Ore's work on lattices led him to the study of equivalence relations, closure relations and Galois connections, and then to the study of graph theory which occupied him to the end of his life. ... [He] had a lively interest in the history of mathematics and in biography of mathematicians. His unusual gift in writing books of wide appeal is manifest in his fine biography of Abel, written first in Norwegian then in English, and his book "Cardano. The Gambling Scholar". One may add parenthetically that he was occasionally interested himself in this aspect of applied probability.

... the results of the theory integrated more fully in the historical and cultural framework [than is usual].

In its own sphere, the book gives a very readable account of the history of (classical) number theory with much serious mathematical thought. In this respect, it is far superior to the usual histories of mathematics.

The present book has grown out of courses on graph theory given from time to time at Yale University. The present century has witnessed a steady development of graph theory which in the last ten to twenty years has blossomed out into a new period of intense activity. Clearly discernible in this process are the effects of the demands from new fields of application: game theory and programming, communications theory, electrical networks and switching circuits as well as problems from biology and psychology. As a consequence of these recent developments the subject of graphs is already so extended that it did not seem feasible to cover all its main ramifications within the framework of a single volume. In the present first volume of an intended two-volume work the emphasis has been placed upon basic concepts and the results of particular systematic interest. An effort has been made to present the subject matter in the book in as simple a form as possible. Almost all proofs have been revised; a considerable number of new results are also included. A systematic terminology is introduced which it is hoped may prove acceptable. For the benefit of the reader a considerable number of problems have been included. Many of these are quite simple; others are more in the nature of proposed research problems; these have been marked with an asterisk. The second volume will be devoted to more special topics: planar graphs, the four-color conjecture, the theory of flow, games, electrical networks, as well as applications to a number of other fields in which graph theory is a principal tool.

... an interesting experiment - a book on graph theory for high school students. It includes introductory accounts of Euler graphs, trees, matchings, directed graphs, planar graphs and the four-colour problem.

It would not be hard to present the history of graph theory as an account of the struggle to prove the four colour conjecture, or at least to find out why the problem is difficult. Such a presentation is almost unavoidable in the special case of planar graphs. [Ore] has included most of the important results connected with the four colour problem in a single text-book. The reviewer recommends this work to all mathematicians interested in the problem. It is also to be recommended as a text book on planar graphs.

The first pair of amicable numbers beyond the classical (220, 284) was obtained by Fermat in 1636. Since that time a considerable number of amicable pairs $(M, N), M < N$, have been discovered. The present calculations have been performed systematically, testing each number up to $M < 10^{6}$. The computations also produce the perfect numbers $< 10^{6}$. Altogether there are 42 pairs of amicable numbers below $10^{6}$. Among these there are nine new ones, not previously listed.

Throughout his life he maintained a deep and knowledgeable interest in the world of art, particularly painting and sculpture. He was an ardent collector of ancient maps, concerning which he was somewhat of an expert. Like many other cultured Scandinavians, he was fluent in several foreign languages.