(1) Introduction au calcul tens oriel et au calcul différentiel absolu (2) From Determinant to Tensor (3) Qüestions de Mecànica Clàssica i Relativista Confrències donades el Gener de 1921 (4) Les Axiomes de la mécanique (Examen critique): Note sur la propagation de la lumière

Abstract

(1) ONE of the most interesting features of Prof. Juvet's book on the calculus of tensors is the preface by Prof. Hadamard. In discussing the value of a book that deals with the pure mathematical theory of tensors, Prof. Hadamard has some hard things to say about the geometrical work of recent years. Henri Poincare once said: “The physicist expects us to solve the problems that he sets us. But in setting us these problems he pays us in advance for the service we do him in solving them. The numbers and symbols of mathematics can form an infinite number of combinations. Of all this multitude how are we to choose those that are worthy of our attention? Should we be guided solely by caprice? … The study of physics prevents us from losing ourselves, or, more important still, prevents our moving constantly in a circle.” Prof. Hadamard thinks that this danger of losing ourselves in a mist of symbolism or of moving continually in a circle of barren argument is, in fact, a characteristic of the innumerable researches of recent years, where “the classical ideas of Gauss, Ossian Bonnet, and Darboux reappear untiringly in all possible orders, somewhat like the performers in a circus, or like the pieces of red, green, and blue paper that our children are made to put together at school in accordance with the methods of Froebel.” Prof. Hadamard concludes: “Whatever view we may hold of the value of the new hypotheses of Einstein's theory, they give geometry a new role, and open out for her a new lease of life … full of infinite fertility. …”

(1) Introduction au calcul tens oriel et au calcul différentiel absolu.

Par Prof. G. Juvet. Pp. iv + 101. (Paris: Albert Blanchard, 1922.) 12 francs.

(2) From Determinant to Tensor.

By Dr. W. F. Sheppard. Pp. 127. (Oxford: Clarendon Press; London: Oxford University Press, 1923.) 8s. 6d. net.

(3) Qüestions de Mecànica Clàssica i Relativista. Confrències donades el Gener de 1921.

Per Prof. T. Levi-Civita. (Publicacions de l'Institut de Ciències. Collecció de Cursos de Física i Matematica.) Pp. viii + 151. (Barcelona: Institut d'Estudis Catalans, n.d.)

(4) Les Axiomes de la mécanique (Examen critique): Note sur la propagation de la lumière.

Par Prof. Paul Painlévé. (Les Maîtres de la Pensée scientifique.) Pp. xvii + 112. (Paris: Gauthier-Villars et Cie, 1922.) 3 francs.