Born into a Newcastle coal mining family, Charles Hutton (1737-1823) displayed mathematical ability from an early age. He rose to become professor of mathematics at the Royal Military Academy and foreign secretary of the Royal Society. First published in 1795-6, this two-volume illustrated encyclopaedia aimed to supplement the great generalist reference works of the Enlightenment by focusing on philosophical and mathematical subjects; the coverage ranges across mathematics, astronomy, natural philosophy and engineering. Almost a century old, the last comparable reference work in English was John Harris' Lexicon Technicum. Hutton's work contains many historical and biographical entries, often with bibliographies, including many for continental analytical mathematicians who would have been relatively unfamiliar to British readers. These features make Hutton's Dictionary a particularly valuable record of eighteenth-century science and mathematics. Volume 1 ranges from abacist (a user of an abacus) to the English physician and Newtonian scientist James Jurin.

Born into a Newcastle coal mining family, Charles Hutton (1737-1823) displayed mathematical ability from an early age. He rose to become professor of mathematics at the Royal Military Academy and foreign secretary of the Royal Society. First published in 1795-6, this two-volume illustrated encyclopaedia aimed to supplement the great generalist reference works of the Enlightenment by focusing on philosophical and mathematical subjects; the coverage ranges across mathematics, astronomy, natural philosophy and engineering. Almost a century old, the last comparable reference work in English was John Harris' Lexicon Technicum. Hutton's work contains many historical and biographical entries, often with bibliographies, including many for continental analytical mathematicians who would have been relatively unfamiliar to British readers. These features make Hutton's Dictionary a particularly valuable record of eighteenth-century science and mathematics. Volume 2 ranges from kalendar to zone. Among the other topics covered are knots, Newton, magnets, and the Moon.

From the Preface: "Jack Kiefer's sudden and unexpected death in August, 1981, stunned his family, friends, and colleagues. Memorial services in Cincinnati, Ohio, Berkeley, California, and Ithaca, New York, shortly after his death, brought forth tributes from so many who shared in his life. But it was only with the passing of time that those who were close to him or to his work were able to begin assessing Jack's impact as a person and intellect. About one year after his death, an expression of what Jack meant to all of us took place at the 1982 annual meeting of the Institute of Mathematical Statistics and the American Statistical Association. Jack had been intimately involved in the affairs of the IMS as a Fellow since 1957, as a member of the Council, as President in 1970, as Wald lecturer in 1962, and as a frequent author in its journals. It was doubly fitting that the site of this meeting was Cincinnati, the place of his birth and residence of his mother, other family, and friends. Three lectures were presented there at a Memorial Session - by Jerry Sacks dealing with Jack's personal life, by Larry Brown dealing with Jack's contributions in statistics and probability, and by Henry Wynn dealing with Jack's contributions to the design of experiments. These three papers, together with Jack's bibliography, were published in the Annals of Statistics and are included as an introduction to these volumes."

In this fascinating book, the author traces the careers, ideas, discoveries, and inventions of two renowned scientists, Athanasius Kircher and Galileo Galilei, one a Jesuit, the other a sincere man of faith whose relations with the Jesuits deteriorated badly. The Author documents Kircher's often intuitive work in many areas, including translating the hieroglyphs, developing sundials, and inventing the magic lantern, and explains how Kircher was a forerunner of Darwin in suggesting that animal species evolve. Galileo's work on scales, telescopes, and sun spots is mapped and discussed, and care is taken to place his discoveries within their cultural environment. While Galileo is without doubt the "winner" in the comparison with Kircher, the latter achieved extraordinary insights by unconventional means. For all Galileo's fine work, the author believes that scientists do need to regain the power of dreaming, vindicating Kirchner's view.

A member of the Academie francaise, Henri Poincare (1854 1912) was one of the greatest mathematicians and theoretical physicists of the late nineteenth and early twentieth centuries. His discovery of chaotic motion laid the foundations of modern chaos theory, and he was acknowledged by Einstein as a key contributor in the field of special relativity. He earned his enduring reputation as a philosopher of mathematics and science with this elegantly written work, which was first published in French as three separate essays: Science and Hypothesis (1902), The Value of Science (1905), and Science and Method (1908). Poincare asserts that much scientific work is a matter of convention, and that intuition and prediction play key roles. George Halsted's authorised 1913 English translation retains Poincare's lucid prose style, presenting complex ideas for both professional scientists and those readers interested in the history of mathematics and the philosophy of science."

This book examines the theoretical foundations underpinning the field of strength of materials/theory of elasticity, beginning from the origins of the modern theory of elasticity. While the focus is on the advances made within Italy during the nineteenth century, these achievements are framed within the overall European context. The vital contributions of Italian mathematicians, mathematical physicists and engineers in respect of the theory of elasticity, continuum mechanics, structural mechanics, the principle of least work and graphical methods in engineering are carefully explained and discussed. The book represents a work of historical research that primarily comprises original contributions and summaries of work published in journals. It is directed at those graduates in engineering, but also in architecture, who wish to achieve a more global and critical view of the discipline and will also be invaluable for all scholars of the history of mechanics.

 From the Preface: “There are three volumes. The first one contains a curriculum vitae, a «Brève Analyse des Travaux» and a Iist of publications, including books and seminars. In addition the volume contains all papers of H. Cartan on analytic functions published before 1939. The other papers on analytic functions, e.g. those on Stein manifolds and coherent sheaves, make up the second volume. The third volume contains, with a few exceptions, all further papers of H. Cartan; among them is a reproduction of exposés 2 to 11 of his 1954/55 Seminar on Eilenberg-MacLane algebras. Each volume is arranged in chronological order. The reader should be aware that these volumes do not fully reflect H. Cartan's work, a large part of which is also contained in his fifteen ENS-Seminars (1948-1964) and in his book "Homological Algebra" with S. Eilenberg... Still, we trust that mathematicians throughout the world will welcome the availability of the "Oeuvres" of a mathematician whose writing and teaching has had such an influence on our generation.�

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1891 Excerpt: ...position of the face B E G F, it is easy to see that the two wedgeshaped figures Bee'b'oc and Pgg'p'ad are exactly equal; this follows from the equality of their corresponding faces. Hence the volume of the sheared figure must be equal to the volume of the right six-face. Now let us suppose in addition that the face B' E' G' P' is again moved in its own plane into the position B" E" G" F," So that B' and E' move along B' E' and p' G' respectively. Then the slant wedge-shaped figures B'b"f"p'ao and E'e"g"p'dc will again be equal, and the volume of the six-face B" E" G" P" A D C O obtained by this second shear will be equal to the volume of the figure obtained by the first shear, and therefore to the volume of the right six-face. But by n, ns of two shears we can move the face B E G P to any position in its plane, B" E" G" P," in which its sides remain parallel to their former position. Hence the volume of a six-face will remain unchanged if, one of its faces, o c D A, remaining fixed, the opposite face, B E G P, be moved anywhere parallel to itself in its own plane. We thus find that the volume of a six-face formed by three pairs of parallel planes is equal to the product of the area of one of its faces and the perpendicular distance between that face and its parallel. For this is the volume of the right six-face into which it may be sheared; and, as we have seen, shear does not alter volume. The knowledge thus gained of the volume of a sixface bounded by three pairs of parallel faces, or of a so-called parallelepiped, enables us to find the volume of an oblique cylinder. A right cylinder is the figure generated by any area moving parallel to itself in such wise that any point p ...

Throughout his early life, Isaac Todhunter (1820-84) excelled as a student of mathematics, gaining a scholarship at the University of London and numerous awards during his time at St John's College, Cambridge. Taking up fellowship of the college in 1849, he became widely known for both his educational texts and his historical accounts of various branches of mathematics. The present work, first published in 1865, describes the rise of probability theory as a recognised subject, beginning with a discussion of the famous 'problem of points', as considered by the likes of the Chevalier de Mere, Blaise Pascal and Pierre de Fermat during the latter half of the seventeenth century. Subsequently, the application of advanced methods that had been developed in classical areas of mathematics led to rapid progress in probability theory. Todhunter traces this growth, closing with a thorough account of Pierre-Simon Laplace's far-reaching work in the area.

From the end of antiquity to the middle of the nineteenth century it was generally believed that Aristotle had said all that there was to say concerning the rules of logic and inference. One of the ablest British mathematicians of his age, Augustus De Morgan (1806-71) played an important role in overturning that assumption with the publication of this book in 1847. He attempts to do several things with what we now see as varying degrees of success. The first is to treat logic as a branch of mathematics, more specifically as algebra. Here his contributions include his laws of complementation and the notion of a universe set. De Morgan also tries to tie together formal and probabilistic inference. Although he is never less than acute, the major advances in probability and statistics at the beginning of the twentieth century make this part of the book rather less prophetic.

In the preface to this work, mathematician Augustus De Morgan (1806 71) claims that 'The most worthless book of a bygone day is a record worthy of preservation.' His purpose in writing this catalogue, published in 1847, was to provide an accurate record of the early history of publishing on arithmetic, but describing only those books which he had examined himself. He surveyed the library of the Royal Society, works in the British Museum, the wares of specialist booksellers, and the private collections of himself and his friends to compile a chronological list of books from 1491 to 1846 (the final book being a work of his own), giving bibliographical details, a description of the contents, and sometimes comments on the mathematics on display. De Morgan's Formal Logic and a Memoir of Augustus De Morgan by his widow are also reissued in the Cambridge Library Collection."

This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject - Cauchy, Riemann, and Weierstrass - it looks at the contributions of authors from d'Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.

This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen I� will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations and also in physics, for example in general relativity. This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry.

In addition to linear perspective, complex numbers and probability were notable discoveries of the Renaissance. While the power of perspective, which transformed Renaissance art, was quickly recognized, the scientific establishment treated both complex numbers and probability with much suspicion. It was only in the twentieth century that quantum theory showed how probability might be molded from complex numbers and defined the notion of "complex probability amplitude". From a theoretical point of view, however, the space opened to painting by linear perspective and that opened to science by complex numbers share significant characteristics. The Art of Science explores this shared field with the purpose of extending Leonardo's vision of painting to issues of mathematics and encouraging the reader to see science as an art. The intention is to restore a visual dimension to mathematical sciences - an element dulled, if not obscured, by historians, philosophers, and scientists themselves.

This book traces the life of Cholesky (1875-1918), and gives his family history. After an introduction to topography, an English translation of an unpublished paper by him where he explained his method for linear systems is given, studied and replaced in its historical context. His other works, including two books, are also described as well as his involvement in teaching at a superior school by correspondence. The story of this school and its founder, Leon Eyrolles, are addressed. Then, an important unpublished book of Cholesky on graphical calculation is analyzed in detail and compared to similar contemporary publications. The biography of Ernest Benoit, who wrote the first paper where Choleskys method is explained, is provided. Various documents, highlighting the life and the personality of Cholesky, end the book.

Sofia Kovalevskaya was a brilliant and determined young Russian woman of the 19th century who wanted to become a mathematician and who succeeded, in often difficult circumstances, in becoming arguably the first woman to have a professional university career in the way we understand it today. This memoir, written by a mathematician who specialises in symplectic geometry and integrable systems, is a personal exploration of the life, the writings and the mathematical achievements of a remarkable woman. It emphasises the originality of Kovalevskaya's work and assesses her legacy and reputation as a mathematician and scientist. Her ideas are explained in a way that is accessible to a general audience, with diagrams, marginal notes and commentary to help explain the mathematical concepts and provide context. This fascinating book, which also examines Kovalevskaya's love of literature, will be of interest to historians looking for a treatment of the mathematics, and those doing feminist or gender studies.

Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended... In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations. Marcel Berger is t he author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.

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.

Describes the development and the ultimate demise of the practice of mathematics in sixteenth century Antwerp. Against the background of the violent history of the Religious Wars the story of the practice of mathematics in Antwerp is told through the lives of two protagonists Michiel Coignet and Peeter Heyns. The book touches on all aspects of practical mathematics from teaching and instrument making to the practice of building fortifications of the practice of navigation.

This first complete English language edition of Euclides vindicatus presents a corrected and revised edition of the classical English translation of Saccheri's text by G.B. Halsted. It is complemented with a historical introduction on the geometrical environment of the time and a detailed commentary that helps to understand the aims and subtleties of the work. Euclides vindicatus, written by the Jesuit mathematician Gerolamo Saccheri, was published in Milan in 1733. In it, Saccheri attempted to reform elementary geometry in two important directions: a demonstration of the famous Parallel Postulate and the theory of proportions. Both topics were of pivotal importance in the mathematics of the time. In particular, the Parallel Postulate had escaped demonstration since the first attempts at it in the Classical Age, and several books on the topic were published in the Early Modern Age. At the same time, the theory of proportion was the most important mathematical tool of the Galilean School in its pursuit of the mathematization of nature. Saccheri's attempt to prove the Parallel Postulate is today considered the most important breakthrough in geometry in the 18th century, as he was able to develop for hundreds of pages and dozens of theorems a system in geometry that denied the truth of the postulate (in the attempt to find a contradiction). This can be regarded as the first system of non-Euclidean geometry. Its later developments by Lambert, Bolyai, Lobachevsky and Gauss eventually opened the way to contemporary geometry. Occupying a unique position in the literature of mathematical history, Euclid Vindicated from Every Blemish will be of high interest to historians of mathematics as well as historians of philosophy interested in the development of non-Euclidean geometries.

This volume commemorates the life, work and foundational views of Kurt Goedel (1906-78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Goedel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Goedel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.

A distinguished mathematician and notable university teacher, Isaac Todhunter (1820 84) became known for the successful textbooks he produced as well as for a work ethic that was extraordinary, even by Victorian standards. A scholar who read all the major European languages, Todhunter was an open-minded man who admired George Boole and helped introduce the moral science examination at Cambridge. His many gifts enabled him to produce the histories of mathematical subjects which form his lasting memorial. First published between 1886 and 1893, the present work was the last of these. Edited and completed after Todhunter's death by Karl Pearson (1857 1936), another extraordinary man who pioneered modern statistics, these volumes trace the mathematical understanding of elasticity from the seventeenth to the late nineteenth century. Volume 1 (1886) begins with Galileo Galilei and extends to the researches of Saint-Venant up to 1850."

A distinguished mathematician and notable university teacher, Isaac Todhunter (1820 84) became known for the successful textbooks he produced as well as for a work ethic that was extraordinary, even by Victorian standards. A scholar who read all the major European languages, Todhunter was an open-minded man who admired George Boole and helped introduce the moral science examination at Cambridge. His many gifts enabled him to produce the histories of mathematical subjects which form his lasting memorial. First published between 1886 and 1893, the present work was the last of these. Edited and completed after Todhunter's death by Karl Pearson (1857 1936), another extraordinary man who pioneered modern statistics, these volumes trace the mathematical understanding of elasticity from the seventeenth to the late nineteenth century. Volume 2 (1893) was split into two parts. Part 1 includes the work of Saint-Venant from 1850 to 1886."

A distinguished mathematician and notable university teacher, Isaac Todhunter (1820 84) became known for the successful textbooks he produced as well as for a work ethic that was extraordinary, even by Victorian standards. A scholar who read all the major European languages, Todhunter was an open-minded man who admired George Boole and helped introduce the moral science examination at Cambridge. His many gifts enabled him to produce the histories of mathematical subjects which form his lasting memorial. First published between 1886 and 1893, the present work was the last of these. Edited and completed after Todhunter's death by Karl Pearson (1857 1936), another extraordinary man who pioneered modern statistics, these volumes trace the mathematical understanding of elasticity from the seventeenth to the late nineteenth century. Volume 2 (1893) was split into two parts. Part 2 covers the work of Neumann, Kirchhoff, Clebsch, Boussinesq, and Lord Kelvin."

A guide to changing how you think about numbers and mathematics, from the prodigy changing the way the world thinks about math. We all know math is important: we live in the age of big data, our lives are increasingly governed by algorithms, and we're constantly faced with a barrage of statistics about everything from politics to our health. But what might be less obvious is how math factors into your daily life, and what memorizing all of those formulae in school had to do with it. Math prodigy Stefan Buijsman is beginning to change that through his pioneering research into the way we learn math. Plusses and Minuses is based in the countless ways that math is engrained in our daily lives, and shows readers how math can actually be used to make problems easier to solve. Taking readers on a journey around the world to visit societies that have developed without the use of math, and back into history to learn how and why various disciples of mathematics were invented, Buijsman shows the vital importance of math, and how a better understanding of mathematics will give us a better understanding of the world as a whole. Stefan Buijsman has become one of the most sought-after experts in math education after he completed his PhD at age 20. In Plusses and Minuses, he puts his research into practice to help anyone gain a better grasp of mathematics than they have ever had.