**Uriel Rothblum**was known to his friends and colleagues as Uri. His parents were Austrian Jews who were living in Vienna in the 1930s. The Nazi party had come to power in Germany in 1933 and their anti-Semitic policies together with a clear desire to take control of Austria made Rothblum's parents realise that they were not safe in Vienna. They escaped to Israel before the German invasion of Austria in 1938 and set up home in Tel Aviv. It was in that city that Uri was born, a couple of years after World War II ended. He was brought up in Tel Aviv and in Ramat Gan in Israel in the [1]:-

He was also brought up in the Zionist tradition. Rothblum's family had been Zionists before moving to Palestine. The main aim of the Zionist movement at this time was the creation of the state of Israel. This took place in 1948, when Rothblum was only one year old, and at that time many Zionist institutions became Israeli government institutions. In particular three Zionist militias combined to become the Israel Defence Forces. The Zionists continued to exist after the creation of the state of Israel, however, and the Rothblum family were involved with them, by that time working to assist Jews who were persecuted in their own countries to emigrate to Israel.European tradition that emphasizes education, music, performing arts, poetry, good manners.

At school, Rothblum showed great abilities and he was particularly passionate about chemistry. After graduating from high school, he did his compulsory military service in the Israel Defence Forces. He began his undergraduate studies at Tel Aviv University where he studied science and applied mathematics. He graduated with a B.Sc. in Applied Mathematics "Magna Cum Laude" in 1969 and remained at Tel Aviv University to study for an M.Sc. degree. He was advised by Robert John Aumann who was born into a Jewish family in Germany that had fled to the United States after the Nazis came to power. Aumann had been awarded a doctorate by the Massachusetts Institute of Technology in 1955 for a thesis on knot theory but had become interested in game theory after meeting with John Nash. He worked in Israel from 1956 onwards and was awarded the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel in 2005:-

Aumann, not surprisingly, gave Rothblum a Master's thesis topic from game theory and he wrote the thesis... for having enhanced our understanding of conflict and cooperation through game-theory analysis.

*Values of Games with a Continuum of Players*. He was awarded an M.Sc. in Mathematics "Summa Cum Laude" in 1971 by Tel Aviv University. It was working with Aumann that led to Rothblum's first mathematical paper, namely

*On orderable set functions and continuity*published in the

*Israel Journal of Mathematics*in 1973. Konrad Jacobs, reviewing the paper, writes:-

After the award of his Master's degree, Rothblum moved to the United States to undertake research for his doctorate funded by a Fulbright Fellowship. He was advised by Arthur F "Pete" Veinott Jr who was an expert in operations research. Rothblum was awarded a Ph.D. for his thesisThe theory of coalition games with a continuum of players has made new demands on the theory of set functions throughout the last decade. The present paper is motivated by the demands of the theory of the Shapley value and follows a pattern set by R J Aumann and L S Shapley[Values of non-atomic games, Princeton Univ. Press, Princeton, N.J.,1973].

*Multiplicative Markov Decision Chains*in 1974. In a paper based on his thesis, Rothblum acknowledges his debt to his thesis advisor:-

Veinott wrote in [4] about supervising Rothblum when he was a postgraduate student:-My deepest thanks are given to my teacher and advisor, Professor Arthur F Veinott Jr, for his guidance and advice, for his insight and perspective during the preparation of this work. Starting with the suggestion of the research topic through the careful reading of the final version, his contributions, improvements and suggestions to this work are too numerous to be listed.

Three papers by Rothblum appeared in 1975, namely:I met Uri in the autumn of1971. He took a Ph.D. course in dynamic programming from me in the spring of1972. ... I served as the advisor of his1974dissertation ... He was a good friend, and a brilliant prolific scholar. He had a quick and creative mind with the ingenuity, energy and background to make beautiful fundamental contributions to many fields.

*Multivariate constant risk posture*;

*Normalized Markov decision chains. I. Sensitive discount optimality*; and

*Algebraic eigenspaces of nonnegative matrices*. Rothblum's own summary of the third of these papers, which formed a part of his thesis, is as follows:-

The terms 'Rothblum bases' and the 'Rothblum index theorem' which are used today refer to results from this paper (and also, of course, from his thesis). Hans Schneider writes in [4] that this paper:-The Perron-Frobenius theory for square, irreducible, nonnegative matrices is generalized by studying the structure of the algebraic eigenspace of an arbitrary square nonnegative matrix corresponding to its spectral radius. We give a constructive proof that this subspace is spanned by a set of semipositive vectors and give a combinatorial characterization of both the index of the spectral radius and dimension of the algebraic eigenspace corresponding to the spectral radius. This involves a detailed study of the standard block triangular representation of nonnegative matrices by giving special attention to those blocks on the diagonal having the same spectral radius as the original matrix. We also show that the algebraic eigenspace corresponding to the spectral radius contains a semipositive vector having the largest set of positive coordinates among all vectors in this subspace.

In the summer of 1974, Rothblum worked as a consultant at the Rand Corporation in Santa Monica, California, before taking up the position of Postdoctoral Fellow and Adjunct Assistant Professor of Computer Sciences at the Courant Institute of Mathematical Sciences in New York. After this one-year post, he was appointed as an Assistant Professor in the School of Organization and Management of Yale University in 1975. He was promoted to Associate Professor in 1978, continuing to work at Yale University until 1984. During much of this time he spent the summers at the Department of Operations Research, Stanford University, where he held various roles such as Research Associate or Visiting Associate Professor. Moshe Haviv did a Ph.D. at Yale supervised by Rothblum. Haviv, who was awarded his Ph.D. for his thesis... had an immediate and a long term major impact on me. It led to12joint papers[with Rothblum]and a friendship that lasted until his untimely death.

*Approximation of Markov Chains and Markov Decision Models*in 1983, writes in [4]:-

In 1984 Rothblum returned to Israel to take up the position of Professor in the Faculty of Industrial Engineering and Management at Technion, the Israel Institute of Technology in Haifa. He was named Alexander Goldberg Professor of Management Science in 1992, a position he retained until his death. Boaz Golany writes [1]:-Uri was not only a great scholar from whom I learned much. He was also a person who cared. He took me under his umbrella and taught me much of what I know today on academic research and education, how to write a paper, and much on academic life in general. He taught me what hard work and dedication entail. When he gave me a paper to read one afternoon, he commenced the discussion next morning from this paper. The idea that I might have done something else in the evening but read the paper, did not cross his mind. It was a pleasure to play tennis with him(he was slightly better)but again no relief: In break times he was worried if the results we derived for real matrices can be generalized to complex matrices.

For example, he held roles at Technion such as: Associate Dean of the Faculty of Industrial Engineering and Management (1986-1989); Dean of the Faculty of Industrial Engineering and Management (1992-1995); Deputy Provost (1998-2000); and Executive Vice President for Academic Affairs (2000-2002).During his28years of service at the Technion, Uri was a member of numerous academic committees, and he was regarded as a leading authority on all the academic issues faced by the university.

In addition to these positions at Technion, Rothblum was pleased to be able to make frequent visits to the United States. He was a Visiting Professor at the State University of New York at Stony Brook during the summers of 1987 and 1988. He was also a Visiting Professor at Rutgers Center for Operations Research, Rutgers University, New Brunswick during visits between 1988 and 1999, and was a Visiting Professor in the Department of Industrial Engineering and Operations Research, Columbia University, New York in 2005 and 2009.

Shmuel Onn explained in [4] some of Rothblum's mathematical contributions while at Technion as well as his support for others:-

Rothblum served on the editorial board of several journals:To many members of the Technion Operations Research group, Uri was the mentor and supporter of entering faculty life. Collaborating with Uri on research was a very enjoyable and fruitful experience. He was always very enthusiastic and the driving force behind whatever topic we were working on, and always brought in his insight and broad perspective of Operations Research on all its subareas.

*Letters in Linear Algebra and Its Application*(1980-81);

*SIAM Journal on Algebraic and Discrete Methods*(1983-87);

*SIAM Journal on Matrix Analysis and Applications*(1988-93);

*Operations Research*(1996-99);

*Journal on Combinatorial Optimization*(2005-2012);

*World Scientific Series on applied mathematics*(2006-2012);

*Linear Algebra and Its Applications*(1982-2012); and

*Mathematics of Operations Research*(1979-2012).

For his outstanding contributions to operations research, Rothblum received awards such as: the New England Academic Excellence Award, 1989; the Operations Research Meritorious Service Award, 1997; the Operations Research Meritorious Service Award, 1999; the Institute for Operations Research and the Management Sciences Fellow Award, 2003; and the Israeli Operational Research Society Prize for Excellence in Research in Operations Research, 2005. This last award was made for his paper *Convex Combinatorial Optimization *(2004) which he published jointly with Shmuel Onn. The authors give this description of their paper:-

The applications they discuss include the bounded rank positive semi-definite quadratic assignment problem and the convex matroid optimisation problem.We introduce the convex combinatorial optimization problem, a far-reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications.

In collaboration with Frank K Hwang, Rothblum published the 2-volume text *Partitions: Optimality and Clustering* (2012). The first volume dealt with the single-parameter case while the second volume dealt with the multi-parameter case. The following is from the publishers information about the book:-

Jean Mailfert writes in a review:-The need for optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The "clustering" problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion. Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory - or why they cannot be.

Uri Rothblum was married to Naomi; they had three children, Maydan, Guy and Ron. Raphael Loewy writes [4]:-This book deals with optimal partition problems. ...[It]contains a lot of theoretical developments and new statements on the topic of optimal clustering. Reading it is, however, difficult and it may best serve upper-level graduate students or engineers.

The webpage [3] contains many tributes to Rothblum from his friends, colleagues and former students. We end this biography by quoting from some of the contributors. Ariela Sofer, George Mason University, writes:-First and foremost Uri was a family man. He was devoted to his wife and their children. He was a kind, generous and unique man. His interests included travelling, which he did extensively and enthusiastically, and the arts - especially the theatre and ballet. Those who knew him remember his grace, his nobility of spirit, his boundless energy, and his capacity for living every moment to its fullest.

Amitabh Trehan, Technion, writes [3]:-Uri was not only an exceptional researcher but also an exceptional teacher. I had the privilege of take a course on recent advances in optimization from Uri while I was a Masters' student at the Technion - some time in the late70's. Uri was absolutely masterful in his exposition, presenting each topic as a riveting mystery, that we(the students)were unravelling, step by logical step. The students were in awe and wonder. Math had rarely been so exciting! Later when I read the papers that Uri described I sometimes wondered whether he had more insight into the topic than the authors of the ideas. He was a brilliant scientist and a brilliant teacher!

Dimitris Bertsimas, Massachusetts Institute of Technology, writes [3]:-I will always remember his singing and whistling in the corridor and the jovial and kind energy he used to bring.

Alan Hoffman, IBM Research, writes [3]:-Uri was a remarkable person: generous, considerate, brilliant, full of life and ideas.

Curtis Eaves, Stanford University, writes [3]:-Uri was one of the nicest people I knew: warm, witty, generous, forgiving, enthusiastic. Collaborating with Uri was like going to a party. And he was interested in Everything: perhaps the most versatile scholar in the mathematics of operations research.

We had such fun writing papers together. ... I was always amused by your definition of a vacation, namely, "the freedom to work unobstructed"; indeed, this is the way you lived. You could do and did many things very well, but nobody, like nobody, could push nasty equations around like you could ...

**Article by:** *J J O'Connor* and *E F Robertson*