Numerous scientists have taken part in the war effort during World War I, but few gave it the passionate energy of the prominent Italian mathematician Volterra. As a convinced supporter of the cause of Britain and France, he struggled vigorously to carry Italy into the war in May 1915 and then developed a frenetic activity to support the war effort, going himself to the front, even though he was 55. This activity found an adequate echo with his French colleagues Borel, Hadamard and Picard. The huge correspondence they exchanged during the war, gives an extraordinary view of these activities, and raises numerous fundamental questions about the role of a scientist, and particularly a mathematician during WW I. It also offers a vivid documentation about the intellectual life of the time; Volterra's and Borel's circles in particular were extremely wide and the range of their interests was not limited to their field of specialization. The book proposes the complete transcription of the aforementioned correspondence, annotated with numerous footnotes to give details on the contents. It also offers a general historical introduction to the context of the letters and several complements on themes related to the academic exchanges between France and Italy during the war.

Originally published in 1987, this important synthesis represented the first effort by modern scholars to convey the variety of ways in which medieval scientists and natural philosophers used mathematics and mathematical modes of thought to describe natural phenomena. Eleven distinguished historians of science contributed original essays on the application of mathematics to natural philosophy, astronomy, cosmology, optics and medicine. The book is a fitting tribute to Professor Marshall Clagett of The Institute for Advanced Study, Princeton, for his significant contributions to the history of medieval science.

In the 18th century, purely scientific interests as well as the practical necessities of navigation motivated the development of new theories and techniques to accurately describe celestial and lunar motion. "Between Theory and Observations" presents a detailed and accurate account, not to be found elsewhere in the literature, of Tobias Mayer's important contributions to the study of lunar motion-including the creation of his famous set of lunar tables, which were the most accurate of their time.

This publication was made possible through a bequest from my beloved late wife. United together in this present collection are those works by the author which have not previously appeared in book form. The following are excepted: Vorlesungen uber Differential und Integralrechnung (Lectures on Differential and Integral Calculus) Vols 1-3, Birkhauser Verlag, Basel (1965-1968); Aufgabensammlung zur Infinitesimalrechnung (Exercises in Infinitesimal Calculus) Vols I, 2a, 2b, and 3, Birkhauser Verlag, Basel (1967-1977); two issues from Memorial des Sciences on Conformal Mapping (written together with C. Gattegno), Gauthier-Villars, Paris (1949); Solution of Equations in Euclidean and Banach Spaces, Academic Press, New York (1973); and Stu- dien uber den Schottkyschen Satz (Studies on Schottky's Theorem), Wepf & Co., Basel (1931). Where corrections have had to be implemented in the text of certain papers, references to these are made at the conclusion of each paper. In the few instances where this system does not, for technical reasons, seem appropriate, an asterisk in the page margin indicates wherever a correction is necessary and this is then given at the end of the paper. (There is one exception: the correc- tions to the paper on page 561 are presented on page 722. The works are published in 6 volumes and are arranged under 16 topic headings. Within each heading, the papers are ordered chronologically according to the date of original publication.

Beginning in 1983, the Swedish Council for Planning and Coordination of Research has organized an annual workshop devoted to some aspect of the behavior and modeling of complex systems. These workshops have been held at the Abisko Research Station of the Swedish Academy of Sciences, a remote location far above the Arctic Circle in northern Sweden. During the period of the midnight sun, from May 4-8, 1987 this exotic venue served as the gathering place for a small group of scientists, scholars, and other connoisseurs of the unknown to ponder the problem of how to model "living systems," a term singling out those systems whose principal components are living agents. The 1987 Abisko Workshop focused primarily upon the general system-theoretic concepts of process, function, and form. In particular, a main theme of the Workshop was to examine how these concepts are actually realized in biological, economic, and linguistic situations. As the Workshop unfolded, it became increasingly evident that the central concern of the participants was directed to the matter of how those quintessential aspects of living systems-metabolism, self-repair, and replication-might be brought into contact with the long-established modeling paradigms employed in physics, chemistry, and engineering.

This monograph is concerned with the fitting of linear relationships in the context of the linear statistical model. As alternatives to the familiar least squared residuals procedure, it investigates the relationships between the least absolute residuals, the minimax absolute residual and the least median of squared residuals procedures. It is intended for graduate students and research workers in statistics with some command of matrix analysis and linear programming techniques.

The astonishing variety and beauty of mathematical elements in stamp design is brought to life in this collection of more than 350 stamps, illustrated with mathematical figures, people, and content, each reproduced in enlarged format, in full color. It's a perfect gift book for anyone interested in stamps, or in the surprising use of mathematics in the real world. The author is widely known in the math community for his regular column on stamps in the magazine The Mathematical Intelligencer.

This is the first full-scale biography of Leonhard Euler (1707-83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler's massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler's work in its multilayered context--personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler's fundamental contributions to almost every area of pure and applied mathematics--especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics--to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory. The narrative takes the reader from Euler's childhood and education in Basel through his first period in St. Petersburg, 1727-41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton's dynamics, and published the best-selling Letters to a German Princess--all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment.

Diese Arbeit enthiilt zwei grof3ere Fallstudien zur Beziehung zwischen theo- retischer Mathematik und Anwendungen im 19. Jahrhundert. Sie ist das Ergebnis eines mathematikhistorischen Forschungsprojekts am Mathemati- schen Fachbereich der Universitiit-Gesamthochschule Wuppertal und wurde dort als Habilitationsschrift vorgelegt. Ohne das wohlwollende Interesse von Herrn H. Scheid und den Kollegen der Abteilung fUr Didaktik der Mathema- tik ware das nicht moglich gewesen: Inhaltlich verdankt sie - direkt oder indirekt - vielen Beteiligten et- was. So wurde mein Interesse an den kristallographischen Symmetriekon- zepten, dem Thema der ersten Fallstudie, durch Anregungen und Hinweise von Herrn E. Brieskorn geweckt. Sowohl von seiner Seite als auch von Herrn J. J. Burckhardt stammen uberdies viele wert volle Hinweise zum Manuskript von Kapitel I. Herrn C. J. Scriba mochte ich fur seine die gesamte Arbeit betreffenden priizisen Anmerkungen danken und Herrn W. Borho ebenso fUr seine ubergreifenden Kommentare und Vorschlage. Beziiglich der in Kapitel II behandelten projektiven Methoden in der Baustatik des 19. Jahrhunderts gilt mein besonderer Dank den Herren K. -E. Kurrer und T. Hiinseroth fUr ihre zum Teil sehr detaillierten Anmerkungen aus dem Blickwinkel der Geschichte der Bauwissenschaften. Schliefilich geht mein Dank an alle nicht namentlich Erwiihnten, die in Gesprachen, technisch oder auch anderweitig zur Fertig- stellung dieser Arbeit beigetragen haben. Fur die vorliegende Publikation habe ich einen Anhang mit einer Skizze von in unserem Zusammenhang besonders wichtig erscheinenden Aspekten der Theorie der kristallographischen Raumgruppen hinzugefUgt. Ich hoffe, daB er zum Verstiindnis des mathematischen Hintergrunds der historischen Arbeiten des ersten Kapitels beitragt.

In recognition of professor Shiing-Shen Chern's long and distinguished service to mathematics and to the University of California, the geometers at Berkeley held an International Symposium in Global Analysis and Global Geometry in his honor in June 1979. The output of this Symposium was published in a series of three separate volumes, comprising approximately a third of Professor Chern's total publications up to 1979. Later, this fourth volume was published, focusing on papers written during the Eighties.

Astronomy Across Cultures: A History of Non-Western Astronomy consists of essays dealing with the astronomical knowledge and beliefs of cultures outside the United States and Europe. In addition to articles surveying Islamic, Chinese, Native American, Aboriginal Australian, Polynesian, Egyptian and Tibetan astronomy, among others, the book includes essays on Sky Tales and Why We Tell Them and Astronomy and Prehistory, and Astronomy and Astrology. The essays address the connections between science and culture and relate astronomical practices to the cultures which produced them. Each essay is well illustrated and contains an extensive bibliography. Because the geographic range is global, the book fills a gap in both the history of science and in cultural studies. It should find a place on the bookshelves of advanced undergraduate students, graduate students, and scholars, as well as in libraries serving those groups.

A collection of inter-connected topics in areas of mathematics which particularly interest the author, ranging over the two millennia from the work of Archimedes to the "Werke" of Gauss. The book is intended for those who love mathematics, including undergraduate students of mathematics, more experienced students and the vast unseen host of amateur mathematicians. It is equally a useful source of material for those who teach mathematics.

The general principles by which the editors and authors of the present edition have been guided were explained in the preface to the first volume of Mathemat ics of the 19th Century, which contains chapters on the history of mathematical logic, algebra, number theory, and probability theory (Nauka, Moscow 1978; En glish translation by Birkhiiuser Verlag, Basel-Boston-Berlin 1992). Circumstances beyond the control of the editors necessitated certain changes in the sequence of historical exposition of individual disciplines. The second volume contains two chapters: history of geometry and history of analytic function theory (including elliptic and Abelian functions); the size of the two chapters naturally entailed di viding them into sections. The history of differential and integral calculus, as well as computational mathematics, which we had planned to include in the second volume, will form part of the third volume. We remind our readers that the appendix of each volume contains a list of the most important literature and an index of names. The names of journals are given in abbreviated form and the volume and year of publication are indicated; if the actual year of publication differs from the nominal year, the latter is given in parentheses. The book History of Mathematics from Ancient Times to the Early Nineteenth Century in Russian], which was published in the years 1970-1972, is cited in abbreviated form as HM (with volume and page number indicated). The first volume of the present series is cited as Bk. 1 (with page numbers)."

This publication was made possible through a bequest from my beloved late wife. United together in this present collection are those works by the author which have not previously appeared in book form. The following are excepted: Vorlesungen fiber Differential und Integralrechnung (Lectures on Differential and Integral Calculus) Vols 1-3, Birkhauser Verlag, Basel (1965-1968); Aufgabensammlung zur Infinitesimalrechnung (Exercises in Infinitesimal Calculus) Vols 1, 2a, 2b, and 3, Birkhauser Verlag, Basel (1967-1977); two issues from Memorial des Sciences on Conformal Mapping (written together with C. Gattegno), Gauthier-Villars, Paris (1949); Solution of Equations in Euclidean and Banach Spaces, Academic Press, New York (1973); and Stu- dien fiber den Schottkyschen Satz (Studies on Schottky'S Theorem), Wepf & Co., Basel (1931). Where corrections have had to be implemented in the text of certain papers, references to these are made at the conclusion of each paper. In the few instances where this system does not, for technical reasons, seem appropriate, an asterisk in the page margin indicates wherever a correction is necessary and this is then given at the end of the paper. (There is one exception: the correc- tions to the paper on page 561 are presented on page 722. The works are published in 6 volumes and are arranged under 16 topic headings. Within each heading, the papers are ordered chronologically according to the date of original publication.

My attention was first drawn to Chuquet' s mathematical manuscript whilst undertaking the necessary research for the preparation of the Open University's History of Mathematics course, presented initially in 1974. It was whilst editing the English edition of Math~matiques et Math~maticiens (P. Dedron and J. Itard, trans. J. Field) that I noted that it was stated that "the whole manuscript *** comprises 324 folios, i. e. 648 pages", and that, in addition to the Triparty (by which the work is generally known) the manuscript includes sections on problems, on the application of algebraic methods to geometry, and on conunercial

I ?nd it impossible to write a preface to this work, without discovering a little of the enthusiasm which I have contracted from an attention to it. Joseph Priestley. The History and Present State of Electricity. It is generally considered bad form in writing, unless on matters autob- graphic, tomakeunbridleduseoftheperpendicularpronoun. Thereaderof the present book, however, may well wonder why one would want to study 1 the life and works of Thomas Bayes, this strangely neglected topic, and it is only by a reluctant use of the ?rst person singular on the part of the author that this legitimate question can be answered. It was in the late 1960s that my interest in various aspects of subjective probability was awakened by some of the papers of I. J. ( Jack ) Good, and this was followed by the reading of works such as Harold Je?reys s Theory of Probability. In many of these the (apparently simple) result known as Bayes s Theorem played a pivotal r ole, and it struck me that it might be interesting to ?nd out a bit more about Thomas Bayes himself. In trying to satisfy this curiosity in spasmodic periods over many years I discovered that little information seemed to be available. Writings by John D."

This book, in three parts, describes three phases in the development of the modern theory and calculation of the Moon's motion. Part I explains the crisis in lunar theory in the 1870s that led G.W. Hill to lay a new foundation for an analytic solution, a preliminary orbit he called the "variational curve." Part II is devoted to E.W. Brown's completion of the new theory as a series of successive perturbations of Hill's variational curve. Part III describes the revolutionary developments in time-measurement and the determination of Earth-Moon and Earth-planet distances that led to the replacement of the Hill-Brown theory in 1984.

A glorious period of Hungarian mathematics started in 1900 when Lipot Fejer discovered the summability of Fourier series.This was followed by the discoveries of his disciples in Fourier analysis and in the theory of analytic functions. At the same time Frederic (Frigyes) Riesz created functional analysis and Alfred Haar gave the first example of wavelets. Later the topics investigated by Hungarian mathematicians broadened considerably, and included topology, operator theory, differential equations, probability, etc. The present volume, the first of two, presents some of the most remarkable results achieved in the twentieth century by Hungarians in analysis, geometry and stochastics.

The book is accessible to anyone with a minimum knowledge of mathematics. It is supplemented with an essay on the history of Hungary in the twentieth century and biographies of those mathematicians who are no longer active. A list of all persons referred to in the chapters concludes the volume. "

Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra or not) to understand and apply the statements and numerous corollaries of the main result, provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view and notation, provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincare, Pascal, Campbell, Baker, Hausdorff and Dynkin, give an outlook on the applications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type) andquickly enable the reader, through a description of the state-of-art and open problems, to understand the modern literature concerning a theorem which, though having its roots in the beginning of the20th century, has not ceased to provide new problems and applications.

The book assumes some undergraduate-level knowledge of algebra and analysis, but apart from that is self-contained. Part II of the monograph is devoted to the proofs of the algebraic background. The monograph may therefore provide a tool for beginners in Algebra."

This volume makes an important contribution toward a nuanced appreciation of the Jesuits' interaction with "modernity," and a greater recognition of their contribution to the mathematization of natural philosophy and experimental science. The six essays provide a cross-section of the complex Jesuit encounter with the mathematical sciences during the 17th century.

The pioneering work of French mathematician Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book was written in honor of the 400th anniversary of his birth, providing readers with an overview of the many properties of Fermat numbers and demonstrating their applications in areas such as number theory, probability theory, geometry, and signal processing. This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers.

For textual studies relating to the ancient mathematical corpus the efforts by the Danish philologist, 1. L. Heiberg (1854-1928), are especially significant. Beginning with his doctoral dissertation, Quaestiones Archimedeae (Copen hagen, 1879), Heiberg produced an astonishing series of editions and critical studies that remain the foundation of scholarship on Greek mathematical 4 science. For comprehensiveness and accuracy, his editions are exemplary. In his textual studies, as also in the prolegomena to his editions, he carefully described the extant evidence, organized the manuscripts into stemmata, and drew out the implications for the state of the text. 5 With regard to his Archimedean work, Heiberg sometimes betrayed signs of the philologist's occupational disease - the tendency to rewrite a text deemed on subjective grounds to be unworthy. 6 But he did so less often than his prominent 7 contemporaries, and not as to detract appreciably from the value of his editions. In examining textual questions bearing on the Archimedean corpus, he attempted to exploit as much as possible evidence from the ancient commentators, and in some instances from the medieval translations. It is here that opportunities abound for new work, extending, and in some instances superseding, Heiberg's findings. For at his time the availability of the medieval materials was limited. In recent years Marshall Clagett has completed a mammoth critical edition of the medieval Latin tradition of Archimedes,8 while the bibliographical instruments for the Arabic tradition are in good order thanks to the work of Fuat Sezgin."

Kurt Godel, together with Bertrand Russell, is the most important name in logic, and in the foundations and philosophy of mathematics of this century. However, unlike Russel, Godel the mathematician published very little apart from his well-known writings in logic, metamathematics and set theory. Fortunately, Godel the philosopher, who devoted more years of his life to philosophy than to technical investigation, wrote hundreds of pages on the philosophy of mathematics, as well as on other fields of philosophy. It was only possible to learn more about his philosophical works after the opening of his literary estate at Princeton a decade ago. The goal of this book is to make available to the scholarly public solid reconstructions and editions of two of the most important essays which Godel wrote on the philosophy of mathematics. The book is divided into two parts. The first provides the reader with an incisive historico-philosophical introduction to Godel's technical results and philosophical ideas. Written by the Editor, this introductory apparatus is not only devoted to the manuscripts themselves but also to the philosophical context in which they were written. The second contains two of Godel's most important and fascinating unpublished essays: 1) the Gibbs Lecture ("Some basic theorems on the foundations of mathematics and their philosophical implications," 1951); and 2) two of the six versions of the essay which Godel wrote for the Carnap volume of the Schilpp series The Library of Living Philosophers ("Is mathematics syntax of language?," 1953-1959)."

A number of years ago, Harriet Sheridan, then Dean of Brown University, organized a series oflectures in which individual faculty members described how it came about that they entered their various fields. I was invited to participate in this series and found in the invitation an opportunity to recall events going back to my early teens. The lecture was well received and its reception encouraged me to work up an expanded version. My manuscript lay dormant all these years. In the meanwhile, sufficiently many other mathematical experiences and encounters accumulated to make this little book. My 1981 lecture is the basis of the first piece: "Napoleon's Theorem. " Although there is a connection between the first piece and the second, the four pieces here are essentially independent. The sec ond piece, "Carpenter and the Napoleon Ascription," has as its object a full description of a certain type of scholar-storyteller (of whom I have known and admired several). It is a pastiche, contain ing a salad bar selection blended together by my own imagination. This piece purports, as a secondary goal, to present a solution to a certain unsolved historical problem raised in the first piece. The third piece, "The Man Who Began His Lectures with 'Namely'," is a short reminiscence of Stefan Bergman, one of my teachers of graduate mathematics. Bergman, a remarkable person ality, was born in Poland and came to the United States in 1939."