Les Cahiers du Fini et de l'Infini abordent ici, sous forme de discussion entre Daniel Ziv et Gerard Fleury, Agrege de mathematiques. Docteur en informatique. Maitre de conferences a l'universite Blaise Pascal deClermont-Fd), la theorie des probabilites. l'etude mathematique des phenomenes caracterises par le hasard et l'incertitude. Cette theorie forme avec la statistique les deux sciences du hasard qui sont partie integrante des mathematiques. Les debuts de l'etude des probabilites correspondent aux premieres observations du hasard dans les jeux ou dans les phenomenes climatiques par exemple.

Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and the Wolfskehl Prize.- Lecture II Recent Results.- 1 Stating the Results.- 2 Explanations.- Lecture III B.K. = Before Kummer.- 1 The Pythagorean Equation.- 2 The Biquadratic Equation.- 3 The Cubic Equation.- 4 The Quintic Equation.- 5 Fermat's Equation of Degree Seven.- Lecture IV The Naïve Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Co.

In 1997, M. Kontsevich proved that every Poisson manifold admits a formal quantization, canonical up to equivalence. In doing so he solved a longstanding problem in mathematical physics. Through his proof and his interpretation of a later proof given by Tamarkin, he also opened up new research avenues in Lie theory, quantum group theory, deformation theory and the study of operads ... and uncovered fascinating links of these topics with number theory, knot theory and the theory of motives. Without doubt, his work on deformation quantization will continue to influence these fields for many years to come. In the three parts of this volume, we will 1) present the main results of Kontsevich's 1997 preprint and sketch his interpretation of Tamarkin's approach, 2) show the relevance of Kontsevich's theorem for Lie theory and 3) explain the idea from topological string theory which inspired Kontsevich's proof. An appendix is devoted to the geometry of configuration spaces.

The philosophy of Gilles Deleuze is increasingly gaining the prestige that its astonishing inventiveness calls for in the Anglo-American theoretical context. His wide-ranging works on the history of philosophy, cinema, painting, literature and politics are being taken up and put to work across disciplinary divides and in interesting and surprising ways. However, the backbone of Deleuze's philosophy - the many and varied sources from which he draws the material for his conceptual innovation - has until now remained relatively obscure and unexplored. This book takes as its goal the examination of this rich theoretical background. Presenting essays by a range of the world's foremost Deleuze scholars, and a number of up and coming theorists of his work, the book is composed of in-depth analyses of the key figures in Deleuze's lineage whose significance - as a result of either their obscurity or the complexity of their place in the Deleuzean text - has not previously been well understood. This work will prove indispensable to students and scholars seeking to understand the context from which Deleuze's ideas emerge.Included are essays on Deleuze's relationship to figures as varied as Marx, Simondon, Wronski, Hegel, Hume, Maimon, Ruyer, Kant, Heidegger, Husserl, Reimann, Leibniz, Bergson and Freud.

The NATO Advanced Study Institute on Numerical Taxonomy took place on the 4th - 16th of July, 1982, at the Kur- und Kongresshotel Residenz in Bad Windsheim, Federal Republic of Germany. This volume is the proceedings of that meeting, and contains papers by over two-thirds of the participants in the Institute. Numerical taxonomy has been attracting increased attention from systematists and evolutionary biologists. It is an area which has been marked by debate and conflict, sometimes bitter. Happily, this meeting took place in an atmosphere of "GemUtlichkeit", though scarcely of unanimity. I believe that these papers will show that there is an increased understanding by each taxonomic school of each others' positions. This augurs a period in which the debates become more concrete and specific. Let us hope that they take place in a scientific atmosphere which has occasionally been lacking in the past. Since the order of presentation of papers in the meeting was affected by time constraints, I have taken the liberty of rearranging them into a more coherent subject ordering. The first group of papers, taken from the opening and closing days of the meeting, debate philosophies of classification. The next two sections have papers on congruence, clustering and ordination. A notable concern of these participants is the comparison and testing of classifications. This has been missing from many previous discussions of numerical classification.