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The volume contains a comprehensive and problem-oriented presentation of ancient Greek mathematics from Thales to Proklos Diadochos. Exemplarily, a cross-section of Greek mathematics is offered, whereby also such works of scientists are appreciated in detail, of which no German translation is available. Numerous illustrations and the inclusion of the cultural, political and literary environment provide a great spectrum of the history of mathematical science and a real treasure trove for those seeking biographical and contemporary background knowledge or suggestions for lessons or lectures. The presentation is up-to-date and realizes tendencies of recent historiography. In this book, the central chapters on Plato, Aristotle and Alexandria have been updated. The explanations of Greek calculus, mathematical geography and mathematics of the early Middle Ages have been expanded and show new points of view. A completely new addition is a unique illustrated account of Roman mathematics. Also newly included are several color illustrations that successfully illustrate the book's subject matter. With more than 280 images, this volume represents a richly illustrated history book on ancient mathematics. The author Dietmar Herrmann studied mathematics and physics at the Technical University of Munich, graduating with a state examination in 1972. In addition to serving as a high school teacher, he was a successful author of books on programming languages and applied mathematics (statistics, numerics). As a lecturer at the Munich University of Applied Sciences he held lectures on mathematics and computer science for 15 years. As a retired director of studies, he devotes himself to the history of mathematics, which has interested him since his student days. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Mathematics --- History --- geschiedenis --- wiskunde --- Mathematics. --- History. --- History of Mathematical Sciences. --- Matemàtica grega --- Història de la matemàtica
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Places Ellis at the heart of early-Victorian Cambridge with in-depth descriptions on his scientific work and tragic life Provides a unique glimpse into Victorian intellectual culture, based on previously unpublished archival materials This open access book brings together for the first time all aspects of the tragic life and fascinating work of the polymath Robert Leslie Ellis (1817–1859), placing him at the heart of early-Victorian intellectual culture. Written by a diverse team of experts, the chapters in the book’s first part contain in-depth examinations of, among other things, Ellis’s family, education, Bacon scholarship and mathematical contributions. The second part consists of annotated transcriptions of a selection of Ellis’s diaries and correspondence. Taken together, A Prodigy of Universal Genius: Robert Leslie Ellis, 1817–1859 is a rich resource for historians of science, historians of mathematics and Victorian scholars alike. Robert Leslie Ellis was one of the most intriguing and wide-ranging intellectual figures of early Victorian Britain, his contributions ranging from advanced mathematical analysis to profound commentaries on philosophy and classics and a decisive role in the orientation of mid-nineteenth century scholarship. This very welcome collection offers both new and authoritative commentaries on the work, setting it in the context of the mathematical, philosophical and cultural milieux of the period, together with fascinating passages from the wealth of unpublished papers Ellis composed during his brief and brilliant career. - Simon Schaffer, Department of History and Philosophy of Science, University of Cambridge
History of Western philosophy --- History of science --- Interdisciplinary studies --- History of mathematics --- Cultural studies --- Robert Leslie Ellis --- the Cambridge network --- mathematical education --- William Whewell --- history of science in Britain --- the history of ideas --- early-Victorian Cambridge --- history of mathematical sciences --- Victorian intellectual culture --- life of Robert Leslie Ellis
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In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.
Axioms. --- Geometry --- Mathematics --- Parallels (Geometry) --- Philosophy --- Foundations --- Axiomes --- Filosofia --- Matemàtica --- Teoria axiomàtica de conjunts --- Mathematical logic. --- Mathematics. --- History. --- Mathematical Logic and Foundations. --- Philosophy of Mathematics. --- History of Mathematical Sciences. --- Philosophy. --- Math --- Science --- Logic of mathematics --- Mathematics, Logic of --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Logic, Symbolic and mathematical.
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The purpose of this volume is to understand and outline the evolution of the objectives and field of action of the International Commission on Mathematical Instruction (ICMI) from its creation in 1908 in Rome until 2008, through an analysis of the main events and protagonists of its history. It consists of three parts, each exploring different facets of these hundred years of ICMI’s life. In Part I, four chapters retrace the three main phases in the century of ICMI's life: The foundation and early period up to WWI (Chapter 1); The rebirth in 1952 as a permanent subcommission of the International Mathematical Union and the broadening of the scope of action until Freudenthal’s innovations (Chapter 2); The “Renaissance” in the late 1960s and further development up to 2008 (Chapter 3). Chapter 4 presents a wide selection of unpublished letters and documents belonging to the period 1908-1974, coming from different archives, especially from the IMU Archives in Berlin. Part II presents useful data about the life of ICMI: The Timeline of ICMI, 1908-2008; The Central and Executive Committees of the Commission (1908 -2009); The Terms of Reference for ICMI (1954-2007); Mathematics Education in the International Congresses of Mathematicians (1897-2006); Maps on the process of internationalization of ICMI; Data concerning the first ICME (Lyon 1969). Part III contains biographical portraits of the 54 members of the Central/Executive Committee of ICMI who passed away in the first hundred years of the Commission, and also includes the portraits of scholars awarded the title of Honorary Member of the Commission during the International Congress of Mathematicians in Oslo (1936), and of Charles-Ange Laisant, one of the founders of the journal L’Enseignement Mathématique, the official organ of ICMI. The portraits in Part III of the volume are designed according to a particular point of view because they focus on the actual involvement of these scholars in ICMI’s development and, more generally, in mathematics education.
Mathematics—Study and teaching. --- Mathematics. --- History. --- Education—History. --- Social history. --- Mathematics Education. --- History of Mathematical Sciences. --- History of Education. --- Social History. --- Descriptive sociology --- Social conditions --- Social history --- History --- Sociology --- Math --- Science --- Ensenyament de la matemàtica --- Història de la matemàtica --- Història de la ciència --- Matemàtica --- Aprenentatge de la matemàtica --- Ensenyament de les matemàtiques --- Ensenyament --- Mathematics --- Education --- Study and teaching . --- Teaching --- Study and teaching.
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During his lifetime, Kurt Gödel was not well known outside the professional world of mathematicians, philosophers and theoretical physicists. Early in his career, for his doctoral thesis and then for his Habilitation (Dr.Sci.), he wrote earthshaking articles on the completeness and provability of mathematical-logical systems, upsetting the hypotheses of the most famous mathematicians/philosophers of the time. He later delved into theoretical physics, finding a unique solution to Einstein’s equations for gravity, the ‘Gödel Universe’, and made contributions to philosophy, the guiding theme of his life. This book includes more details about the context of Gödel’s life than are found in earlier biographies, while avoiding an elaborate treatment of his mathematical/scientific/philosophical works, which have been described in great detail in other books. In this way, it makes him and his times more accessible to general readers, and will allow them to appreciate the lasting effects of Gödel’s contributions (the latter in a more up-to-date context than in previous biographies, many of which were written 15–25 years ago). His work spans or is relevant to a wide spectrum of intellectual endeavor, and this is emphasized in the book, with recent examples. This biography also examines possible sources of his unusual personality, which combined mathematical genius with an almost childlike naiveté concerning everyday life, and striking scientific innovations with timidity and hesitancy in practical matters. How he nevertheless had a long and successful career, inspiring many younger scholars along the way, with the help of his loyal wife Adele and some of his friends, is a fascinating story in human nature.
Mathematical logic --- History of philosophy --- Pure sciences. Natural sciences (general) --- Mathematics --- History --- wetenschapsgeschiedenis --- filosofie --- geschiedenis --- wiskunde --- logica --- Astronomer --- Physicists --- Mathematics. --- History. --- Mathematical logic. --- Astronomers --- Science --- Philosophy --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Biographies of Physicists and Astronomers. --- History of Science. --- History of Philosophy. --- Biography. --- Matemàtics --- Gödel, Kurt. --- Àustria --- Gödel, Kurt --- Logic, Symbolic and mathematical.
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This volume offers English translations of three early works by Ernst Schröder (1841-1902), a mathematician and logician whose philosophical ruminations and pathbreaking contributions to algebraic logic attracted the admiration and ire of figures such as Dedekind, Frege, Husserl, and C. S. Peirce. Today he still engages the sympathetic interest of logicians and philosophers. The works translated record Schröder’s journey out of algebra into algebraic logic and document his transformation of George Boole’s opaque and unwieldy logical calculus into what we now recognize as Boolean algebra. Readers interested in algebraic logic and abstract algebra can look forward to a tour of the early history of those fields with a guide who was exceptionally thorough, unfailingly honest, and deeply reflective.
Mathematical logic --- Logic --- Didactics of mathematics --- Algebra --- Mathematics --- History --- algebra --- didactiek --- geschiedenis --- wiskunde --- logica --- Logic. --- Mathematical logic. --- Universal algebra. --- Mathematics. --- History. --- Mathematics—Study and teaching. --- Mathematical Logic and Foundations. --- General Algebraic Systems. --- History of Mathematical Sciences. --- Mathematics Education. --- Logic, Symbolic and mathematical. --- Algebra, Universal.
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The first book-length study to address issues in modal logic at the eve of the Renaissance, this monograph provides important new insights into the way the debates on modal logic during the post-medieval period tied in with the so-called Wegestreit, the divide between the via antiqua and via moderna that dominated the discourse on logic during the 15th and early 16th centuries. The focus of the book is on the logic and philosophy of language of John Fabri of Valenciennes (fl. c. 1500), one of the last exponents of the terminist approach to logic that was bitterly criticized by the humanist movement. By means of a careful reconstruction of Fabri’s text, the book argues that Fabri's modal logic ultimately goes back to the work of John Buridan, and represents the same approach to the topic as the modal logics that were developed by adherents of the via moderna in Paris. This has significant implications for the historiography of post-medieval philosophy. Fabri was active in Louvain, which until the late 16th century was the most important intellectual center in the Low Countries. According to a long-standing tradition in the scholarship, Louvain was one of the few bulwarks of via antiqua logic on the map of post-medieval Europe. The book argues that this thesis is at least in part a scholarly fiction, and thus in need of revision. By shedding light on an author whose thought has thus far remained entirely unstudied, it also constitutes a valuable step towards a history of philosophy without any gaps. The book is aimed at graduate students and researchers in the history of logic and philosophy, but will also be of interest to intellectual historians, historians of ideas, and to any contemporary modal logician who is interested in the historical roots of their discipline.
Modality (Logic) --- Semantics (Philosophy) --- Intension (Philosophy) --- Logical semantics --- Semantics (Logic) --- Semeiotics --- Significs --- Syntactics --- Unified science --- Language and languages --- Logic, Symbolic and mathematical --- Logical positivism --- Meaning (Psychology) --- Philosophy, Modern --- Semiotics --- Signs and symbols --- Symbolism --- Analysis (Philosophy) --- Definition (Philosophy) --- Modal logic --- Logic --- Nonclassical mathematical logic --- Bisimulation --- Philosophy --- Logic. --- Science --- Mathematics. --- History. --- History of Philosophy. --- History of Science. --- History of Mathematical Sciences. --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Psychology --- Reasoning --- Thought and thinking --- Math --- Methodology
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During his lifetime, Kurt Gödel was not well known outside the professional world of mathematicians, philosophers and theoretical physicists. Early in his career, for his doctoral thesis and then for his Habilitation (Dr.Sci.), he wrote earthshaking articles on the completeness and provability of mathematical-logical systems, upsetting the hypotheses of the most famous mathematicians/philosophers of the time. He later delved into theoretical physics, finding a unique solution to Einstein’s equations for gravity, the ‘Gödel Universe’, and made contributions to philosophy, the guiding theme of his life. This book includes more details about the context of Gödel’s life than are found in earlier biographies, while avoiding an elaborate treatment of his mathematical/scientific/philosophical works, which have been described in great detail in other books. In this way, it makes him and his times more accessible to general readers, and will allow them to appreciate the lasting effects of Gödel’s contributions (the latter in a more up-to-date context than in previous biographies, many of which were written 15–25 years ago). His work spans or is relevant to a wide spectrum of intellectual endeavor, and this is emphasized in the book, with recent examples. This biography also examines possible sources of his unusual personality, which combined mathematical genius with an almost childlike naiveté concerning everyday life, and striking scientific innovations with timidity and hesitancy in practical matters. How he nevertheless had a long and successful career, inspiring many younger scholars along the way, with the help of his loyal wife Adele and some of his friends, is a fascinating story in human nature.
Matemàtics --- Gödel, Kurt. --- Àustria --- Científics --- Dones matemàtiques --- Matemàtica --- Gödel, Kurt, --- Autriche --- Österreich --- República d'Àustria --- Republik Österreich --- Europa central --- Països de la Unió Europea --- Països de parla alemanya --- Alta Àustria (Àustria) --- Baixa Àustria (Àustria) --- Estíria (Àustria) --- Salzkammergut (Àustria) --- Semmering (Àustria : Port de muntanya) --- Tirol (Àustria) --- Viena (Àustria) --- Vorarlberg (Àustria) --- Àustria-Hongria --- Sacre Imperi Romanogermànic --- Mathematicians --- Mathematics. --- Gödel, Kurt. --- Math --- Science --- Gkentel, Kourt --- גדל --- Gödel, Kurt --- History. --- Mathematical logic. --- Physicists --- Astronomers --- Philosophy --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Biographies of Physicists and Astronomers. --- History of Science. --- History of Philosophy. --- Biography. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism
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