To me, as undoubtedly to many who attended Yeshiva College in the early 1950s, the subject of mathematics was identified with one remarkable individual, Professor Jekuthiel Ginsburg. ... In the classroom, he communicated to his students the innate beauty of abstract mathematical ideas. ... It is hard to imagine a professional career that owes more to one individual and to one institution than my own career owes to Jekuthiel Ginsberg and Yeshiva University. Over and beyond the mathematics I learned, I experienced the love of mathematics blended with human-kindness, an experience I can only wish I could replicate for others.

... while still an undergraduate, I was exposed to a series of high-level lectures in advanced topics given by prominent professors who visited [Yeshiva College] from a number of institutions. These included Samuel Eilenberg and Ellis Kolchin from Columbia University, Jesse Douglas from City College, and Abe Gelbart who travelled from Syracuse University.

The author gives an elegant set of postulates for groups in terms of a single binary operation which occurs quite frequently in group theoretic analyses, ab-1 .
Let G be a system with an operation a*b such that
   (1) a*b in G for any a, b in G,
   (2) (a*c)*(b*c)=a*b for any a, b, c in G,
   (3) a*G = G for any a in G.
Then it follows that there is an e in G such that a*a = e for all a in G, that G is a group under the operation ab=a*(e*b), and that a*b = ab-1 . If in addition (c*b)*(c*a) = a*b for all a, b, c in G, then G is abelian. In analogy with semi-groups, a "half-group" is a system G satisfying (1) and (2). (Not every half-group is a group.) A structure theorem for half-groups is demonstrated.

In this work the limitations of the classical prediction theory of stochastic processes are first discussed. In the light of this discussion a new prediction theory for single time-sequences is formulated. The ideas uncovered in the course of this development are shown to have interesting ramifications outside prediction theory proper. ... the work stands as a first-rate and highly original dissertation on a very difficult subject.

This very readable book discusses some recent applications, due principally to the author, of dynamical systems and ergodic theory to combinatorics and number theory. It is divided into three parts. In Part I, entitled "Recurrence and uniform recurrence in compact spaces", the author gives an introduction to recurrence in topological dynamical systems, and then proves the multiple Birkhoff recurrence theorem ... From this theorem a multidimensional version of van der Waerden's theorem on arithmetic progressions is deduced, and applications to Diophantine inequalities are given. Part II carries the title "Recurrence in measure preserving systems". After a short introduction to the relevant part of measure-theoretic ergodic theory, this section is devoted to a proof of the multiple recurrence theorem ... From this result the author deduces a multidimensional version of Szemerédi's theorem on the existence of arbitrarily long arithmetic progressions in sequences of integers with positive density. Part III, called "Dynamics and large sets of integers", investigates the connections between recurrence in topological dynamics and combinatorial results concerning finite partitions of the integers (e.g., Hindman's theorem, Rado's theorem). Here the notion of proximality plays a central role. In reading this book, the reviewer found that the first part tickled his imagination and made him want to continue, the second part provided a good deal of work and tested his technical ability, while the last part led him to imagine the future possibilities for research. An excellent work!

... ground-breaking work in ergodic theory and probability, Lie groups and topological dynamics.

Professor Furstenberg's immigration to Israel had great influence on the field of mathematics in the country, and helped transformed Israel into an important international centre in ergodic theory in particular and in mathematics in general. In Jerusalem, which was the centre of his academic activities, he continued producing a long series of monumental mathematical works. In 1975 he inaugurated, along with Professor Benjamin Weiss, an ergodic theory research year in Jerusalem. That year is still remembered as the year that entirely changed the face of research in the field. Through the years, he has been a guest lecturer at many universities around the world, including Stanford, Yale, and others. Professor Furstenberg has taught and guided many students studying towards advanced degrees in his field of research and in other, wider fields - thus ushering a new generation of mathematicians who today serve as professors at institutions of higher learning in Israel and abroad.

... for his profound contributions to ergodic theory, probability, topological dynamics, analysis on symmetric spaces and homogenous flows.

Professor Harry Furstenberg is one of the great masters of probability theory, ergodic theory and topological dynamics. Among his contributions: the application of ergodic theoretic ideas to number theory and combinatorics and the application of probabilistic ideas to the theory of Lie groups and their discrete subgroups. In probability theory he was a pioneer in studying products of random matrices and showing how their limiting behaviour was intimately tied to deep structure theorems in Lie groups. This result has had a major influence on all subsequent work in this area - which has emerged as a major branch not only in probability, but also in statistical physics and other fields. In topological dynamics, Furstenberg's proof of the structure theorem for minimal distal flows, introduced radically new techniques and revolutionized the field. His theorem that the horocycle flow on surfaces of constant negative curvature is uniquely ergodic, has become a major part of the dynamical theory of Lie group actions. In his study of stochastic processes on homogenous spaces, he introduced stationary methods whose study led him to define what is now called the Furstenberg Boundary of a group. His analysis of the asymptotic behaviour of random walks on groups, has had a lasting influence on subsequent work in this area, including the study of lattices in Lie groups and co-cycles of group actions. In ergodic theory, Furstenberg developed the fundamental concept of dynamical embedding. This led him to spectacular applications in combinatorics, including a new proof of the Szemerédi Theorem on arithmetical progressions and far-reaching generalizations thereof.