This book presents diverse topics in mathematical logic such as proof theory, meta-mathematics, and applications of logic to mathematical structures. The collection spans the first 100 years of modern logic and is dedicated to the memory of Irving Anellis, founder of the journal 'Modern Logic', whose academic work was essential in promoting the algebraic tradition of logic, as represented by Charles Sanders Peirce. Anellis's association with the Russian logic community introduced their school of logic to a wider audience in the USA, Canada and Western Europe. In addition, the collection takes a historical perspective on proof theory and the development of logic and mathematics in Eastern Logic, the Soviet Union and Russia. The book will be of interest to historians and philosophers in logic and mathematics, and the more specialized papers will also appeal to mathematicians and logicians.

Joseph Larmour (1857-1942) was a theoretical physicist who made important discoveries in relation to the electron theory of matter, as espoused in his 1900 work Aether and Matter. Originally published in 1929, this is the second part of a two-volume set containing Larmour's collected papers. The papers are presented in chronological order across the volumes, enabling readers to understand their theoretical development and framing them in an accessible form for 'future historical interests'. Authorial notes and appendices are also included. This book will be of value to anyone with an interest in the word of Larmour, mathematics physics and the history of science.

Abraham Adrian Albert (1905-72) was an American mathematician primarily known for his groundbreaking work on algebra. In this book, which was originally published in 1938, Albert provides a detailed exposition of 'modern abstract algebra', taking into account numerous discoveries in the field during the preceding ten years. A glossary is included. This is a highly informative book that will be of value to anyone with an interest in the development of algebra and the history of mathematics.

This biography of the mathematician, Sophie Germain, paints a rich portrait of a brilliant and complex woman, the mathematics she developed, her associations with Gauss, Legendre, and other leading researchers, and the tumultuous times in which she lived. Sophie Germain stood right between Gauss and Legendre, and both publicly recognized her scientific efforts. Unlike her female predecessors and contemporaries, Sophie Germain was an impressive mathematician and made lasting contributions to both number theory and the theories of plate vibrations and elasticity. She was able to walk with ease across the bridge between the fields of pure mathematics and engineering physics. Though isolated and snubbed by her peers, Sophie Germain was the first woman to win the prize of mathematics from the French Academy of Sciences. She is the only woman who contributed to the proof of Fermat's Last Theorem. In this unique biography, Dora Musielak has done the impossible she has chronicled Sophie Germain's brilliance through her life and work in mathematics, in a way that is simultaneously informative, comprehensive, and accurate.

This open access book explores commentaries on an influential text of pre-Copernican astronomy in Europe. It features essays that take a close look at key intellectuals and how they engaged with the main ideas of this qualitative introduction to geocentric cosmology. Johannes de Sacrobosco compiled his Tractatus de sphaera during the thirteenth century in the frame of his teaching activities at the then recently founded University of Paris. It soon became a mandatory text all over Europe. As a result, a tradition of commentaries to the text was soon established and flourished until the second half of the 17th century. Here, readers will find an informative overview of these commentaries complete with a rich context. The essays explore the educational and social backgrounds of the writers. They also detail how their careers developed after the publication of their commentaries, the institutions and patrons they were affiliated with, what their agenda was, and whether and how they actually accomplished it. The editor of this collection considers these scientific commentaries as genuine scientific works. The contributors investigate them here not only in reference to the work on which it comments but also, and especially, as independent scientific contributions that are socially, institutionally, and intellectually contextualized around their authors.

This book is a collection of essays on the reception of Leibniz's thinking in the sciences and in the philosophy of science in the 19th and 20th centuries. Authors studied include C.F. Gauss, Georg Cantor, Kurd Lasswitz, Bertrand Russell, Ernst Cassirer, Louis Couturat, Hans Reichenbach, Hermann Weyl, Kurt Goedel and Gregory Chaitin. In addition, we consider concepts and problems central to Leibniz's thought and that of the later authors: the continuum, space, identity, number, the infinite and the infinitely small, the projects of a universal language, a calculus of logic, a mathesis universalis etc. The book brings together two fields of research in the history of philosophy and of science (research on Leibniz, and the research concerned with some major developments in the 19th and 20th centuries); it describes how Leibniz's thought appears in the works of these authors, in order to better understand Leibniz's influence on contemporary science and philosophy; but it also assesses that reception critically, confronting it in particular with the current state of Leibniz research and with the various editions of his work.

This book is a unique collection of challenging geometry problems and detailed solutions that will build students' confidence in mathematics. By proposing several methods to approach each problem and emphasizing geometry's connections with different fields of mathematics, Methods of Solving Complex Geometry Problems serves as a bridge to more advanced problem solving. Written by an accomplished female mathematician who struggled with geometry as a child, it does not intimidate, but instead fosters the reader's ability to solve math problems through the direct application of theorems. Containing over 160 complex problems with hints and detailed solutions, Methods of Solving Complex Geometry Problems can be used as a self-study guide for mathematics competitions and for improving problem-solving skills in courses on plane geometry or the history of mathematics. It contains important and sometimes overlooked topics on triangles, quadrilaterals, and circles such as the Menelaus-Ceva theorem, Simson's line, Heron's formula, and the theorems of the three altitudes and medians. It can also be used by professors as a resource to stimulate the abstract thinking required to transcend the tedious and routine, bringing forth the original thought of which their students are capable. Methods of Solving Complex Geometry Problems will interest high school and college students needing to prepare for exams and competitions, as well as anyone who enjoys an intellectual challenge and has a special love of geometry. It will also appeal to instructors of geometry, history of mathematics, and math education courses.

Luis Antonio Santalo (Spain 1911 - Argentina 2001) contributed to several branches of Geometry, his laying of the mathematical foundations of Stereology and its applications perhaps being his most outstanding achievement. A considerable power of abstraction, a brilliant geometric intuition and an outstanding gift as a disseminator of science were among his virtues. The present volume contains a selection of his best papers. Part I consists of a short biography and some photographs together with a complete list of his publications, classified into research papers, books, and articles on education and the popularization of mathematics, as well as a comprehensive analysis of his contribution to science. Part II, the main part of the book, includes selected papers, arranged into five sections according to the nature of their contents: Differential Geometry, Integral Geometry, Convex Geometry, Affine Geometry, and Statistics and Stereology. Each section is preceded by a commentary by a renowned specialist: Teufel, Langevin, Schneider, Leichtweiss, and Cruz-Orive, respectively. Finally, Part III emphasizes the influence of his work. It contains commentaries by several specialists regarding modern results based on, or closely related to, those of Santalo, some book reviews written by Santalo, as well as some reviews of his books. As a curious addendum, a ranking of his articles, given by Santalo himself, is included.

An important figure in the development of modern mathematical logic and abstract algebra, Augustus De Morgan (1806-71) was also a witty writer who made a hobby of collecting evidence of paradoxical and illogical thinking from historical sources as well as contemporary pamphlets and periodicals. Based on articles that had appeared in The Athenaeum during his lifetime, this work was edited by his widow and published in book form in 1872. It parades all varieties of crackpot, from circle-squarers to inventors of perpetual motion machines, all for the reader's entertainment and education. Filled with anecdotes, personal opinions and 'squibs' of every kind, the book remains enjoyable reading for those who are amused rather than appalled by the human condition. Also reissued in the Cambridge Library Collection are the Memoir of Augustus De Morgan (1882), prepared by his wife, and his ambitious Formal Logic (1847).

This monograph provides a concise introduction to the tangled issues of communication between Russian and Western scientists during the Cold War. It details the extent to which mid-twentieth-century researchers and practitioners were able to communicate with their counterparts on the opposite side of the Iron Curtain. Drawing upon evidence from a range of disciplines, a decade-by-decade account is first given of the varying levels of contact that existed via private correspondence and conference attendance. Next, the book examines the exchange of publications and the availability of one side's work in the libraries of the other. It then goes on to compare general language abilities on opposite sides of the Iron Curtain, with comments on efforts in the West to learn Russian and the systematic translation of Russian work. In the end, author Christopher Hollings argues that physical accessibility was generally good in both directions, but that Western scientists were afflicted by greater linguistic difficulties than their Soviet counterparts whose major problems were bureaucratic in nature. This volume will be of interest to historians of Cold War science, particularly those who study communications and language issues. In addition, it will be an ideal starting pointing for anyone looking to know more about this fascinating area.

Originally published in 1946, this book explains important aspects of the world through the lens of mathematics. McKay discusses important questions such as time, the size of the earth and 'numbers that mean too much' in language that is enthusiastic and easily accessible to non-mathematicians. This book will be of value to anyone with an interest in the history of mathematics.

Newton's Principia paints a picture of the earth as a spinning, gravitating ball. However, the earth is not completely rigid and the interplay of forces will modify its shape in subtle ways. Newton predicted a flattening at the poles, yet others disagreed. Plenty of books have described the expeditions which sought to measure the shape of the earth, but very little has appeared on the mathematics of a problem which remains of enduring interest even in an age of satellites. Published in 1874, this two-volume work by Isaac Todhunter (1820-84), perhaps the greatest Victorian historian of mathematics, takes the mathematical story from Newton, through the expeditions which settled the matter in Newton's favour, to the investigations of Laplace which opened a new era in mathematical physics. Volume 1 traces developments from Newton up to 1780, including coverage of the work of Maupertuis, Clairaut and d'Alembert.

Originally published in 1946 as number thirty-nine in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding linear groups. Appendices are also included. This book will be of value to anyone with an interest in linear groups and the history of mathematics.

Originally published in 1911 as number thirteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book presents a general survey of the problem of the 27 lines upon the cubic surface. Illustrative figures and a bibliography are also included. This book will be of value to anyone with an interest in cubic surfaces and the history of mathematics.

Originally published in 1915, this book contains an English translation of a reconstructed version of Euclid's study of divisions of geometric figures, which survives only partially and in only one Arabic manuscript. Archibald also gives an introduction to the text, its transmission in an Arabic version and its possible connection with Fibonacci's Practica geometriae. This book will be of value to anyone with an interest in Greek mathematics, the history of science or the reconstruction of ancient texts.

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.

After studying both classics and mathematics at the University of Cambridge, Sir Thomas Little Heath (1861-1940) used his time away from his job as a civil servant to publish many works on the subject of ancient mathematics, both popular and academic. First published in 1926 as the second edition of a 1908 original, this book contains the first volume of his three-volume English translation of the thirteen books of Euclid's Elements, covering Books One and Two. This detailed text will be of value to anyone with an interest in Greek geometry and the history of mathematics.

After studying both classics and mathematics at the University of Cambridge, Sir Thomas Little Heath (1861-1940) used his time away from his job as a civil servant to publish many works on the subject of ancient mathematics, both popular and academic. First published in 1926 as the second edition of a 1908 original, this book contains the second volume of his three-volume English translation of the thirteen books of Euclid's Elements, covering Books Three to Nine. This detailed text will be of value to anyone with an interest in Greek geometry and the history of mathematics.

After studying both classics and mathematics at the University of Cambridge, Sir Thomas Little Heath (1861-1940) used his time away from his job as a civil servant to publish many works on the subject of ancient mathematics, both popular and academic. First published in 1926 as the second edition of a 1908 original, this book contains the third and final volume of his three-volume English translation of the thirteen books of Euclid's Elements, covering Books Ten to Thirteen. This detailed text will be of value to anyone with an interest in Greek geometry and the history of mathematics.

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.