We mathematicians believe that half of the success in our field comes from just hitting upon the right idea. When our publications appear in print we are happy to find out that people make references to them, use them, sometimes modify them or suggest suitable generalizations. In short, we are happy to give others "a task to do".

Still, a greater satisfaction for the author is to have a fact named after him which
subsequently becomes part of the literature. The *Kirk theorem* immediately gained
such a status. But this was only a beginning. Conferences started and new contacts were
established. A huge number of publications directly came to refer to Art's ideas. All
this has led to the establishment of a new discipline in mathematics, namely the
*Metric Fixed Point Theory*.

Art was never tired of work, however: he kept on publishing, gave advice, acted as supervisor and visited those departments with which he thought he could establish cooperation and from which he could learn about new ideas.

This year we celebrate the sixtieth anniversary of the foundation of Maria Curie-Skłodowska University, but we mathematicians have our own anniversary too - the thirtieth anniversary of Art's first visit to Lublin in June 1974. To my knowledge this was his first visit to a center which had been consistently developing his theory. Well, there are many such centers in the world now. During these thirty years specialists in metric theory of fixed points visited and worked in many important places round the world: in USA, Canada, Brazil, Argentina and Chile, in Australia and South America, Israel, China, Japan, Korea. Also in Europe: in Belgium, France, Spain, Italy, the former Soviet Union, Romania and, of course, Poland. The international community of mathematicians has grown in number and strength. Mutual visits, contacts and conferences have become more frequent, attracting new adherents. Today's Honorary Doctor has been in all those places, and Lublin has seen the cream of famous professors, his followers, students and friends.

For the past fifteen years specialist conferences have been organized, devoted
exclusively to the *Metric Fixed Point Theory*, and at large conferences, special
sessions are devoted to this theory. Each year new books, handbooks and monographs are
published. Lately, under Professor Brailey Sims and our "doctoral student's" editorship,
a monumental work has been published, surveying the state of the theory thirty years
after. Five out of nineteen contributions have been written by mathematicians from Maria
Curie-Skłodowska University. New aficionados of the field keep appearing on the scene,
most recent ones coming from Mexico and Thailand. Today a great many young people write
their dissertations on themes related to the theory.

Professor Kirk can indeed be proud of the fruit his work has produced. I think the
facts confirm my thesis: **Art is a fortunate mathematician**.

But there is more to it. Art is a personality who attracts others. All his colleagues, all mathematicians are under his spell. Art is a person with whom one can spend hours, sometimes talking, arguing, sometimes without saying a word, thinking. The long list of co-authors of his publications shows that something new has been created. I myself have experienced this more than once. We had never planned joint research. Sometimes one of us said something, the other contributed and out of this a new idea was born, to be subsequently developed.

Today, Maria Curie-Skłodowska University is bestowing on Professor William Kirk the highest distinction a university can offer - a title of Honorary Doctor. We confer this title on him for his splendid academic career, for enabling us to make use of his vast knowledge and talent. For making it possible to share with him his "mathematical luck."

Dear friend Art, we hope that you will always cherish at the bottom of your heart the Lublin mathematicians who sometimes have tried - albeit to a tiny degree - to help your luck.

*Kazimierz Goebel*