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In this book, the author pays tribute to Bernhard Riemann (1826-1866), a mathematician with revolutionary ideas, whose work on the theory of integration, the Fourier transform, the hypergeometric differential equation, etc. contributed immensely to mathematical physics. The text concentrates in particular on Riemann's only work on prime numbers, including ideas – new at the time – such as analytical continuation into the complex plane and the product formula for entire functions. A detailed analysis of the zeros of the Riemann zeta-function is presented. The impact of Riemann's ideas on regularizing infinite values in field theory is also emphasized. This revised and enhanced new edition contains three new chapters, two on the application of Riemann's zeta-function regularization to obtain the partition function of a Bose (Fermi) oscillator and one on the zeta-function regularization in quantum electrodynamics. Appendix A2 has been re-written to make the calculations more transparent. A summary of Euler-Riemann formulae completes the book.

'The influence of Ramanujan on number theory is without parallel in mathematics. His papers, problems, and letters have spawned a remarkable number of later results by many different mathematicians. Here, his 37 published papers, most of his first two and last letters to Hardy, the famous 58 problems submitted to the Journal of the Indian Mathematical Society, and the commentary of the original editors (Hardy, Seshu Aiyar and Wilson) are reprinted again, after having been unavailable for some time. In this printing of Ramanujan's collected papers, Bruce Berndt provides an annotated guide to Ramanujan's work and to the mathematics it inspired over the last three-quarters of a century. The historical development of ideas is traced in the commentary and by citations to the copious references. The editor has done the mathematical world a tremendous service that few others would be qualified to do'--Provided by publisher.

This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the main focus of this selection, though it also contains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner onthe convexity of hypersurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collection pays tribute to one of the most distinguished mathematicians.

'Published with the support of Unione Matematica Italiana and Scuola Normale Superiore.'

This volume contains eighteen papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics. Some of the topics explored includeArabic editions of Euclid's Elements from the thirteenth century and their role in the assimilation of Euclidean geometry into the Islamic intellectual traditionPortuguese sixteenth century recreational mathematics as found in the Tratado de Prática Darysmetica A Cambridge correspondence course in arithmetic for women in England in the late nineteenth centuryThe mathematical interests of the famous Egyptologist Thomas Eric (T. E.) Peet The history of Zentralblatt für Mathematik and Mathematical Reviews and their role in creating a publishing infrastructure for a global mathematical literatureThe use of Latin squares for agricultural crop experiments at the Rothamsted Experimental StationThe many contributions of women to the advancement of computing techniques at the Cavendish Laboratory at the University of Cambridge in the 1960sThe volume concludes with two short plays, one set in Ancient Mesopotamia and the other in Ancient Egypt, that are well suited for use in the mathematics classroom.Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.

This book is dedicated to V.A. Yankov's seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic.The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov's results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics.The book also contains an exposition of Yankov's revolutionary approach to constructive proof theory. The editors also include Yankov's contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.

This volume contains eleven papers that have been collected by the Canadian Society for History and Philosophy of Mathematics/Société canadienne d'histoire et de philosophie des mathématiques. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics. Topics considered includeThe mathematics and astronomy in Nathaniel Torperly's only published work, Diclides Coelometricae, seu valvae astronomicae universalConnections between the work of Urbain Le Verrier, Carl Gustav Jacob Jacobi, and Augustin-Louis Cauchy on the algebraic eigenvalue problemAn evaluation of Ken Manders'argument against conceiving of the diagrams in Euclid's Elements in semantic termsThe development of undergraduate modern algebra courses in the United StatesWays of using the history of mathematics to teachthe foundations of mathematical analysisWritten by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.

This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert).The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade.These essays will be of interest to all students and researchers interested in the nature and future of logic.

Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and is best-known for the first formulation of the axiom of choice. However, his papers also include pioneering work in applied mathematics and mathematical physics.This edition of his collected papers consists of two volumes. The present Volume II covers Ernst Zermelo's work on the calculus of variations, applied mathematics, and physics.The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field who comments on the historical background, motivation, accomplishments, and influence.

The twentieth century is the period during which the history of Greek mathematics reached its greatest acme. Indeed, it is by no means exaggerated to say that Greek mathematics represents the unique field from the wider domain of the general history of science which was included in the research agenda of so many and so distinguished scholars, from so varied scientific communities (historians of science, historians of philosophy, mathematicians, philologists, philosophers of science, archeologists etc.), while new scholarship of the highest quality continues to be produced. This volume includes 19 classic papers on the history of Greek mathematics that were published during the entire 20th century and affected significantly the state of the art of this field. It is divided into six self-contained sections, each one with its own editor, who had the responsibility for the selection of the papers that are republished in the section, and who wrote the introduction of the section. It constitutes a kind of a Reader book which is today, one century after the first publications of Tannery, Zeuthen, Heath and the other outstanding figures of the end of the 19th and the beg- ning of 20th century, rather timely in many respects.

Jacques Tits was awarded the Wolf Prize in 1993 and the Abel Prize (jointly with John Thompson) in 2008. The impact of his contributions in algebra, group theory and geometry made over a span of more than five decades is incalculable. Many fundamental developments in several fields of mathematics have their origin in ideas of Tits. A number of Tits'papers mark the starting point of completely new directions of research. Outstanding examples are papers on quadratic forms, on Kac–Moody groups and on what subsequently became known as the Tits-alternative. These volumes contain an almost complete collection of Tits'mathematical writings. They include, in particular, a number of published and unpublished manuscripts which have not been easily accessible until now. This collection of Tits'contributions in one place makes the evolution of his mathematical thinking visible. The development of his theory of buildings and BN-pairs and its bearing on the theory of algebraic groups, for example, reveal a fascinating story. Along with Tits'mathematical writings, these volumes contain biographical data, survey articles on aspects of Tits'work and comments by the editors on the content of some of his papers. With the publication of these volumes, a major piece of 20th century mathematics is being made available to a wider audience.

One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians'activities as given, and go on to ask what philosophical morals one might perhaps find in their story. On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield. Such scrutiny can scarcely help relying on philosophical ideas and principles. In other words it can scarcely help being literally a study of language, truth and logic in mathematics, albeit not necessarily in the spirit of AJ. Ayer. As its title indicates, the essays included in the present volume represent the latter approach. In most of them one of the fundamental concepts in the foundations of mathematics and logic is subjected to a scrutiny from a largely novel point of view. Typically, it turns out that the concept in question is in need of a revision or reconsideration or at least can be given a new twist. The results of such a re-examination are not primarily critical, however, but typically open up new constructive possibilities. The consequences of such deconstructions and reconstructions are often quite sweeping, and are explored in the same paper or in others.

This book contains a series of research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields. Some of the authors have been specifically invited to present papers, discussing the influence of Abel in a mathematical-historical context. Others have submitted papers presented at the Abel Bicentennial Conference, Oslo June 3-8, 2002. The idea behind the book has been to produce a text covering a substantial part of the legacy of Abel, as perceived at the beginning of the 21st century. It is accompanied by a CD-ROM with a large amount of information related to Niels Henrik Abel, such as on the Abel Centennial in 1902 and the Abel Bicentennial Conference in 2002, the launching of the Abel Prize, Abel monuments, and stamps, banknotes, coins etc. issued in honour of Niels Henrik Abel.

Ernst Zermelo (1871-1953) is regarded as the founder of axiomatic set theory and best-known for the first formulation of the axiom of choice. However, his papers include also pioneering work in applied mathematics and mathematical physics. This edition of his collected papers will consist of two volumes. Besides providing a biography, the present Volume I covers set theory, the foundations of mathematics, and pure mathematics and is supplemented by selected items from his Nachlass and part of his translations of Homer's Odyssey. Volume II will contain his work in the calculus of variations, applied mathematics, and physics. The papers are each presented in their original language together with an English translation, the versions facing each other on opposite pages. Each paper or coherent group of papers is preceded by an introductory note provided by an acknowledged expert in the field which comments on the historical background, motivations, accomplishments, and influence.

Matroid theory was invented in the middle of the 1930s by two mathematicians independently, namely, Hassler Whitney in the USA and Takeo Nakasawa in Japan. Whitney became famous, but Nakasawa remained anonymous until two decades ago. He left only four papers to the mathematical community, all of them written in the middle of the 1930s. It was a bad time to have lived in a country that had become as eccentric as possible. Just as Nazism became more and more flamboyant in Europe in the 1930s, Japan became more and more esoteric and fanatical in the same time period. This book explains the little that is known about Nakasawa's personal life in a Japan that had, among other failures, lost control over its military. This book contains his four papers in German and their English translations as well as some extended commentary on the history of Japan during those years. The book also contains 14 photos of him or his family. Although the veil of mystery surrounding Nakasawa's life hasonly been partially lifted, the work presented in this book speaks eloquently of a tragic loss to the mathematical community.

A flexagon is a motion structure that has the appearance of a ring of hinged polygons. It can be flexed to display different pairs of faces, usually in cyclic order. Flexagons can be appreciated as toys or puzzles, as a recreational mathematics topic, and as the subject of serious mathematical study. Workable paper models of flexagons are easy to make and entertaining to manipulate. The mathematics of flexagons is complex, and how a flexagon works is not immediately obvious on examination of a paper model. Recent geometric analysis, included in the book, has improved theoretical understanding of flexagons, especially relationships between different types. This profusely illustrated book is arranged in a logical order appropriate for a textbook on the geometry of flexagons. It is written so that it can be enjoyed at both the recreational mathematics level, and at the serious mathematics level. The only prerequisite is some knowledge of elementary geometry, including properties of polygons. A feature of the book is a compendium of over 100 nets for making paper models of some of the more interesting flexagons, chosen to complement the text. These are accurately drawn and reproduced at half full size. Many of the nets have not previously been published. Instructions for assembling and manipulating the flexagons are included.

John Corcoran was a very well-known logician who worked on several areas of logic. He produced decisive works giving a better understanding of two major figures in the history of logic, Aristotle and Boole. Corcoran had a close association with Alfred Tarski, a prominent 20th-century logician. This collaboration manifested in Corcoran's substantial introduction to Tarski's seminal book, Logic, Semantics, Metamathematics (1956). Additionally, Corcoran's posthumous editorial involvement in'What are logical notions?'(1986) breathed new life into this seminal paper authored by Tarski. His scholarly pursuits extended to the intricate explication of fundamental concepts in modern logic, including variables, propositions, truth, consequences, and categoricity. Corcoran's academic curiosity extended further to the intersection of ethics and logic, reflecting his contemplation of their interrelation. Beyond these theoretical contributions, Corcoran was deeply engaged in the pedagogical dimensions of logic instruction. This volume serves as a compilation of articles contributed by Corcoran's students, colleagues, and international peers. By encompassing a diverse range of subjects, this collection aptly mirrors Corcoran's wide-ranging interests, offering insights that not only deepen our understanding of his work but also advance the theoretical frameworks he explored.

Although she was famous as the'mother of modern algebra,'Emmy Noether's life and work have never been the subject of an authoritative scientific biography. Emmy Noether – Mathematician Extraordinaire represents the most comprehensive study of this singularly important mathematician to date. Focusing on key turning points, it aims to provide an overall interpretation of Noether's intellectual development while offering a new assessment of her role in transforming the mathematics of the twentieth century.Hermann Weyl, her colleague before both fled to the United States in 1933, fully recognized that Noether's dynamic school was the very heart and soul of the famous Göttingen community. Beyond her immediate circle of students, Emmy Noether's lectures and seminars drew talented mathematicians from all over the world. Four of the most important were B.L. van der Waerden, Pavel Alexandrov, Helmut Hasse, and Olga Taussky. Noether's classic papers on ideal theory inspiredvan der Waerden to recast his research in algebraic geometry. Her lectures on group theory motivated Alexandrov to develop links between point set topology and combinatorial methods. Noether's vision for a new approach to algebraic number theory gave Hasse the impetus to pursue a line of research that led to the Brauer–Hasse–Noether Theorem, whereas her abstract style clashed with Taussky's approach to classical class field theory during a difficult time when both were trying to find their footing in a foreign country.Although similar to Proving It Her Way: Emmy Noether, a Life in Mathematics, this lengthier study addresses mathematically minded readers. Thus, it presents a detailed analysis of Emmy Noether's work with Hilbert and Klein on mathematical problems connected with Einstein's theory of relativity. These efforts culminated with her famous paper'Invariant Variational Problems,'published one year before she joined the Göttingen faculty in 1919.

Marking 94 years since its first appearance, this book provides an annotated translation of Sainte-Laguë's seminal monograph Les réseaux (ou graphes), drawing attention to its fundamental principles and ideas. Sainte-Laguë's 1926 monograph appeared only in French, but in the 1990s H. Gropp published a number of English papers describing several aspects of the book. He expressed his hope that an English translation might sometime be available to the mathematics community. In the 10 years following the appearance of Les réseaux (ou graphes), the development of graph theory continued, culminating in the publication of the first full book on the theory of finite and infinite graphs in 1936 by Dénes König. This remained the only well-known text until Claude Berge's 1958 book on the theory and applications of graphs. By 1960, graph theory had emerged as a significant mathematical discipline of its own. This book will be of interest to graph theoristsand mathematical historians.

This book covers the works of Bhāskara, in particular, his monumental treatise on astronomy, the Siddhāntaśiromaṇi, his astronomical handbook, the Karaṇakutūhala, and his two mathematical treatises, the Līlavatī and the Bījagaṇita, on arithmetic and algebra, respectively. It is a collection of selected papers presented at Bhāskara 900, an international conference commemorate the 900th birth anniversary of the great Indian mathematician Bhāskarācārya. Bhāskara-prabhā, the radiance of Bhāskara, presents the Indian mathematical tradition and the place of Bhāskara in it. The aim of this book is to instill a sense of pride in younger generations of one of their most celebrated thinkers, by sketching some details of his mathematical achievements and capturing their imagination through his poetic flair. It is intended to raise a greater awareness among studentsand teachers of India's rich mathematical heritage.

This is the first extensive biography of the influential German mathematician, Peter Gustav Lejeune Dirichlet (1805 – 1859). Dirichlet made major contributions to number theory in addition to clarifying concepts such as the representation of functions as series, the theory of convergence, and potential theory. His mathematical methodology was explicitly based on a thorough knowledge of the work of his predecessors and his belief in the underlying unity of the branches of mathematics. This unified approach is exemplified in a paper that effectively launched the field of analytic number theory. The same orientation pervaded his teaching, which had a profound influence on the work of many mathematicians of subsequent generations. Chapters dealing with his mathematical work alternate with biographical chapters that place Dirichlet's life and those of some of his notable associates in the context of the political, social, and artistic culture of the period. This book will appeal notonly to mathematicians but also to historians of mathematics and sciences, and readers interested in the cultural and intellectual history of the nineteenth century.

Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Almost every chapter is organized around excerpts from a research paper in which a new perspective was brought on the genus or on one of the objects to which this notion applies. The author was motivated by the belief that a subject may best be understood and communicated by studying its broad lines of development, feeling the way one arrives at the definitions of its fundamental notions, and appreciating the amount of effort spent in order to explore its phenomena.

This monograph is devoted to two distinguished mathematicians, Karel Löwner (1893–1968) and Lipman Bers (1914–1993), whose lives are dramatically interlinked with key historical events of the 20th century. K. Löwner, Professor of Mathematics at the German University in Prague (Czechoslovakia), was dismissed from his position because he was a Jew, and emigrated to the USA in 1939 (where he changed his name to Charles Loewner). Earlier, he had published several outstanding papers in complex analysis and a masterpiece on matrix functions. In particular, his ground-breaking parametric method in geometric function theory from 1923, which led to Löwner's celebrated differential equation, brought him world-wide fame and turned out to be a cornerstone in de Branges'proof of the Bieberbach conjecture. Unexpectedly, Löwner's differential equation has gained recent prominence with the introduction of a conformally invariant stochastic process called stochastic Loewner evolution (SLE) by O. Schramm in 2000. SLE features in two Fields Medal citations from 2006 and 2010. L. Bers was the final Prague Ph.D. student of K. Löwner. His dissertation on potential theory (1938), completed shortly before his emigration and long thought to be irretrievably lost, was found in 2006. It is here made accessible for the first time, with an extensive commentary, to the mathematical community. This monograph presents an in-depth account of the lives of both mathematicians, with special emphasis on the pre-war period. Löwner's teaching activities and professional achievements are presented in the context of the prevailing complex political situation and against the background of the wider development of mathematics in Europe. Each of his publications is accompanied by an extensive commentary, tracing the origin and motivation of the problem studied, and describing the state-of-art at the time of the corresponding mathematical field. Special attention is paid to the impact of the results obtained and to the later development of the underlying ideas, thus connecting Löwner's achievements to current research activity. The text is based on an extensive archival search, and most of the archival findings appear here for the first time. Anyone with an interest in mathematics and the history of mathematics will enjoy reading this book about two famous mathematicians of the 20th century.

Karl Menger, one of the founders of dimension theory, is among the most original mathematicians and thinkers of the twentieth century. He was a member of the Vienna Circle and the founder of its mathematical equivalent, the Viennese Mathematical Colloquium. Both during his early years in Vienna and, after his emigration, in the United States, Karl Menger made significant contributions to a wide variety of mathematical fields, and greatly influenced many of his colleagues. These two volumes contain Menger's major mathematical papers, based on his own selection from his extensive writings. They deal with topics as diverse as topology, geometry, analysis and algebra, and also include material on economics, sociology, logic and philosophy. The Selecta Mathematica is a monument to the diversity and originality of Menger's ideas.

'One cannot talk about mathematics in the 16th and 17th centuries without seeing a Jesuit at every corner,'George Sarton observed in 1940. • Sarton, of course, was not the first to recognize the disproportionate representation of members of the Society of Jesus in the scientific enterprise of the early modern period. However, unlike many historians who belittled the discernible numerical strength of the Jesuits on the grounds that they lacked originality and were generally hostile to new ideas, Sarton correlated numerical strength with significance. Hence his plea for collecting the papers of that industrious historian of Jesuit science, Henri Bosmans, was quite refreshing. Yet Sarton's appeal went unheeded, and not only with respect to Bosmans'papers. The perception of the Jesuits as plodding pedagogues and obscurantists remained as ingrained as ever, virtually sanctioning the disregard of their activities. Such neglect meant that the exact nature of the Jesuit contribution to the Scientific Revolution remained sketchy at best; only recently - owing to a long-overdue examination of the Order's archives and of published texts - have new contours begun to emerge. Striking in this reassessment is a more nuanced appreciation of the Jesuits'interaction with'modernity'and a far greater recognition of the Jesuit contribution to the two poles of modern science: the mathematization of natural philosophy and experimental science.

It has only been a couple of decades since Benoit Mandelbrot published his famous picture of what is now called the Mandelbrot set. That picture, now seeming graphically primitive, has changed our view of the mathematical and physical universe. The properties and circumstances of the discovery of the Mandelbrot Set continue to generate much interest in the research community and beyond. This book contains the hard-to-obtain original papers, many unpublished illustrations dating back to 1979 and extensive documented historical context showing how Mandelbrot helped change our way of looking at the world.

Karl Menger, one of the founders of dimension theory, is among the most original mathematicians and thinkers of the twentieth century. He was a member of the Vienna Circle and the founder of its mathematical equivalent, the Viennese Mathematical Colloquium. Both during his early years in Vienna and, after his emigration, in the United States, Karl Menger made significant contributions to a wide variety of mathematical fields, and greatly influenced many of his colleagues. These two volumes contain Menger's major mathematical papers, based on his own selection from his extensive writings. They deal with topics as diverse as topology, geometry, analysis and algebra, and also include material on economics, sociology, logic and philosophy. The Selecta Mathematica is a monument to the diversity and originality of Menger's ideas.

This edited review book on Godunov methods contains 97 articles, all of which were presented at the international conference on Godunov Methods: Theory and Applications, held at Oxford in October 1999, to commemo­ rate the 70th birthday of the Russian mathematician Sergei K. Godunov. The meeting enjoyed the participation of 140 scientists from 20 countries; one of the participants commented: everyone is here, meaning that virtu­ ally everybody who had made a significant contribution to the general area of numerical methods for hyperbolic conservation laws, along the lines first proposed by Godunov in the fifties, was present at the meeting. Sadly, there were important absentees, who due to personal circumstance could not at­ tend this very exciting gathering. The central theme o{ the meeting, and of this book, was numerical methods for hyperbolic conservation laws fol­ lowing Godunov's key ideas contained in his celebrated paper of 1959. But Godunov's contributions to science are not restricted to Godunov's method.

At its meeting in April 1990 at the University of Cambridge, the Executive Committee of the International Mathematical Union (IMU) decided that the largely unorganized archives of the Union should be properly arranged and catalogued. Simultaneously, the Executive Committee expressed the wish that a history of the Union should be written [1). As Secretary of the Union, I had proposed that these issues be dis­ cussed at the Cambridge meeting, but without having had in mind any personal role in the practical execution of such projects. At that time, the papers of the IMU were stored in Zurich, at the Eidgenossische Technische Hochschule, and I saw no reason why they could not remain there. At about this time, Professor K. Chandrasekharan produced a handwritten article titled'The Prehistory of the International Mathematical Union'[2), and it seemed to me that this might serve as the beginning of a more compre­ hensive history. I had first thought that Tuulikki MakeUiinen, who during eight years as the Office Secretary ofthe IMU had become well acquainted with the Union, would do the arranging of the archives in Zurich. She had a preliminary look at the material there, but it soon became clear that the amount of work required to bring order to it was too great to be accomplished in a few short visits from Helsinki. The total volume of material was formidable.

In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems.But between 1916 and 1950, the theorem was poorly understood and Noether's name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the various popular or historical accounts they wrote. Worse, earlier attempts which had been eclipsed by Noether's achievements were remembered, and sometimes figure in quick historical accounts of the time. This book carries a translation of Noether's original paper into English, and then describes the strange history of its reception and the responses to her work. Ultimately the theorems became decisive in a shift from basing fundamental physics on conservations laws to basing it on symmetries, or at the very least, in thoroughly explaining the connection between these two families of ideas. The real significance of this book is that it shows very clearly how long it took before mathematicians and physicists began to recognize the seminal importance of Noether's results. This book is thoroughly researched and provides careful documentation of the textbook literature. Kosmann-Schwarzbach has thus thrown considerable light on this slow dance in which the mathematical tools necessary to study symmetry properties and conservation laws were apparently provided long before the orchestra arrives and the party begins.

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell's own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.

Mathematicians do not work in isolation. They stand in a long and time honored tradition. They write papers and (sometimes) books, they read the publications of fellow workers in the?eld, and they meet other mathematicians at conferences all over the world. In this way, in contact with colleagues far away and nearby, from the past (via their writings) and from the present, scienti?c results are obtained whicharerecognizedasvalid.Andthat–remarkablyenough–regardlessofethnic background, political inclination or religion. In this process, some distinguished individuals play a special and striking role. They assume a position of leadership. They guide the people working with them through uncharted territory, thereby making a lasting imprint on the?eld. So- thing which can only be accomplished through a combination of rare talents: - usually broad knowledge, unfailing intuition and a certain kind of charisma that binds people together. AllofthisispresentinIsraelGohberg,themantowhomthisbookisdedicated,on theoccasionof his 80thbirthday.This comes to the foregroundunmistakably from the contributions from those who worked with him or whose life was a?ected by him. Gohberg'sexceptionalqualitiesarealsoapparentfromthe articleswritten by himself, sometimes jointly with others, that are reproduced in this book. Among these are stories of his life, some dealing with mathematical aspects, others of a more general nature. Also included are reminiscences paying tribute to a close colleaguewho isnotamongusanymore,speechesorreviewshighlightingthework and personality of a friend or esteemed colleague, and responses to the laudatio's connected with the several honorary degrees that were bestowed upon him.

Females consistently score lower than males on standardized tests of mathematics - yet no such differences exist in the classroom. These differences are not trivial, nor are they insignificant. Test scores help determine entrance to college and graduate school and therefore, by extension, a person's job and future success. If females receive lower test scores then they also receive fewer opportunities. Why does this discrepancy exist? This book presents a series of papers that address these issues by integrating the latest research findings and theories. Authors such as Diane Halpern, Jacquelynne Eccles, Beth Casey, Ronald Nuttal, James Byrnes, and Frank Pajares tackle these questions from a variety of perspectives. Many different branches of psychology are represented, including cognitive, social, personality/self-oriented, and psychobiological. The editors then present an integrative chapter that discusses the ideas presented and other areas that the field should explore.

The unpublished writings of Helmut Hasse, consisting of letters, manuscripts and other papers, are kept at the Handschriftenabteilung of the University Library at Göttingen. Hasse had an extensive correspondence; he liked to exchange mathematical ideas, results and methods freely with his colleagues. There are more than 8000 documents preserved. Although not all of them are of equal mathematical interest, searching through this treasure can help us to assess the development of Number Theory through the 1920s and 1930s. The present volume is largely based on the letters and other documents its author has found concerning the Brauer-Hasse-Noether Theorem in the theory of algebras; this covers the years around 1931. In addition to the documents from the literary estates of Hasse and Brauer in Göttingen, the author also makes use of some letters from Emmy Noether to Richard Brauer that are preserved at the Bryn Mawr College Library (Pennsylvania, USA).

This monograph meticulously examines the contributions of French mathematician Michel Chasles to 19th-century geometry. Through an in-depth analysis of Chasles'extensive body of work, the author examines six pivotal arguments which collectively reshape the foundations of geometry. Chasles introduces a novel form of polarity, termed'parabolic,'to the graphic context, so expressing the metric properties by means of this specific polarity—a foundational argument. Beyond the celebrated'Chasles theorem,'he extends his analysis to the movement of a rigid body, employing concepts derived from projective geometry. This approach is consistently applied across diverse domains. Chasles employs the same methodology to analyze systems of forces. The fourth argument examined by the author concerns the principle of virtual velocities, which can also be addressed through a geometric analysis. In the fifth chapter, Chasles'philosophy of duality is explained. It is grounded on theduality principles of projective geometry. Finally, the author presents Chasles'synthetic solution for the intricate problem of ellipsoid attraction—the sixth and concluding chapter. Throughout these explorations, Chasles engages in a dynamic scientific dialogue with leading physicists and mathematicians of his era, revealing diverse perspectives and nuances inherent in these discussions.Tailored for historians specializing in mathematics and geometry, this monograph also beckons philosophers of mathematics and science, offering profound insights into the philosophical, epistemological, and methodological dimensions of Chasles'groundbreaking contributions. Providing a comprehensive understanding of Chasles'distinctive perspective on 19th-century geometry, this work stands as a valuable resource for scholars and enthusiasts alike.

Inspired by recent developments in dependent type theory and infinity categories, this book presents a history of ideas around the topics of truth, proof, equality and equivalence. Besides selected ideas of Platon, Aristoteles, Leibniz, Kant, Frege and others, the results of Gödel and Tarski on incompleteness, undecidability and truth in deductive systems and their semantic models are covered. The main focus of this textbook is on dependent type theory and its recent variant homotopy type theory. Such theories contain identity types, which give a new understanding of equality, symmetry, equivalence and isomorphism in a conceptual way. The interaction of type theory and infinity category theory yields a new paradigm for a structural view on mathematics. This supports the tendencies towards formalising mathematics with the help of proof assistants. This book was first published in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.

This volume brings together scholars across various domains of the history and philosophy of mathematics, investigating duality as a multi-faceted phenomenon. Encompassing both systematic analysis and historical examination, the book endeavors to elucidate the status, roles, and dynamics of duality within the realms of 19th and 20th-century mathematics. Eschewing a priori notions, the contributors embrace the diverse interpretations and manifestations of duality, thus presenting a nuanced and comprehensive perspective on this intricate subject. Spanning a broad spectrum of mathematical topics and historical periods, the book uses detailed case studies to investigate the different forms in which duality appeared and still appears in mathematics, to study their respective histories, and to analyze interactions between the different forms of duality. The chapters inquire into questions such as the contextual occurrences of duality in mathematics, the influence of chosen forms of representation, the impact of investigations of duality on mathematical practices, and the historical interconnections among various instances of duality. Together, they aim to answer a core question: Is there such a thing as duality in mathematics, or are there just several things called by the same name and similar in some respect? What emerges is that duality can be considered as a basic structure of mathematical thinking, thereby opening new horizons for the research on the history and the philosophy of mathematics and the reflection on mathematics in general. The volume will appeal not only to experts in the discipline but also to advanced students of mathematics, history, and philosophy intrigued by the complexities of this captivating subject matter.

In this captivating historical novel, Daniele Struppa skillfully weaves a fictional autobiography, bringing Fibonacci to life with vivid details of his upbringing and adult years in Medieval Europe. As we explore the historical context of Fibonacci's time, we delve into the intriguing aspects of a bygone era, painting a compelling picture of a man whose contributions to mathematics continue to resonate today. From his groundbreaking work on congruent numbers to the famous numerical sequence that bears his name, the author invites readers to imagine the creative sparks that ignited Fibonacci's mathematical innovations. When historical evidence is elusive, accuracy and passion are seamlessly combined, offering plausible scenarios grounded in documented facts. A meticulously crafted apparatus of notes distinguishes fact from fiction, providing readers with a clear guide to navigate this enthralling reconstruction of Fibonacci's life. Step into the medieval world of Leonardo Fibonacci, one of the most celebrated mathematicians in history, and discover the man behind the mathematical genius. Mathematicians and curious readers alike will appreciate the allure of Fibonacci's mathematical brilliance.

Dieses Buch macht die überraschende Vielfalt der Personen und Tätigkeiten in der Radioaktivitätsforschung sichtbar. Dabei wird der Begriff der wissenschaftlichen Arbeit neu konzeptualisiert. Neben die Forschungsarbeit im Labor treten scheinbare Rand-, Neben- und Routinetätigkeiten, die für die Radioaktivitätsforschung als Disziplin von zentraler Bedeutung waren.Badeärzte, Industriechemiker und Bergbaubeamte waren an der Erforschung der neuen Substanzen und Strahlen ebenso beteiligt wie eine vergleichsweise hohe Zahl von Frauen. Die erste umfassende Studie zur deutschsprachigen Radioaktivitätsforschung im vorderen Teil des Buches offenbart die Ausnahmestellung der Hauptstädte Berlin und Wien für die Forschung ebenso wie fruchtbares akademisches Leben in der Provinz; sie zeigt, wie das neue Gebiet an den Hochschulen in die Lehre einzog und welchen Beitrag Professoren, Privatdozenten und Promovierende zur Forschung leisteten. Erstmals wird auch die Bedeutung der Wasseruntersuchungen aufgezeigt, die durch die Hoffnung auf radioaktive Heilquellen angetrieben wurden.Im zweiten Teil werden in internationaler Perspektive unsichtbare und in der Geschichtsschreibung oft wenig beachtete Facetten der „Arbeit mit dem Radium“ untersucht. So mussten Instrumente und radioaktive Präparate überhaupt erst hergestellt und in Umlauf gebracht werden. Auch die Etablierung von Nachweismethoden für Radioaktivität erforderte viel Arbeit, von der niemand sprach. Dienstleistungen wie die Entwicklung therapeutisch nutzbarer Präparate, Gutachtertätigkeiten, die Herausgabe einer Zeitschrift oder die Organisation eines Kongresses werden als integraler Bestandteil der wissenschaftlichen Arbeit in ihrer Bedeutung dargestellt. Eine Reflexion zur Arbeitsorganisation und zum disziplinären Status bündelt die Ergebnisse in einer neuen Gesamtsicht auf die frühe Radioaktivitätsforschung.

This book, which is aimed at general readers interested in maths as well as professional mathematicians, addresses numerous aspects of this spell-binding science. In particular, the book shows how mathematics is structured and how it works. Practical examples are discussed as well as the general role of maths in culture and art, in nature and in everyday life. The topics covered range from forms of logical argumentation to numerical analysis, from simple applications in ancient civilisations to sophisticated tools in modern cultures, from natural shapes to artistic creations. Furthermore, it provides a comprehensible and comprehensive insight into the fascinating panorama of mathematics, emphasizing its importance in human history. It assumes only that readers have a grasp of the basic concepts of school maths, allowing them access to the exciting world of mathematics and to fall under its spell. Numerous examples and illustrations clarify the text. Rik Verhulst is Prof. emeritus in maths at the Karel de Grote University of Applied Sciences in Antwerp. He is the coordinator and co-author of several series of maths textbooks for secondary schools. He is well-known in professional circles for his numerous lectures at congresses and colloquia and for his contributions to various journals. As a collaborator and lecturer at the Belgian Centre for Methodology of Mathematics, the Vliebergh-Sencie courses, the Centre for Didactics of Mathematics at the Catholic University of Leuven and the Flemish Mathematical Olympiad, he has long been involved in the training of teachers and the preparation of pupils for the International Mathematical Olympiad.

This book both articulates and responds to increasing scholarly interest in the materiality of the book. Taking as its base the unique collection of mathematical books in the Russell Library at Maynooth, it addresses questions related to printing techniques and print culture, book production, provenance, and reading practices. It considers the histories of individual items of the Russell Collection, their previous locations and owners, and explores ways in which annotations, underlinings, hand-drawn diagrams, and the like reveal patterns of reading and usage. Finally, it seeks to elicit more information on a previously under-researched topic: the historical role of mathematics in the extensive network of Irish colleges that once covered Catholic Europe, located in places such as Salamanca, Rome, Douai, and Prague. Alongside delivering important new insights into print culture as a medium for transmitting scientific ideas, Mathematical Book Histories is thus also intended to contribute to a broader understanding of the role and significance of mathematics in the context of clerical instruction and more broadly in the academic tradition of Ireland up to the beginning of the twentieth century. Many of the volumes in the Russell Library reflect the remarkably rich book-trade that flourished in seventeenth and early eighteenth century Dublin and which was quite distinct from that in London. Booksellers often bought in their wares directly from abroad, with the result that publications could enter collections that did not enter the purview of contemporary English or Scottish scholars in Britain.

This book celebrates Gert Schubring's 80th birthday and honors his impactful contributions to the field of history of mathematics and its education. Recognized with the prestigious Hans Freudenthal Award in 2019, Schubring's academic work sets the tone for this volume. The thoughtfully curated articles in this collection offer insightful studies on textbooks and biographies of key figures in mathematics and mathematics education, contextualizing their significance within the broader historical landscape, and providing the readers with a deeper understanding of the development of the history of mathematics and its education. Researchers as well as curious readers and students will find this collection to be a valuable resource in the field.

This publication, now in its second edition, includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728–1777) written in the 1760s: Vorläufige Kenntnisse für die, so die Quadratur und Rectification des Circuls suchen and Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques. The translations, as in the first edition, are accompanied by a contextualised study of each of these works and provide an overview of Lambert's contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself.Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Mémoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle.

The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques

This book covers the following topics: Mathematical Philosophy; Mathematical Logic; the Structure of Number Sets and the Theory of Real Numbers, Arithmetic and Axiomatic Number Theory, and Algebra (including the study of Sequences and Series); Matrices and Applications in Input-Output Analysis and Linear Programming; Probability and Statistics; Classical Euclidean Geometry, Analytic Geometry, and Trigonometry; Vectors, Vector Spaces, Normed Vector Spaces, and Metric Spaces; basic principles of non-Euclidean Geometries and Metric Geometry; Infinitesimal Calculus and basic Topology (Functions, Limits, Continuity, Topological Structures, Homeomorphisms, Differentiation, and Integration, including Multivariable Calculus and Vector Calculus); Complex Numbers and Complex Analysis; basic principles of Ordinary Differential Equations; as well as mathematical methods and mathematical modeling in the natural sciences (including physics, engineering, biology, and neuroscience) and in the social sciences (including economics, management, strategic studies, and warfare problems).

Sobald Sie sich eingehender mit der Geschichte der Mathematik beschäftigen, werden Sie auch auf Personen stoßen, deren Namen Ihnen bislang unbekannt waren oder von deren Bedeutung für die Entwicklung der Mathematik Sie bisher nichts wussten. Dieses Buch bietet Ihnen einen Einblick in das Leben und Wirken von 67 besonderen Persönlichkeiten aus dem europäischen Raum – und geht bei der Betrachtung der Einzelschicksale jeweils auch der Frage nach, warum diese Personen vergleichsweise unbekannt sind, warum sie regelrecht „vergessen“ wurden. Die Gründe dafür sind vielfältig und meist in den jeweiligen politischen, gesellschaftlichen oder individuellen Lebensumständen zu finden – viele wurden diskriminiert und konnten ihre Fähigkeiten gar nicht erst entfalten, andere waren Ihrer Zeit voraus und blieben lange Zeit unverstanden. Über die historische Einordnung hinaus werden einige der mathematischen Beiträge dieser Personen dargestellt – so ausgewählt, dass sie mit denin der gymnasialen Oberstufe üblicherweise vermittelten Kenntnissen nachvollzogen werden können. Die in diesem Buch enthaltenen Darstellungen beginnen mit Persönlichkeiten aus dem 16. Jahrhundert und schließen somit chronologisch an das Buch Geschichten aus der Mathematik desselben Autors an, sind aber unabhängig davon lesbar. Das Buch richtet sich an alle, die sich für die Entwicklung der Wissenschaften interessieren und dabei insbesondere ein tieferes Verständnis für die menschlichen Aspekte der Mathematik entwickeln möchten.

Zu seinen Lebzeiten war Kurt Gödel außerhalb der Fachwelt der Mathematiker, Philosophen und theoretischen Physiker kaum bekannt. Zu Beginn seiner Karriere schuf er beeindruckende Arbeiten zur Vollständigkeit und Beweisbarkeit formaler logischer Systeme, die zu seiner Dissertation und seiner Habilitations-schrift wurden und ihn unter Fachleuten weltberühmt machten. Seine Unvoll-ständigkeitssätze läuteten das Ende der formal-logischen Programme der Logizisten (Russell et al.) und der Formalisten (Hilbert et al.) ein. Später erzielte er auch signifikante Ergebnisse in der Mengenlehre. Nach seiner Emigration in die USA (Princeton), widmete er sich mehr der Philosophie, dem Leitmotiv seines Lebens, und er fand auch eine einzigartige Lösung zu Einsteins Feld-gleichungen der Gravitation, sein “Gödel-Universum“. Dieses Buch beschreibt sowohl den Gödel, der ein genialer Wissenschaftler war, und der gewagte und neuartige Hypothesen zu den Fundamenten der Mathe-matik und Physik hervorbrachte, ‒ als auch den Gödel, der ein perfekter Rationalist war, aber sein Alltagsleben nur mit Mühe meistern konnte und zeitlebens unter Depressionen, Angstneurosen und Hypochondrie litt. Ein Leben voller Paradoxen, in dem er trotz all seiner psychischen Probleme Beachtliches leistete und zu einem Vorbild für viele jüngere Wissenschaftler wurde. Das Buch liefert den Kontext zu seinen Errungenschaften, die ein verblüffend breites Spektrum intellektueller Unternehmungen darstellen, und zu seiner zunehmenden Geisteskrankheit; und es zeigt, wie er eine lange und erfolgreiche Karriere mit Hilfe seiner loyalen Ehefrau Adele und einigen seiner Freunde durchlaufen konnte. Dies ist eine faszinierende Geschichte der wissen-schaftlichen Genialität und der menschlichen Natur.

This textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Part I, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are usedto study and classify mathematical structures. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced are still preceded by remarks that motivate the material, but the exposition is more formal, and includes more advanced topics. The focus is on the notion of countable categoricity, which analyzed in detail using examples from the first two parts of the book. This textbook is suitable for graduate students in mathematical logic and set theory and will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.

Dieses Buch versucht, die schrittweise Entwicklung der wichtigsten Forschungsinstitute zur Zahlentheorie in Südindien, Punjab, Mumbai, Bengalen und Bihar zu beschreiben, einschließlich der Gründung des Tata Institute of Fundamental Research (TIFR) in Mumbai, einem bahnbrechenden Ereignis in der Geschichte der Zahlentheorie-Forschung in Indien. Die Forschung zur Zahlentheorie in Indien begann in der modernen Zeit mit dem Auftreten des ikonischen Genies Srinivasa Ramanujan, das Mathematiker auf der ganzen Welt inspirierte. Das Buch diskutiert die nationale und internationale Wirkung der Forschung indischer Zahlentheoretiker und enthält eine sorgfältig zusammengestellte, umfassende Bibliographie bedeutender indischer Zahlentheoretiker des 20. Jahrhunderts. Es ist wichtig für die historische Dokumentation und eine wertvolle Ressource für Forscher auf diesem Gebiet. Das Buch diskutiert auch kurz die Bedeutung der Zahlentheorie in der modernen Mathematik, einschließlich Anwendungen der Ergebnisse indigener Zahlentheoretiker in praktischen Bereichen. Da das Buch aus der Perspektive der Wissenschaftsgeschichte geschrieben ist, wurden technische Fachbegriffe und mathematische Ausdrücke so weit wie möglich vermieden.Die Übersetzung wurde mit Hilfe von künstlicher Intelligenz durchgeführt. Eine anschließende menschliche Überarbeitung erfolgte vor allem in Bezug auf den Inhalt.

Indispensable for understanding Henri Poincaré's vast activity in the mathematical sciences. Provides new sources revealing Poincaré's involvement as president of the'Commission permanente du Répertoire bibliographique des sciences mathématiques'as an actor in the'Dreyfus Affair,'and on his links with the editors of the major mathematical journals.The letters, many of which are unpublished, are fully annotated with an emphasis on the academic, cultural and technical contexts. An introduction underlines the lessons that can be drawn from the reading of these correspondences on Poincaré's position in the mathematical and academic communities. Three indexes facilitate the reading.Le volume de la correspondance de Poincaré consacré à ses échanges avec les mathématiciens permet de suivre son investissement dans le champ des sciences mathématiques de ses débuts comme étudiant brillant et prometteur préparant une thèse jusqu'à ses derniers jours, où devenu une icone pourla communauté mathématique depuis de longues années, sa correspondance traduit autant son activité dans la recherche que son implication dans les questions académiques, institutionnelles et organisationnelles. Les questions liées à la théorie des équations différentielles et l'entreprise du Répertoire bibliographique des sciences mathématiques ont suscité une activité épistolaire particulièrement sensible par le nombre de lettres qui y font allusion et par la diversité des correspondants qui abordent les questions de bibliographie mathématique. Les correspondances sont aussi l'occasion de multiples partages d'informations mathématiques, académiques et éditoriales.