The book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-nineteenth century to its consolidation by 1930, and then it considers several attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea. First published in the series Science Networks Historical Studies, Vol. 17 (1996). In the second rev. edition the author has eliminated misprints, revised the chapter on Richard Dedekind, and updated the bibliographical index.

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The larger part of Yearbook 6 of the Institute Vienna Circle constitutes the proceedings of a symposium on Alfred Tarski and his influence on and interchanges with the Vienna Circle, especially those on and with Rudolf Carnap and Kurt Gödel. It is the first time that this topic has been treated on such a scale and in such depth. Attention is mainly paid to the origins, development and subsequent role of Tarski's definition of truth. Some contributions are primarily historical, others analyze logical aspects of the concept of truth. Contributors include Anita and Saul Feferman, Jan Wolenski, Jan Tarski and Hans Sluga. Several Polish logicians contributed: Gzegorczyk, Wójcicki, Murawski and Rojszczak. The volume presents entirely new biographical material on Tarski, both from his Polish period and on his influential career in the United States: at Harvard, in Princeton, at Hunter, and at the University of California at Berkeley. The high point of the analysis involves Tarski's influence on Carnap's evolution from a narrow syntactical view of language, to the ontologically more sophisticated but more controversial semantical view. Another highlight involves the interchange between Tarski and Gödel on the connection between truth and proof and on the nature of metalanguages. The concluding part of Yearbook 6 includes documentation, book reviews and a summary of current activities of the Institute Vienna Circle. Jan Tarski introduces letters written by his father to Gödel; Paolo Parrini reports on the Vienna Circle's influence in Italy; several reviews cover recent books on logical empiricism, on Gödel, on cosmology, on holistic approaches in Germany, and on Mauthner.

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A committed terrorist in Russia, an admired professor in America: the astounding story of Sergei Degaev's double life, told in full detail for the first time Sergei Degaev (1857-1921), a political terrorist in tsarist Russia, disappeared after participating in the assassination of the chief of Russia's security organization in 1883. Those who later knew and admired the quietly brilliant Professor Alexander Pell at the University of South Dakota never guessed this was actually Degaev, who had triple-crossed friends and associates while entangled in the revolutionary movement of his homeland. This book is the first in any language to tell in detail the extraordinary story of one of the world's most intriguing revolutionaries, his role in building and betraying the earliest political terrorist network, and his subsequent conventional academic career in America. The well-known historian Richard Pipes uses previously unexplored Russian archives to draw a brilliant psychological, political, and sociological portrait of Degaev. Pipes pursues his protagonist on a twisting journey of changing loyalties and fateful collaborations within the network that provided the model for all modern terrorist organizations. A cunning conspirator, Degaev went on to reinvent himself in the United States as a beloved mathematics professor. Either of his lives would be considered remarkable; that Degaev lived both is nothing short of amazing.

In 1942, Lt. Herman H. Goldstine, a former mathematics professor, was stationed at the Moore School of Electrical Engineering at the University of Pennsylvania. It was there that he assisted in the creation of the ENIAC, the first electronic digital computer. The ENIAC was operational in 1945, but plans for a new computer were already underway. The principal source of ideas for the new computer was John von Neumann, who became Goldstine's chief collaborator. Together they developed EDVAC, successor to ENIAC. After World War II, at the Institute for Advanced Study, they built what was to become the prototype of the present-day computer. Herman Goldstine writes as both historian and scientist in this first examination of the development of computing machinery, from the seventeenth century through the early 1950s. His personal involvement lends a special authenticity to his narrative, as he sprinkles anecdotes and stories liberally through his text.

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ++++ The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to ensure edition identification: ++++ Annals Of Mathematics, Volumes 7-8 Ormond Stone, Joseph Henry Maclagan Wedderburn, Solomon Lefschetz, Harvard University, University of Virginia, Princeton University, Institute for Advanced Study (Princeton, N.J.) Ormond Stone, Joseph Henry Maclagan Wedderburn, Solomon Lefschetz Princeton University Press, 1893 Education; Teaching Methods & Materials; Mathematics; Education / Teaching Methods & Materials / Mathematics; Juvenile Nonfiction / Mathematics / General; Mathematics; Mathematics / Calculus; Mathematics / General; Mathematics / History & Philosophy; Mathematics / Mathematical Analysis; Mathematics / Study & Teaching

The aim of this book is to explain the shape of Greek mathematical thinking. It can be read on three levels: as a description of the practices of Greek mathematics; as a theory of the emergence of the deductive method; and as a case-study for a general view on the history of science. The starting point for the enquiry is geometry and the lettered diagram. Reviel Netz exploits the mathematicians' practices in the construction and lettering of their diagrams, and the continuing interaction between text and diagram in their proofs, to illuminate the underlying cognitive processes. A close examination of the mathematical use of language follows, especially mathematicians' use of repeated formulae. Two crucial chapters set out to show how mathematical proofs are structured and explain why Greek mathematical practice manages to be so satisfactory. A final chapter looks into the broader historical setting of Greek mathematical practice.

Published in 1938: The new volume presents a full and profusely illustrated account of progress made during the eighteenth century in Mathematics, Mechanics, Astronomy, Physics, Meteorology, Geography, Chemistry, Biology, Medicine, Psychology, Demography, Economics, Philosophy, and Technology.

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The Law of Causality and its Limits was the principal philosophical work of the physicist turned philosopher, Philipp Frank. Born in Vienna on March 20, 1884, Frank died in Cambridge, Massachusetts on July 21, 1966. He received his doctorate in 1907 at the University of Vienna in theoretical physics, having studied under Ludwig Boltzmann; his sub sequent research in physics and mathematics was represented by more than 60 scientific papers. Moreover his great success as teacher and expositor was recognized throughout the scientific world with publication of his collaborative Die Differentialgleichungen der Mechanik und Physik, with Richard von Mises, in 1925-27. Frank was responsible for the second volume, on physics, and especially noted for his authoritative article on classical Hamiltonian mechanics and optics. Among his earliest papers were those, beginning in 1908, devoted to special relativity, which together with general relativity and physical cosmology occupied him throughout his life. Already in 1907, Frank published his seminal paper 'Kausalgesetz und Erfahrung' ('Experience and the Law of Causality'), much later collected with a splendid selection of his essays on philosophy of science, in English (1941c and 1949g, in our Bibliography). Joining the first 'Vienna Circle' in the first decade of the 20th century, with Hans Hahn, mathematician, and Otto Neurath, sociologist and economist, and deeply influenced by studies of Ernst Mach's critical conceptual histories of science and by the striking challenge of Poincare and Duhem, Frank continued his epistemological investigations.

Heralds of Science: As Represented by Two Hundred Epochal Books and Pamphlets is a comprehensive guide to the most significant scientific publications in history. Written by Bern Dibner, a renowned collector of rare scientific books and manuscripts, this book features 200 seminal works that have shaped the course of scientific progress. The book is divided into six sections, each covering a different area of science: astronomy, mathematics, physics, chemistry, medicine, and technology. Each section includes a brief introduction to the field, followed by a selection of books and pamphlets that have had a significant impact on that area of study. The book is beautifully illustrated with full-color photographs of the featured publications, as well as portraits of the scientists who wrote them. The text is written in an accessible style, making it easy for readers of all levels of scientific knowledge to understand and appreciate the importance of these works. Heralds of Science is a must-read for anyone interested in the history of science and the key figures and publications that have shaped our understanding of the world around us. It is a valuable resource for students, researchers, and anyone with a passion for science and its impact on society.This is a new release of the original 1955 edition.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

The transformation of mathematics from its ancient Greek practice to its development in the medieval Arab-speaking world is approached by focusing on a single problem proposed by Archimedes and the many solutions offered. From a practice of mathematics based on the localized solution (originating in the polemical practices of early Greek science), we see a transition to a practice of mathematics based on the systematic approach (grounded in the deuteronomic practices of Late Antiquity and the Middle Ages). A radically new interpretation is accordingly offered of the historical trajectory of pre-modern mathematics.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. • The entire range of modal logic is covered• Serves as a singular contribution to the intellectual history of the 20th century• Contains the latest scholarly discoveries and interpretative insights