Science Networks. Historical Studies – serie

This monograph presents a groundbreaking scholarly treatment of the German mathematician Jost Bürgi’s original work on logarithms, Arithmetische und Geometrische Progreß Tabulen.  It provides the first-ever English translation of Bürgi’s text and illuminates his role in the development of the conception of logarithms, for which John Napier is traditionally given priority.  High-resolution scans of each page of the his handwritten text are reproduced for the reader and as a means of preserving an important work for which there are very few surviving copies.The book begins with a brief biography of Bürgi to familiarize readers with his life and work, as well as to offer an historical context in which to explore his contributions.  The second chapter then describes the extant copies of the Arithmetische und Geometrische Progreß Tabulen, with a detailed description of the copy that is the focus of this book, the 1620 “Graz manuscript”.  A complete facsimile of the text is included in the next chapter, along with a corresponding transcription and an English translation; a transcription of a second version of the manuscript (the “Gdansk manuscript”) is included alongside that of the Graz edition so that readers can easily and closely examine the differences between the two.  The final chapter considers two important questions about Bürgi’s work, such as who was the copyist of the Graz manuscript and what the relationship is between the Graz and Gdansk versions.  Appendices are also included that contain a timeline of Bürgi’s life, the underlying concept of Napier’s construction of logarithms, and scans of all 58 sheets of the tables from Bürgi’s text.Anyone with an appreciation for the history of mathematics will find this book to be an insightful and interesting look at an important and often overlooked work.  It will also be a valuable resource for undergraduates taking courses in the history of mathematics, researchers of the history of mathematics, and professors of mathematics education who wish to incorporate historical context into their teaching.

This monograph presents a groundbreaking scholarly treatment of the German mathematician Jost Bürgi’s original work on logarithms, Arithmetische und Geometrische Progreß Tabulen.  It provides the first-ever English translation of Bürgi’s text and illuminates his role in the development of the conception of logarithms, for which John Napier is traditionally given priority.  High-resolution scans of each page of the his handwritten text are reproduced for the reader and as a means of preserving an important work for which there are very few surviving copies.The book begins with a brief biography of Bürgi to familiarize readers with his life and work, as well as to offer an historical context in which to explore his contributions.  The second chapter then describes the extant copies of the Arithmetische und Geometrische Progreß Tabulen, with a detailed description of the copy that is the focus of this book, the 1620 “Graz manuscript”.  A complete facsimile of the text is included in the next chapter, along with a corresponding transcription and an English translation; a transcription of a second version of the manuscript (the “Gdansk manuscript”) is included alongside that of the Graz edition so that readers can easily and closely examine the differences between the two.  The final chapter considers two important questions about Bürgi’s work, such as who was the copyist of the Graz manuscript and what the relationship is between the Graz and Gdansk versions.  Appendices are also included that contain a timeline of Bürgi’s life, the underlying concept of Napier’s construction of logarithms, and scans of all 58 sheets of the tables from Bürgi’s text.Anyone with an appreciation for the history of mathematics will find this book to be an insightful and interesting look at an important and often overlooked work.  It will also be a valuable resource for undergraduates taking courses in the history of mathematics, researchers of the history of mathematics, and professors of mathematics education who wish to incorporate historical context into their teaching.

This first of three volumes starts with a short introduction to historical metrology as a scientific discipline and goes on with an anthology of acient and modern measurement systems of all kind, scientific measures, units of time, weights, currencies etc. It concludes with an exhaustive list of references.Units of measurement are of vital importance in every civilization through history. Since the early ages, man has through necessity devised various measures to assist him in everyday life. They have enabled and continue to enable us to trade in commonly and equitably understood amounts, and to investigate, understand, and control the chemical, physical, and biological processes of the natural world.The essence of the work is an alphabetically ordered, comprehensive list of measurement nomenclature, units and scales. It provides an understanding of almost all quantitative expressions observed in all imaginable situations, including spelling variants and the abbreviations and symbols for units, and various acronyms used in metrology. It will be of use not only to historians of science and technology, but also to economic and social historians and should be in every major academic and national library as standard reference work on the topic.

This second volume of Gyllenbok's encyclopaedia of historical metrology comprises the first part of the compendium of measurement systems and currencies of all sovereign states of the modern World (A-I).Units of measurement are of vital importance in every civilization through history. Since the early ages, man has through necessity devised various measures to assist him in everyday life. They have enabled and continue to enable us to trade in commonly and equitably understood amounts, and to investigate, understand, and control the chemical, physical, and biological processes of the natural world.The encyclopeadia will be of use not only to historians of science and technology, but also to economic and social historians and should be in every major academic and national library as standard reference work on the topic.

This third volume of Gyllenbok's encyclopaedia of historical metrology comprises the second part of the compendium of measurement systems and currencies of all sovereign states of the modern World (J-Z).Units of measurement are of vital importance in every civilization through history. Since the early ages, man has through necessity devised various measures to assist him in everyday life. They have enabled and continue to enable us to trade in commonly and equitably understood amounts, and to investigate, understand, and control the chemical, physical, and biological processes of the natural world.The encyclopeadia will be of use not only to historians of science and technology, but also to economic and social historians and should be in every major academic and national library as standard reference work on the topic.

While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised?Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete.In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.

Drawing on published works, correspondence and manuscripts, this book offers the most comprehensive reconstruction of Boscovich’s theory within its historical context. It explains the genesis and theoretical as well as epistemological underpinnings in light of the Jesuit tradition to which Boscovich belonged, and contrasts his ideas with those of Newton, Leibniz, and their legacy. Finally, it debates crucial issues in early-modern physical science such as the concept of force, the particle-like structure of matter, the idea of material points and the notion of continuity, and shares novel insights on Boscovich’s alleged influence on later developments in physics.With its attempt to reduce all natural forces to one single law, Boscovich’s Theory of Natural Philosophy, published in 1758, left a lasting impression on scientists and philosophers of every age regarding the fundamental unity of physical phenomena. The theory argues that every pair of material points is subject toone mutual force — and always the same force — which is their propensity to be mutually attracted or repelled, depending on their distance from one another. Furthermore, the action of this unique force is visualized through a famous diagram that fascinated generations of scientists. But his understanding of key terms of the theory — such as the notion of force involved and the very idea of a material point — is only ostensibly similar to our current conceptual framework. Indeed, it needs to be clarified within the plurality of contexts in which it has emerged rather than being considered in view of later developments.The book is recommended for scholars and students interested in the ideas of the early modern period, especially historians and philosophers of science, mathematicians and physicists with an interest in the history of the discipline, and experts on Jesuit science and philosophy.

Drawing on published works, correspondence and manuscripts, this book offers the most comprehensive reconstruction of Boscovich’s theory within its historical context. It explains the genesis and theoretical as well as epistemological underpinnings in light of the Jesuit tradition to which Boscovich belonged, and contrasts his ideas with those of Newton, Leibniz, and their legacy. Finally, it debates crucial issues in early-modern physical science such as the concept of force, the particle-like structure of matter, the idea of material points and the notion of continuity, and shares novel insights on Boscovich’s alleged influence on later developments in physics.With its attempt to reduce all natural forces to one single law, Boscovich’s Theory of Natural Philosophy, published in 1758, left a lasting impression on scientists and philosophers of every age regarding the fundamental unity of physical phenomena. The theory argues that every pair of material points is subject toone mutual force — and always the same force — which is their propensity to be mutually attracted or repelled, depending on their distance from one another. Furthermore, the action of this unique force is visualized through a famous diagram that fascinated generations of scientists. But his understanding of key terms of the theory — such as the notion of force involved and the very idea of a material point — is only ostensibly similar to our current conceptual framework. Indeed, it needs to be clarified within the plurality of contexts in which it has emerged rather than being considered in view of later developments.The book is recommended for scholars and students interested in the ideas of the early modern period, especially historians and philosophers of science, mathematicians and physicists with an interest in the history of the discipline, and experts on Jesuit science and philosophy.

French aeronautics shone brightly in the first decade of the twentieth Century, but declined after the Great War. To remedy this situation, a new Ministry of Air launched in 1929 a large national program of scientific research in fluid mechanics, including the creation of four institutes and five teaching centers in the faculties of sciences in Paris and the provinces. This visionary policy, supported by considerable means, started a quite creative period and led to important achievements notably in the fields of atmospheric turbulence, thermoconvection and wake vortices. The usual picture of a period exclusively dominated by German and British contributions (and growing North-American ones), comes out significantly revised. The fruits of this policy will allow France to play a major role in the creation, after World War II, of the International Union of Theoretical and Applied Mechanics, and are still visible today in the French teaching and research organization. Based on original materials unearthed from a variety of archival sources and scientific papers, the present book recounts this history in all its intertwined scientific, industrial, political and cultural dimensions.Peer-review recommendation: “The text is tremendously well written, and it remains clear and accessible even in its most scientifically advanced dimensions. The author is thus able to address both connoisseurs of the field, who will enjoy reading - and discovering not only scientific but also literary elements and references - and neophytes who are never left by the wayside as the chapters progress. An exceptional and original iconography usefully completes this picture, without overloading it.”L'aéronautique française, qui a tant brillé au début du XXe siècle, décline nettement après la Grande Guerre. Afin de redresser la situation, un nouveau ministère de l'Air lance alors, en 1929, un ambitieux programme en faveur de la recherche en mécanique des fluides, incluant la création de quatre instituts et cinq centres d'enseignement dans les facultés des sciences de Paris et de province. Cette politique visionnaire, dotée de moyens considérables, initie une période très dynamique et créative, en particulier dans les domaines de la turbulence atmosphérique, de la thermoconvection et des tourbillons de sillage. L'image d'un demi-siècle exclusivement dominé par les contributions allemandes et anglaises (et ensuite américaines) s'en trouve notablement transformée. Les fruits de cette politique permettront à la France de jouer un rôle majeur dans la création, après la Seconde Guerre mondiale, de l'Union internationale de mécanique théorique et appliquée, et demeurent visibles aujourd'hui encore dans les structures d'enseignement et de recherche. Fondé sur des documents originaux issus de nombreuses archives et publications, le présent livre raconte cette histoire dans ses différentes dimensions scientifique, industrielle, politique et culturelle.

»Philosophy of Mathematics« is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods. These include, for example, questions about the ontological status of mathematical objects (e.g., what is the nature of mathematical objects?) and the epistemological status of mathematical theorems (e.g., from what sources do we draw when we prove mathematical theorems?). The answers given by Plato, Aristotle, Euclid, Descartes, Locke, Leibniz, Kant, Cantor, Frege, Dedekind, Hilbert and others will be studied in detail. This will lead us to deep insights, not only into the history of mathematics, but also into the conception of mathematics as it is commonly held in the present time.The book is a translation from the German, however revised and considerably expanded. Various chapters have been completely rewritten.

»Philosophy of Mathematics« is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods. These include, for example, questions about the ontological status of mathematical objects (e.g., what is the nature of mathematical objects?) and the epistemological status of mathematical theorems (e.g., from what sources do we draw when we prove mathematical theorems?). The answers given by Plato, Aristotle, Euclid, Descartes, Locke, Leibniz, Kant, Cantor, Frege, Dedekind, Hilbert and others will be studied in detail. This will lead us to deep insights, not only into the history of mathematics, but also into the conception of mathematics as it is commonly held in the present time.The book is a translation from the German, however revised and considerably expanded. Various chapters have been completely rewritten.

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.

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.

Delving into previously undisclosed archival sources, this monograph offers a meticulously researched portrayal of Italian Jewish mathematicians amidst the turmoil sparked by the 1938 Italian Racial Laws. Forced migration due to fascist anti-Semitism saw the exodus of numerous Jewish intellectuals. Highlighting the experiences of select academic mathematicians such as Guido Fubini, Gino Fano, Beniamino Segre, Alessandro Terracini, and others who fled Italy, this work casts a light on a diaspora that presents unique aspects thanks to pre-existing networks of international scientific solidarity. Despite challenges stemming from language, society, and institutions, their narratives reveal the profound human dimensions of adversity, choice, and camaraderie.Suitable for scholars and students of 20th-century history, as well as a wider audience intrigued by Italy's complex past, these pages offer invaluable insights into a dark chapter of the country's history.

Delving into previously undisclosed archival sources, this monograph offers a meticulously researched portrayal of Italian Jewish mathematicians amidst the turmoil sparked by the 1938 Italian Racial Laws. Forced migration due to fascist anti-Semitism saw the exodus of numerous Jewish intellectuals. Highlighting the experiences of select academic mathematicians such as Guido Fubini, Gino Fano, Beniamino Segre, Alessandro Terracini, and others who fled Italy, this work casts a light on a diaspora that presents unique aspects thanks to pre-existing networks of international scientific solidarity. Despite challenges stemming from language, society, and institutions, their narratives reveal the profound human dimensions of adversity, choice, and camaraderie.Suitable for scholars and students of 20th-century history, as well as a wider audience intrigued by Italy's complex past, these pages offer invaluable insights into a dark chapter of the country's history.

L’objectif de cet ouvrage, issu d’un colloque et d’une exposition à la bibliothèque Mazarine organisés à l’occasion du tricentenaire du décès de Pierre Varignon (1654-1722), est de retracer la trajectoire de ce mathématicien dans son contexte historique, et de faire le point sur les recherches menées sur lui ces dernières décennies.Même si Varignon ne fait pas partie du panthéon des mathématiciens, c’est un savant « normal », ni génial ni méconnu, et c’est en cela qu’il mérite d’être étudié. Géomètre et mécanicien reconnu par ses contemporains, membre puissant de l’Académie royale des sciences, en contact épistolaire avec Leibniz, Newton ou encore les frères Bernoulli, Varignon fut aussi le premier titulaire de la première chaire de mathématiques du collège Mazarin et professeur au Collège royal. Ses travaux situés à une époque de transition sont marqués par le cartésianisme mais contribuent aussi à l’introduction de l’analyse leibnizienne en France et à la naissance de la mécanique analytique.Cette collection d'essais sera précieuse pour les étudiant(e)s et les chercheur(e)s intéressé(e)s par l'héritage de Varignon et le contexte historique des sciences aux XVIIe et XVIIIe siècles.***This book originates from a symposium and an exhibition at the Mazarine Library in Paris organized to commemorate the trecentenary of Pierre Varignon's death (1654-1722), and it aims to retrace the trajectory of this notable mathematician within his historical context, as well as to take stock of the research carried out on him in recent decades. A respected geometer and "mechanic" of his time, he was a prominent member of the Paris Académie royale des sciences, and part of an extended international network including Leibniz, Newton and the Bernoullis. He held the first chair of mathematics, established at the Collège Mazarin, and was a professor at the Collège Royal.This collection of essays will be invaluable to students and scholars interested in Varignon’s legacy and the historical context of science in the 17th and 18th centuries.

This unique reference work systematically presents and studies mathematical terms, sourcing literature from antiquity until the 20th century.The book provides detailed and reliable information on the origins and developments of more than 1,000 mathematical terms from all branches of mathematics. The dictionary is based on extensive research of the primary literature, cites from original sources, provides historical illustrations, discusses synonyms and competing terms, and quotes critical or approving comments on newly created terms. Each entry is self-contained and includes a bibliography. All major mathematical fields are represented, ranging from geometry and arithmetic to, for example, calculus, topology, and category theory. This is the first of two volumes, covering terms that begin with the letters A through I.

This unique reference work systematically presents and studies mathematical terms, sourcing literature from antiquity until the 20th century.The book provides detailed and reliable information on the origins and developments of more than 1,000 mathematical terms from all branches of mathematics. The dictionary is based on extensive research of the primary literature, cites from original sources, provides historical illustrations, discusses synonyms and competing terms, and quotes critical or approving comments on newly created terms. Each entry is self-contained and includes a bibliography. All major mathematical fields are represented, ranging from geometry and arithmetic to, for example, calculus, topology, and category theory. This is the second of two volumes, covering terms that begin with the letters J through Z.

This unique reference work systematically presents and studies mathematical terms, sourcing literature from antiquity until the 20th century.The book provides detailed and reliable information on the origins and developments of more than 1,000 mathematical terms from all branches of mathematics. The dictionary is based on extensive research of the primary literature, cites from original sources, provides historical illustrations, discusses synonyms and competing terms, and quotes critical or approving comments on newly created terms. Each entry is self-contained and includes a bibliography. All major mathematical fields are represented, ranging from geometry and arithmetic to, for example, calculus, topology, and category theory.This set comprises both volumes I and II, covering the letters from A through Z.

This open access book examines the historical development of the concept of the virtual particle, from the first prominent appearance of virtual entities in quantum physics in the Bohr-Kramers-Slater (BKS) theory (1924) to the most common representation of virtual particles in Feynman diagrams (1949).Through a pragmatically informed approach to concept formation, focusing on the different representations of virtual entities and their role in theoretical practice, this work unravels the (dis)connections between the concepts of “virtual oscillators” (early 1920s), “virtual transitions” (the late 1920s to mid-1940s), and, finally, “virtual particles” (mid-1930s to late 1940s). The shifts and continuities in the conceptual development must be understood within the broader transformation of the theoretical framework, from the so-called Old Quantum Theory to the emergence of quantum electrodynamics (QED) and quantum field theory of the 1930s, culminating in the reconfiguration of the practice of QED in the hands of Richard Feynman in the late 1940s. A key pragmatically informed feature uniting these concepts is their shared function: they extended the set of possible processes and rendered these possibilities effective.This book will be of interest to historians and philosophers of physics and mathematics.

A contemporary of Christopher Wren, Robert Boyle, and Isaac Newton, and close friend of all but Newton, Robert Hooke (1635-1703), one of the founders of the early scientific revolution, faded into almost complete obscurity after his death and remained there for nearly three centuries. The result has been that his role in the scientific revolution has been almost totally ignored. He was the first professional scientist worthy of the name, working for the young Royal Society of London as its curator of experiments for four decades. He became the Society’s intellectual center, and for a while its Secretary, roles which led to confrontation with Newton. He made important contributions to pneumatics, mechanics, microscopy, astronomy, and geology, and was partner to Wren in rebuilding London after the Fire.

In this book the author presents a comprehensive study of Diophantos’ monumental work known as Arithmetika, a highly acclaimed and unique set of books within the known Greek mathematical corpus. Its author, Diophantos, is an enigmatic figure of whom we know virtually nothing.Starting with Egyptian, Babylonian and early Greek mathematics the author paints a picture of the sources the Arithmetika may have had. Life in Alexandria, where Diophantos lived, is described and, on the basis of the limited available evidence, his biography is outlined.Of Arithmetika’s 13 books only 6 survive in Greek. It was not until 1971 that these were complemented by the discovery of 4 other books in an Arab translation. This allows the author to describe the structure, the contents and the mathematics of the Arithmetika in detail. Furthermore it is shown that Diophantos had a remarkable skill to solve higher degree equations.In the second part, the author draws our attention to the survival of Diophantos’ work in both Arab and European mathematical cultures. Once Xylander’s critical 1575 edition reached its European public, the fame of the Arithmetika grew. It was studied, translated and modified by such authors as Bombelli, Stevin and Viète. It reached its pinnacle of fame in 1621 with the publication of Bachet’s translation into Latin. The marginal notes by Fermat in his copy of Diophantos, including his famous “Last Theorem”, were the starting point of a whole new research subject: the theory of numbers.

Despite the rapidly expanding ambit of physical research and the continual appearance of new branches of physics, the main thrust in its development was and is the attempt at a theoretical synthesis of the entire body of physical knowledge. The main triumphs in physical science were, as a rule, associ­ ated with the various phases of this synthesis. The most radical expression of this tendency is the program of construction of a unified physical theory. After Maxwellian electrodynamics had unified the phenomena of electricity, magnetism, and optics in a single theoretical scheme on the basis of the con­ cept of the electromagnetic field, the hope arose that the field concept would become the precise foundation of a new unified theory of the physical world. The limitations of an electromagnetic-field conception of physics, however, already had become clear in the first decade of the 20th century. The concept of a classical field was developed significantly in the general theory of relativity, which arose in the elaboration of a relativistic theory of gravitation. It was found that the gravitational field possesses, in addition to the properties inherent in the electromagnetic field, the important feature that it expresses the metric structure of the space-time continuum. This resulted in the following generalization of the program of a field synthesis of physics: The unified field representing gravitation and electromagnetism must also describe the geometry of space-time.

Oliver Heaviside's electromagnetic investigations - from the publication of his first electrical paper in 1972 to the public recognition awarded to him by Lord Kelvin in 1889 - have consistently attracted attention over the years, and of late have become a major source for the study of the development of field theory after Maxwell. "From Obscurity to Enigma" is the only comprehensive, in-depth analysis of Heaviside's work. It analyses and elucidates his brilliant but often close-to-indecipherable Electrical Papers and traces the evolution of his ideas against the background of growing knowledge in basic electromagnetic theory, telegraphy and telephony during these years. The book will be appreciated by historians of science and technology in the late 19th and early 20th centuries and by physicists and electrical engineers, many of whom are aware of Heaviside's contributions to their respective fields.

This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos’ celebrated book Proofs and Refutations. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly anything but superficial, as the present book also offers new theoretical insights into the methodology of the development of mathematics (proof-processing), with implications for the historiography of mathematics.

This book concerns the origins of mathematical problem solving at the internationally active Osram and Telefunken Corporations during the golden years of broadcasting and electron tube research. The woman scientist Iris Runge, who received an interdisciplinary education at the University of Göttingen, was long employed as the sole mathematical authority at these companies in Berlin. It will be shown how mathematical connections were made between statistics and quality control, and between physical-chemical models and the actual problems of mass production. The organization of industrial laboratories, the relationship between theoretical and experimental work, and the role of mathematicians in these settings will also be explained. By investigating the social, economic, and political conditions that unfolded from the time of the German Empire until the end of the Second World War, the book hopes to build a bridge between specialized fields – mathematics and engineering – and the generalculture of a particular era. It hopes, furthermore, to build a bridge between the history of science and industry, on the one hand, and the fields of Gender and Women’s Studies on the other. Finally, by examining the life and work of numerous industrial researchers, insight will be offered into the conditions that enabled a woman to achieve a prominent professional position during a time when women were typically excluded from the scientific workforce.

In this volume, a distinguished set of international scholars examine the nature of collaboration between life partners in the sciences, with particular attention to the ways in which personal and professional dynamics can foster or inhibit scientific practice. Breaking from traditional gender analyses which focus on divisions of labor and the assignment of credit, the studies scrutinize collaboration as a variable process between partners living in the nineteenth and twentieth centuries who were married and divorced, heterosexual and homosexual, aristocratic and working-class and politically right and left. The contributors analyze cases shaped by their particular geographical locations, ranging from retreat settings like the English countryside and Woods Hole, Massachusetts, to university laboratories and urban centers in Berlin, Stockholm, Geneva and London. The volume demonstrates how the terms and meanings of collaboration, variably shaped by disciplinary imperatives, cultural mores, and the agency of the collaborators themselves, illuminate critical intellectual and institutional developments in the modern sciences.

In this book the author presents a comprehensive study of Diophantos’ monumental work known as Arithmetika, a highly acclaimed and unique set of books within the known Greek mathematical corpus. Its author, Diophantos, is an enigmatic figure of whom we know virtually nothing.Starting with Egyptian, Babylonian and early Greek mathematics the author paints a picture of the sources the Arithmetika may have had. Life in Alexandria, where Diophantos lived, is described and, on the basis of the limited available evidence, his biography is outlined.Of Arithmetika’s 13 books only 6 survive in Greek. It was not until 1971 that these were complemented by the discovery of 4 other books in an Arab translation. This allows the author to describe the structure, the contents and the mathematics of the Arithmetika in detail. Furthermore it is shown that Diophantos had a remarkable skill to solve higher degree equations.In the second part, the author draws our attention to the survival of Diophantos’ work in both Arab and European mathematical cultures. Once Xylander’s critical 1575 edition reached its European public, the fame of the Arithmetika grew. It was studied, translated and modified by such authors as Bombelli, Stevin and Viète. It reached its pinnacle of fame in 1621 with the publication of Bachet’s translation into Latin. The marginal notes by Fermat in his copy of Diophantos, including his famous “Last Theorem”, were the starting point of a whole new research subject: the theory of numbers.

We bring into full light some excerpts on musical subjects which were until now scattered throughout the most famous scientific texts. The main scientific and musical cultures outside of Europe are also taken into consideration. The first and most important property to underline in the scientific texts examined here is the language they are written in. This means that our multicultural history of the sciences necessarily also becomes a review of the various dominant languages used in the different historical contexts. In this volume, the history of the development of the sciences is told as it happened in real contexts, not in an alienated ideal world.