Thomas Hankins and Robert Silverman investigate an array of instruments from the seventeenth through the nineteenth century that seem at first to be marginal to science--magnetic clocks that were said to operate by the movements of sunflower seeds, magic lanterns, ocular harpsichords (machines that played different colored lights in harmonious mixtures), Aeolian harps (a form of wind chime), and other instruments of "natural magic" designed to produce wondrous effects. By looking at these and the first recording instruments, the stereoscope, and speaking machines, the authors show that "scientific instruments" first made their appearance as devices used to evoke wonder in the beholder, as in works of magic and the theater.

The authors also demonstrate that these instruments, even though they were often "tricks," were seen by their inventors as more than trickery. In the view of Athanasius Kircher, for instance, the sunflower clock was not merely a hoax, but an effort to demonstrate, however fraudulently, his truly held belief that the ability of a flower to follow the sun was due to the same cosmic magnetic influence as that which moved the planets and caused the rotation of the earth. The marvels revealed in this work raise and answer questions about the connections between natural science and natural magic, the meaning of demonstration, the role of language and the senses in science, and the connections among art, music, literature, and natural science.

Originally published in 1999.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Asymptotic methods belong to the, perhaps, most romantic area of modern mathematics. They are widely known and have been used in me chanics, physics and other exact sciences for many, many decades. But more than this, asymptotic ideas are found in all branches of human knowledge, indeed in all areas of life. In this broader context they have not and perhaps cannot be fully formalized. However, they are mar velous, they leave room for fantasy, guesses and intuition; they bring us very near to the border of the realm of art. Many books have been written and published about asymptotic meth ods. Most of them presume a mathematically sophisticated reader. The authors here attempt to describe asymptotic methods on a more accessi ble level, hoping to address a wider range of readers. They have avoided the extreme of banishing formulae entirely, as done in some popular science books that attempt to describe mathematical methods with no mathematics. This is impossible (and not wise). Rather, the authors have tried to keep the mathematics at a moderate level. At the same time, using simple examples, they think they have been able to illustrate all the key ideas of asymptotic methods and approaches, to depict in de tail the results of their application to various branches of knowledg- from astronomy, mechanics, and physics to biology, psychology and art. The book is supplemented by several appendices, one of which con tains the profound ideas of R. G.

L.E.J. Brouwer (1881-1966) is best known for his revolutionary ideas on topology and foundations of mathematics (intuitionism). The present collection contains a mixture of letters; university and faculty correspondence has been included, some of which shed light on the student years, and in particular on the exchange of letters with his PhD adviser, Korteweg. Acting as the natural sequel to the publication of Brouwer's biography, this book provides instrumental reading for those wishing to gain a deeper understanding of Brouwer and his role in the twentieth century. Striking a good balance of biographical and scientific information, the latter deals with innovations in topology (Cantor-Schoenflies style and the new topology) and foundations. The topological period in his research is well represented in correspondence with Hilbert, Schoenflies, Poincare, Blumenthal, Lebesgue, Baire, Koebe, and foundational topics are discussed in letters exchanged with Weyl, Fraenkel, Heyting, van Dantzig and others. There is also a large part of correspondence on matters related to the interbellum scientific politics. This book will appeal to both graduate students and researchers with an interest in topology, the history of mathematics, the foundations of mathematics, philosophy and general science.

Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

This two volume set presents over 50 of the most groundbreaking contributions of Menahem M Schiffer. All of the reprints of Schiffer's works herein have extensive annotation and invited commentaries, giving new clarity and insight into the impact and legacy of Schiffer's work. A complete bibliography and brief biography make this a rounded and invaluable reference.

This is a collection of Harald Cramer's extensive work on number theory, probability, mathematical statistics and insurance mathematics. Many of these are not easily found in their original sources nowadays, for instance his pioneering work on risk theory published in the Skandia Insurance Company's jubilee volumes in 1930 and 1955. Despite their age, these eminent examples of Cramer's expository style remain highly readable. Cramer was one of the "fathers" of modern mathematical statistics. His famous book on the subject is still an important reference. His statistical papers included here were seminal to the subsequent development of the subject. The collection includes a complete bibliography of Cramer's work.

The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area."

This publication was made possible through a bequest from my beloved late wife. United together in this present collection are those works by the author which have not previously appeared in book form. The following are excepted: Vorlesungen uber Differential und Integralrechnung (Lectures on Differential and Integral Calculus) Vols 1-3, Birkhauser Verlag, Basel (1965-1968); Aufgabensammlung zur Infinitesimalrechnung (Exercises in Infinitesimal Calculus) Vols 1, 2a, 2b, and 3, Birkhauser Verlag, Basel (1967-1977); two issues from Memorial des Sciences on Conformal Mapping (written together with C. Gattegno), Gauthier-Villars, Paris (1949); Solution of Equations in Euc1idean and Banach Spaces, Academic Press, New York (1973); and Stu- dien uber den Schottkyschen Satz (Studies on Schottky's Theorem), Wepf & Co., Basel (1931). Where corrections have had to be implemented in the text of certain papers, references to these are made at the conc1usion of each paper. In the few instances where this system does not, for technical reasons, seem appropriate, an asterisk in the page margin indicates wherever a correction is necessary and this is then given at the end of the paper. (There is one exception: the correc- tions to the paper on page 561 are presented on page 722. The works are published in 6 volumes and are arranged under 16 topic headings. Within each heading, the papers are ordered chronologically according to the date of original publication.

In recognition of professor Shiing-Shen Chern s long and distinguished service to mathematics and to the University of California, the geometers at Berkeley held an International Symposium in Global Analysis and Global Geometry in his honor in June 1979. The output of this Symposium was published in a series of three separate volumes, comprising approximately a third of Professor Chern s total publications up to 1979. Later, a fourth volume was published, focusing on papers written during the Eighties. This first volume comprises selected papers written between 1932 and 1975. In making the selections, Professor Chern gave preference to shorter and lesser-known papers."

The Origins of Husserl's Totalizing Act At noon on Monday, October 24th, 1887, Dr. Edmund G. Husserl defended the dissertation that would qualify him as a university lecturer at Halle. Entitled "On the Concept of Number," it was written under Carl Stumpf who, like Husserl, had been a student of Franz Brentano. In this, his first published philosophical work, Husserl sought to secure the foundations of mathematics by deriving its most fundamental concepts from psychical acts. In the same year, Heinrich Hertz published an article entitled, "Con cerning an Influence of Ultraviolet Light on the Electrical Discharge." The article detailed his discovery of a new "relation between two entirely different forces," those of light and electricity. Hermann von Helmholtz, whose theory guided Hertz's initial research, called it the "most important physical discovery of the century," and Hertz became an immediate sensation. He lectured on his discovery in 1889 before a general session of the German Association meeting in Heidelberg. In this lecture that, as he wrote beforehand to Emil Cohn, he was deter mined should not be "entirely unintelligible to the laity," Hertz explained that light ether and electro-magnetic forces were interdependent. He went on to tell his audience that they need not expect their senses to grant them access to these phenomena. Indeed, he said, the latter are not only insusceptible of sense perception, but are false from the standpoint of the senses."

A unique series of fascinating 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.

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

Apollonius's Conics was one of the greatest works of advanced mathematics in antiquity. The work comprised eight books, of which four have come down to us in their original Greek and three in Arabic. By the time the Arabic translations were produced, the eighth book had already been lost. In 1710, Edmond Halley, then Savilian Professor of Geometry at Oxford, produced an edition of the Greek text of the Conics of Books I-IV, a translation into Latin from the Arabic versions of Books V-VII, and a reconstruction of Book VIII. The present work provides the first complete English translation of Halley's reconstruction of Book VIII with supplementary notes on the text. It also contains 1) an introduction discussing aspects of Apollonius's Conics 2) an investigation of Edmond Halley's understanding of the nature of his venture into ancient mathematics, and 3) an appendices giving a brief account of Apollonius's approach to conic sections and his mathematical techniques. This book will be of interest to students and researchers interested in the history of ancient Greek mathematics and mathematics in the early modern period.

Aus Paulis letztem Lebensjahrzehnt sind uber 2000 Briefe erhalten und in diesem grundlegenden Werk zur Physikgeschichte der Nachkriegszeit zusammengefasst. Neben der Physik wird hier auch der allgemeinere geistesgeschichtliche Hintergrund unserer Naturwissenschaft beleuchtet. Dieser Teilband enthalt wissenschaftliche Korrespondez uber grundlegende und andere allgemeine Fragen der Physik der Jahre 1955-1956. In diese Zeit fallen der Beginn der axiomatischen Feldtheorie, die Anfange von CERN, der Berner Relativitatskongress zur 50-Jahr-Feier von Einsteins Entdeckung sowie N. Bohrs 70. Geburtstag und naturlich die fruhe Geschichte des Neutrinos. Pauli und seine Briefpartner nehmen aktiv an diesen Ereignissen teil und beleuchten sie in eindrucksvoller Weise in ihrer Korrespondenz. Die reich annotierten und kommentierten Briefe sind chronologisch angeordnet und durch Verzeichnisse und Register erschlossen. From the final decade of Pauli's life, nearly 2000 letters survive. These are collected in this fundamental work on the history of physics in the post-war era. Going beyond physics, these letters also shed light on the cultural and philosophical background of our natural sciences. This part of the collection contains scientific correspondence about fundamental and other general questions concerning physics in the years 1955-1956. This period saw the beginnings of axiomatic field theories, the birth of CERN, the Berner Relativity Congress marking the 50th Anniversary of Einstein's discovery, and N. Bohr's 70th birthday. They were also the formative years of neutrino physics. Pauli and his correspondence partners played an active role in these events and illuminate them in an impressive manner in their letters. The extensively annotated and commented letters are organized chronologically and complemented by indexes and references.

The ancient Greeks played a fundamental role in the history of mathematics and their ideas were reused and developed in subsequent periods all the way down to the scientific revolution and beyond. In this, the first complete history for a century. Reviel Netz offers a panoramic view of the rise and influence of Greek mathematics and its significance in world history. He explores the Near Eastern antecedents and the social and intellectual developments underlying the subject's beginnings in Greece in the fifth century BCE. He leads the reader through the proofs and arguments of key figures like Archytas, Euclid and Archimedes, and considers the totality of the Greek mathematical achievement which also includes, in addition to pure mathematics, such applied fields as optics, music, mechanics and, above all, astronomy. This is the story not only of a major historical development, but of some of the finest mathematics ever created.

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

Emmy Noether (1882-1935) was one of the most influential mathematicians of the 20th century. The development of abstract algebra, which is one of the most distinctive innovations of 20th century mathematics, can largely be traced back to her - in her published papers, lectures and her personal influence on her contemporaries. By now her contributions have become so thoroughly absorbed into our mathematical culture that only rarely are they specifically attributed to her. This book presents an extensive collection of her work. Albert Einstein wrote in a letter to the New York Times of May 1st, 1935: "In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians." Emmy Noether leistete grundlegende Arbeiten zur Abstrakten Algebra. Ihre Auffassung von Mathematik war sehr nutzlich fur die damalige Physik, aber wurde auch kontrovers diskutiert. Die Debatte ging darum, ob Mathematik eher konzeptuell und abstract (intuitionistisch) oder mehr physikalisch basiert und angewandt (konstruktionistisch) sein sollte. Noethers konzeptuelle Auffassung der Algebra fuhrte zu neuen Grundlagen, die Algebra, Geometrie, Lineare Algebra, Topologie und Logik vereinheitlichten."

Ten amazing curves personally selected by one of today's most important math writers Curves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of one curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bezier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves-and now you can share in this adventure. Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling.

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

During his lifetime, Henri Poincare published three major philosophical books which achieved great success: "La science et l'hypothese" (1902), "La valeur de la science" (1905) and "Science et methode" (1908). After his death in 1913, a fourth volume of his philosophical works was published by his heirs as "Dernieres pensees" (1913). The four books constitute the core of Poincare's philosophic works and were given an ovation by scientific and general public. Around 1919, Gustave Le Bon wrote to Poincare's widow. As the director of the "Bibliotheque de Philosophie Scientifique at Flammarion," he asked her permission to publish a second posthumous volume. "L'Opportunisme scientifique" was intended to be the fifth and final volume of Poincare's philosophical writings. Louis Rougier had elaborated the project, with the collaboration of Gustave Le Bon, and the approval of the philosopher Emile Boutroux and his son Pierre. Because of the reservations of the mathematician's heirs, this book was never published and Dernieres pensees remained his last philosophical book. Nevertheless Poincare's correspondence - which is kept in the Poincare Archives at University Nancy 2 - contains a large amount of documents concerning the project, its justification and the discussions between Louis Rougier and the mathematician's heirs. The aim of this book is to restore this episode, which gives some crucial informations about editorial practices of Poincare and about the posterity of his philosophic thinking."

An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo-whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp-Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau's Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird's-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.

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

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

To mark the centenary of the 1910 to 1913 publication of the monumental Principia Mathematica by Alfred N. Whitehead and Bertrand Russell, this collection of fifteen new essays by distinguished scholars considers the influence and history of PM over the last hundred years.