Bøger i Science Networks. Historical Studies serien

Volterra's interest in the application of mathematics to the non physical sciences, and to biology and economics in particular, dates back to the turn of the century and was expressed in his inaugural address at the University of Rome for the academic year 1900/01 (VOLTERRA 1901).

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.

FOREWORD This book came about as a result of two events: an exhibition on the Solvay Physics Councils, held in Brussels in May 1995, and a conference on the same theme which took place at the Free University of Brussels (ULB) on May 1Oth 1995.

The planet Venus is the closest neighbour to the Earth and in several respects similar to our globe. Not only was Venus' period of rotation thought to be close to that of the Earth, it was also p- sible (and indeed common) to imagine intelligent life on Venus.

Kvasz's book is a contribution to the history and philosophy of mat- matics, or, as one might say, the historical approach to the philosophy of mathematics. The ?rst signi?cant work in the history and philosophy of science is perhaps William Whewell's Philosophy of the Inductive Sciences, founded upon their History.

Presents the features of the Wasan tradition, which is the indigenous mathematics that developed in Japan during the Edo period (1600-1868). This work offers a description of the mathematical textbooks published in the 17th century, then shifts to the work of the two leading mathematicians of this tradition, Seki Takakazu and Takebe Katahiro.

This book deals with one of the earliest surviving "abbacus" treatises, one that is by far more orderly than any of the extant predecessors and is also the first to contain a presentation of algebra. In addition, it features an extensive discussion of the contents of the treatise and its location within early abbacus culture.

Philanthropic societies funded by the Rockefeller family were prominent in the social history of the twentieth century, for their involvement in medicine and applied science. This book provides the first detailed study of their relatively brief but nonetheless influential foray into the field of mathematics.

Die Entstehung des chemischen Verbindungsbegriffs, ein Fundamentalbegriff der neuzeitlichen Chemie, ist kaum untersucht, weil er für eine blosse Präzisierung des naturphilosophischen Atomkonzepts gehalten wurde. Das Buch widerlegt diese Ansicht als ideengeschichtliches Vorurteil und weist minutiös nach, dass der Verbindungsbegriff als Resultat der begrifflichen Strukturierung des empirischen Wissens entstand, das aus der gewerblichen chemischen Praxis des 16. und 17. Jahrhunderts stammte. Damit rekonstruiert die Autorin nicht allein den Beginn der wissenschaftlichen Chemie in einer grundlegend neuen historischen, begrifflichen und methodischen Ordnung. Sie zeigt darüber hinaus, wie diese "chemische Revolution" in den Kontext der wissenschaftlichen Revolution des 17. Jahrhunderts einzuordnen ist, nämlich als die einer "baconischen Wissenschaft" (Kuhn), die das Erfahrungswissen einer neuartigen gewerblichen Praxis ohne Rückgriffsmöglichkeiten auf brauchbare Theorietraditionen in eine wissenschaftliche Theorie überführte. Das Buch ist so zugleich ein substanzieller Beitrag zum Verständnis wissenschaftlicher Revolutionen, der insbesondere zum Überdenken der wissenschaftstheoretischen Annahme einer Theoriedominanz bei der Entstehung und Entwicklung der Wissenschaften nötigt. Es ist deswegen nicht nur für Chemiehistoriker, für die es zum neuen Standardwerk über die Chemie des 17. Jahr- hunderts werden dürfte, von Interesse, sondern ebenso für Wissenschaftshistoriker allgemein sowie für Wissenschaftstheoretiker, Philosophen und Kulturhistoriker.

In 1920s, a long-lasting controversy on the interpretation of nuclear beta spectrum arose between Lise Meitner and Charles Drummond Ellis. A new dispute, this time between Niels Bohr and Wolfgang Pauli, broke out. Pauli argued for a new particle, and Bohr for a new theory;

The significance of foundational debate in mathematics that took place in the 1920s seems to have been recognized only in circles of mathematicians and philosophers. A period in the history of mathematics when mathematics and philosophy, usually so far away from each other, seemed to meet.

The tremendous success of indivisibles methods in geometry in the seventeenth century, responds to a vast project: installation of infinity in mathematics. The pathways by the authors are very diverse, as are the characterizations of indivisibles, but there are significant factors of unity between the various doctrines of indivisible; the permanence of the language used by all authors is the strongest sign.These efforts do not lead to the stabilization of a mathematical theory (with principles or axioms, theorems respecting these first statements, followed by applications to a set of geometric situations), one must nevertheless admire the magnitude of the results obtained by these methods and highlights the rich relationships between them and integral calculus.The present book aims to be exhaustive since it analyzes the works of all major inventors of methods of indivisibles during the seventeenth century, from Kepler to Leibniz. It takes into account the rich existing literature usually devoted to a single author. This book results from the joint work of a team of specialists able to browse through this entire important episode in the history of mathematics and to comment it.The list of authors involved in indivisibles¿ field is probably sufficient to realize the richness of this attempt; one meets Kepler, Cavalieri, Galileo, Torricelli, Gregoire de Saint Vincent, Descartes, Roberval, Pascal, Tacquet, Lalouvère, Guldin, Barrow, Mengoli, Wallis, Leibniz, Newton.

George Boole (1815-1864) is well known to mathematicians for his research and textbooks on the calculus, but his name has spread world-wide for his innovations in symbolic logic and the development and applications made since his day.

To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer­ ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt.

The controversy between the wave theory and the emission theory of light early in the nineteenth century has been a subject of numerous studies. It examines the impact of the concept of interference of light on the development of the early nineteenth century optics in general, and the theory of light, in particular.

The Latin "Version II", till now attributed to Adelard of Bath, is edited here for the first time. But a comparison of the text of version II with those of versions I and III yields little or no reason to assume that Adelard was the author of version II. Version II must have been written later than version I and before version III;

Die allgemeine Relativitästheorie lässt sich nur mit Hilfe des Tensorkalküls formulieren. Diesen lernte Einstein 1912 in Form des absoluten Differentialkalküls kennen. Dessen Schöpfer war Gregorio Ricci, dem zusammen mit Sophus Lie und anderen der Ausbau der Theorie der Differentialinvarianten gelang. Der absolute Differentialkalkül passte zur allgemeinen Relativitätstheorie wie ein Schlüssel zum Schloss: der in den Jahren 1884-92 von Ricci entwickelte Kalkül erfüllte in der Tat genau das physikalische Konzept der allgemeinen Relativitätstheorie, das Einstein 1907-15 ausarbeitete. Ein derartiges Zusammenpassen war nur dadurch möglich, weil sowohl Ricci innerhalb der Mathematik als auch Einstein innerhalb der Physik vergleichbare Fragen stellten, nämlich Fragen nach Invarianten bei speziellen Transformationen. Es wird versucht, den historischen Weg so genau wie möglich anhand der Quellen nachzuzeichnen. Neu ist die Herausarbeitung des invariantentheoretischen Aspekts, dem gegenüber die Bedeutung der Differentialgeometrie für die Entwicklung des Tensorkalküls in den Hintergrund treten muss.

Die Akustik ist ein Gebiet, das erstaunlicherweise in der wissenschaftshistorischen Literatur nur relativ selten zu finden ist. Darstellungen langerer Epochen in der Entwicklung dieses Fachgebietes haben noch groBeren Seltenheitswert. Nach dem Zweiten Weltkrieg erschien bisher lediglich F.V. HUNTS "Origins in acoustics", das im wesentlichen die Zeitepoche von der Antike bis NEWTON beschreibt. Ein Buch, das in gewisser Weise aIs eine Fortsetzung betrachtet werden kann, ist CANNON/DoSTROVSKYS "The evolution of dynamics: Vibration theory from 1687 to 1742". Es setzt jedoch gemlill seinem Titel ganz bestimmte Akzente. Mit NEWTONS "Principia" von 1687 beginnt eine Periode ausgesprochen theoretischer Forschung auf dem Gebiet der Akustik, fUr die Namen wie z.B. TAYLOR, SAUVEUR, EULER, D'ALEMBERT, JOHANN und DANIEL BERNOULLI Zeugnis ablegen. Dieses Uberwiegen der Theorie wird 1787 mit dem Auftreten CHLADNIS wieder zugunsten des Experiments verschoben. Da es tiber die Tatigkeit der eben genannten Forscher bereits einige ausfUhrliche DarsteIlungen gibt, beginnt die detaillierte Betrachtung in diesem Buch erst im Erscheinungsjahr von CHLADNIS Erstlingswerk. Ziel dieses Buches ist es, nicht nur die akustischen Arbeiten CHLADNIS zu beschreiben, sondem auch seinen Einflull auf die Forschung bis in die Mitte des 19.

1 Aim and General Description of the Anthology The purpose of this anthology is to introduce the English speaking public to the wide spectrum of texts authored predominently by physicists portraying the ac­ tual and perceived role of physics in the Nazi state. Up to now no broad and well­ balanced documentation of German physics during this time has been available in English, despite the significant role physics has played both politically (e. g. , in weaponry planning) and ideologically (e. g. , in the controversy over the value of theoretical ('Jewish') vs. experimental ('Aryan') physics), and even though prominent figures like the scientist-philosopher and emigre Albert Einstein and the controversial nuclear physicist Werner Heisenberg have become household names. This anthology will attempt to bridge this gap by presenting contempo­ rary documents and eye-witness accounts by the physicists themselves. Authors were chosen to represent the various political opinions and specialties within the physics community, omitting some of the more readily accessible texts by leading physicists (e. g. , Einstein, Heisenberg, Lenard) in favor of those by less well-known but nonetheless important figures (e. g. , Finkelnburg, Max Wien, Ramsauer). In this way we hope not only to circumvent the constricted 'Great Men' approach to history but also to offer a broader picture of the activities and conflicts within the field and the effects of the political forces exerted upon them.

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.

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.

In addition to tracing the life and times of the mathematician Iris Runge, this book shows how a mathematical bridge was constructed between statistics and quality control of mass products, and between physical-chemical models and concrete product problems.

In the 5th century, the Indian mathematician Aryabhata wrote a small but famous work on astronomy in 118 verses called the Aryabhatiya. Its second chapter gives a summary of Hindu mathematics up to that point, and 200 years later, the Indian astronomer Bhaskara glossed that chapter.

Die allgemeine Relativitästheorie lässt sich nur mit Hilfe des Tensorkalküls formulieren. Diesen lernte Einstein 1912 in Form des absoluten Differentialkalküls kennen. Dessen Schöpfer war Gregorio Ricci, dem zusammen mit Sophus Lie und anderen der Ausbau der Theorie der Differentialinvarianten gelang. Der absolute Differentialkalkül passte zur allgemeinen Relativitätstheorie wie ein Schlüssel zum Schloss: der in den Jahren 1884-92 von Ricci entwickelte Kalkül erfüllte in der Tat genau das physikalische Konzept der allgemeinen Relativitätstheorie, das Einstein 1907-15 ausarbeitete. Ein derartiges Zusammenpassen war nur dadurch möglich, weil sowohl Ricci innerhalb der Mathematik als auch Einstein innerhalb der Physik vergleichbare Fragen stellten, nämlich Fragen nach Invarianten bei speziellen Transformationen. Es wird versucht, den historischen Weg so genau wie möglich anhand der Quellen nachzuzeichnen. Neu ist die Herausarbeitung des invariantentheoretischen Aspekts, dem gegenüber die Bedeutung der Differentialgeometrie für die Entwicklung des Tensorkalküls in den Hintergrund treten muss.

In the 5th century, the Indian mathematician Aryabhata wrote a small but famous work on astronomy in 118 verses called the Aryabhatiya. Volume 1 of this work was an English translation of Bhaskara's commentary, and this volume contains explanations for each verse commentary translated in volume 1.

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. This allows the author to describe the structure, the contents and the mathematics of the Arithmetika in detail.

The controversy between the wave theory and the emission theory of light early in the nineteenth century has been a subject of numerous studies. It examines the impact of the concept of interference of light on the development of the early nineteenth century optics in general, and the theory of light, in particular.

Die Entstehung des chemischen Verbindungsbegriffs, ein Fundamentalbegriff der neuzeitlichen Chemie, ist kaum untersucht, weil er für eine blosse Präzisierung des naturphilosophischen Atomkonzepts gehalten wurde. Das Buch widerlegt diese Ansicht als ideengeschichtliches Vorurteil und weist minutiös nach, dass der Verbindungsbegriff als Resultat der begrifflichen Strukturierung des empirischen Wissens entstand, das aus der gewerblichen chemischen Praxis des 16. und 17. Jahrhunderts stammte. Damit rekonstruiert die Autorin nicht allein den Beginn der wissenschaftlichen Chemie in einer grundlegend neuen historischen, begrifflichen und methodischen Ordnung. Sie zeigt darüber hinaus, wie diese "chemische Revolution" in den Kontext der wissenschaftlichen Revolution des 17. Jahrhunderts einzuordnen ist, nämlich als die einer "baconischen Wissenschaft" (Kuhn), die das Erfahrungswissen einer neuartigen gewerblichen Praxis ohne Rückgriffsmöglichkeiten auf brauchbare Theorietraditionen in eine wissenschaftliche Theorie überführte. Das Buch ist so zugleich ein substanzieller Beitrag zum Verständnis wissenschaftlicher Revolutionen, der insbesondere zum Überdenken der wissenschaftstheoretischen Annahme einer Theoriedominanz bei der Entstehung und Entwicklung der Wissenschaften nötigt. Es ist deswegen nicht nur für Chemiehistoriker, für die es zum neuen Standardwerk über die Chemie des 17. Jahr- hunderts werden dürfte, von Interesse, sondern ebenso für Wissenschaftshistoriker allgemein sowie für Wissenschaftstheoretiker, Philosophen und Kulturhistoriker.

The Latin "Version II", till now attributed to Adelard of Bath, is edited here for the first time. But a comparison of the text of version II with those of versions I and III yields little or no reason to assume that Adelard was the author of version II. Version II must have been written later than version I and before version III;

To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer­ ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt.