This is a translated autobiography of applied mathematician N. N. Moiseev, providing an insider's view of the history of the Soviet Union from its founding in 1917 to its collapse in 1991, as well as a little of the aftermath.We see vividly the precariousness of life just after the October Revolution; his happy family life during the years 1921-28 of Lenin's New Economic Policy; the subsequent destruction of his family by Stalin's regime; his trials as a social outcast; his student days at Moscow State University; his experiences as a Soviet Air Force Engineer in World War II, including sorties as a gunner and a brush with an NKVD agent; post-war euphoria, marriage, and another round of ostracism; and then the vicissitudes of a highly varied academic career. Here we meet many famous Soviet and Western engineers and scientists. The last several chapters are devoted more to wide-ranging reflections on God, philosophy, science, communism, modelling the biosphere, and the threat of nuclear winter. His thoughts concerning the impending and then final collapse of the USSR, as well as hopes for Russia's future, conclude the journey through Moiseev's life.

Originally published in 1913 as number fourteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding the properties of the twisted cubic. A bibliography and appendix section are also included. This book will be of value to anyone with an interest in the twisted cubic and the history of mathematics.

Originally published in 1910 as number eleven in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book deals with differential calculus and its underlying structures. Appendices on further reading and clarification of certain points are also included. This tract will be of value to anyone with an interest in the history of mathematics or calculus.

Originally published in 1932 as number twenty=seven in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account of the theory of modular invariants as embodied in the work of Dickson, Glenn and Hazlett. Appendices are included. This book will be of value to anyone with an interest in modular invariants and the history of mathematics.

First published in 1913, as the second edition of a 1905 original, this book is the first volume in the Cambridge Tracts in Mathematics and Mathematical Physics Series. The text provides a concise account regarding volume and surface integrals used in physics. This book will be of value to anyone with an interest in integrals and physics.

Originally published in 1915 as number eighteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, and here reissued in its 1952 reprinted form, this book contains a condensed account of Dirichlet's Series, which relates to number theory. This tract will be of value to anyone with an interest in the history of mathematics or in the work of G. H. Hardy.

Originally published in 1908 as number nine in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding the invariant theory connected with a single quadratic differential form. This book will be of value to anyone with an interest in quadratic differential forms and the history of mathematics.

Originally published in 1914 as number fifteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise proof of Cauchy's Theorem, along with some applications of the theorem to the evaluation of definite integrals. 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 2 is largely devoted to the work of Laplace, tracing developments up to 1825.

First published in 1930, as the third edition of a 1907 original, this book forms number six in the Cambridge Tracts in Mathematics and Mathematical Physics Series. The text gives a concise account of the theory of equations according to the ideas of Galois. This book will be of value to anyone with an interest in algebra and the history of mathematics.

Originally published in 1910 as number twelve in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides an up-to-date version of Du Bois-Reymond's Infinitarcalcul by the celebrated English mathematician G. H. Hardy. This tract will be of value to anyone with an interest in the history of mathematics or the theory of functions.

Originally published in 1914 as number sixteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding the theory of linear associative algebras. Textual notes are incorporated throughout. This book will be of value to anyone with an interest in algebra and the history of mathematics.

Originally published in 1936 as part of the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding the rational quartic curve in space of three and four dimensions. Textual notes are also included. This book will be of value to anyone with an interest in rational curves and the history of mathematics.

This open access book provides an overview of Felix Klein's ideas, highlighting developments in university teaching and school mathematics related to Klein's thoughts, stemming from the last century. It discusses the meaning, importance and the legacy of Klein's ideas today and in the future, within an international, global context. Presenting extended versions of the talks at the Thematic Afternoon at ICME-13, the book shows that many of Klein's ideas can be reinterpreted in the context of the current situation, and offers tips and advice for dealing with current problems in teacher education and teaching mathematics in secondary schools. It proves that old ideas are timeless, but that it takes competent, committed and assertive individuals to bring these ideas to life. Throughout his professional life, Felix Klein emphasised the importance of reflecting upon mathematics teaching and learning from both a mathematical and a psychological or educational point of view. He also strongly promoted the modernisation of mathematics in the classroom, and developed ideas on university lectures for student teachers, which he later consolidated at the beginning of the last century in the three books on elementary mathematics from a higher standpoint.

The aim of this monograph is to describe Greek mathematics as a literary product, studying its style from a logico-syntactic point of view and setting parallels with logical and grammatical doctrines developed in antiquity. In this way, major philosophical themes such as the expression of mathematical generality and the selection of criteria of validity for arguments can be treated without anachronism. Thus, the book is of interest for both historians of ancient philosophy and specialists in Ancient Greek, in addition to historians of mathematics. This volume is divided into five parts, ordered in decreasing size of the linguistic units involved. The first part describes the three stylistic codes of Greek mathematics; the second expounds in detail the mechanism of "validation"; the third deals with the status of mathematical objects and the problem of mathematical generality; the fourth analyzes the main features of the "deductive machine," i.e. the suprasentential logical system dictated by the traditional division of a mathematical proposition into enunciation, setting-out, construction, and proof; and the fifth deals with the sentential logical system of a mathematical proposition, with special emphasis on quantification, modalities, and connectors. A number of complementary appendices are included as well.

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.

This book is dedicated to V.A. Yankov's seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov's results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics. The book also contains an exposition of Yankov's revolutionary approach to constructive proof theory. The editors also include Yankov's contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.

Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the social and political problems of their times. What we have sought to document is mathematics' central position in the culture of our day. Space has been made not only for the great mathematicians but also for literary texts, including contributions by two apparent interlopers, Robert Musil and Raymond Queneau, for whom mathematical concepts represented a valuable tool for resolving the struggle between 'soul and precision.'

Karl Menger (1902--1985), a pure mathematician of distinction, also took an active interest in both philosophy and economics. In this memoir, which he was composing at the time of his death, he relates how all these subjects developed and flourished against the Viennese background (itself described in depth and with affection), and did so despite the political developments of the '20s and '30s, which depressed but did not silence him. He continued his work in the United States. The memoir describes his membership of the Vienna Circle (the scientifically minded philosophers that gathered around Moritz Schlick) for whom he was an invaluable intermediary, bringing them into contact with Brouwer's intuitionism, with the work of the Polish logicians, especially that of Tarski, but more generally with rigorous mathematical thinking. Indeed, the other Viennese group described here is the Mathematical Colloquium, which he founded, whose Proceedings (still read) show it to have been a powerhouse of ideas. There are also valuable chapters on philosophy and mathematics in the Poland of the '20s and '30s and the U.S. of the '30s and '40s. The memoir devotes particular attention to Wittgenstein (with whose family Menger was acquainted) and to GAdel, whom he was instrumental in bringing to America. The genesis of Menger's own writings on philosophy is also described and the work abounds in mathematical examples lucidly applied to that subject. This volume (which can now be placed beside the two by Menger already published in the Vienna Circle Collection) gives an unequalled impression of the fruitful interdisciplinarity of the tradition to which he partly belonged and partly created. It testifiesboth to Menger's power to inspire and to the critical eye he always turned on even the philosophers he most approved of. A brief account of his life is given in an Introduction by the Editors (all of whom knew him personally), and his important contribution to the social sciences -- only touched on in the text -- is elucidated by Professor Lionello Punzo.

This proceedings volume collects the stories of mathematicians and scientists who have spent and developed parts of their careers and life in countries other than those of their origin. The reasons may have been different in different periods but were often driven by political or economic circumstances: The lack of suitable employment opportunities in their home countries, adverse political systems, and wars have led to the emigration of scientists. The volume shows that these movements have played an important role in spreading scientific knowledge and have often changed the scientific landscape, tradition and future of studies and research fields. The book analyses in particular: aspects of Euler's, Lagrange's and Boscovich's scientific biographies, migrations of scientists from France, Spain and Greece to Russia in the eighteenth and nineteenth centuries, and from Russia to France in the twentieth century, exiles from Italy before the Italian Risorgimento, migrations inside Europe and the escape of mathematicians from Nazi-fascist Europe, between the two World Wars, as well as the mobility of experts around the world. It includes selected contributions from the symposium In Foreign Lands: The Migration of Scientists for Political or Economic Reasons held at the Conference of the International Academy of the History of Science in Athens (September 2019).

William Burnside [1852-1927] was a scholar of international renown, a colourful figure, and a pure mathematician who established abstract algebra as a subject of serious study in Britain. This edition of Collected Papers, enhanced by a series of critical essays, is of major importance to scholars in group theory and the history of mathematics.

This volume contains fourteen papers that were presented at the 2016 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Societe Canadienne d'Histoire et de Philosophie des Mathematiques, held at the University of Calgary in Alberta, Canada. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics, this meeting also honored the life and work of the logician and philosopher of mathematics Aldo Antonelli (1962-2015). The first four papers in this book are part of that remembrance and have a philosophical focus. Included in these are a discussion of Bolzano's objections to Kant's philosophy of mathematics and an examination of the influence of rhetorical and poetic aesthetics on the development of symbols in the 16th and 17th Centuries. The remaining papers deal with the history of mathematics and cover such subjects as Early schemes for polar ordinates in the work of L'Hopital, based on lessons given to him by Bernoulli A method devised by Euler for determining if a number is a sum of two squares Playfair's Axiom and what it reveals about the history of 19th-Century mathematics education The modern library classification system for mathematical subjects An exploration of various examples of sundials throughout Paris Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.

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 ...

The book offers a collection of essays on various aspects of Leibniz's scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz's logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz's scientific works through modern mathematical tools, and compare Leibniz's results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz's work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz's researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.

Professor Atiyah is one of the greatest living mathematicians and is well known throughout the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still at the peak of his career. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into six volumes, divided thematically for easy reference by individuals interested in a particular subject.
This sixth volume in Michael Atiyah's collected works contains a selection of his publications since 1987, including his work on skyrmions, "Atiyah's axioms" for topological quantum field theories, monopoles, knots, K-theory, equivariant problems, point particles, and M-theory.