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| david hilbert: David Hilbert and the Axiomatization of Physics (1898–1918) L. Corry, 2013-06-29 David Hilbert (1862-1943) was the most influential mathematician of the early twentieth century and, together with Henri Poincaré, the last mathematical universalist. His main known areas of research and influence were in pure mathematics (algebra, number theory, geometry, integral equations and analysis, logic and foundations), but he was also known to have some interest in physical topics. The latter, however, was traditionally conceived as comprising only sporadic incursions into a scientific domain which was essentially foreign to his mainstream of activity and in which he only made scattered, if important, contributions. Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert’s intense, original, well-informed, and highly influential involvement with physics, that spanned his entire career and that constituted a truly main focus of interest in his scientific horizon. His program for axiomatizing physical theories provides the connecting link with his research in more purely mathematical fields, especially geometry, and a unifying point of view from which to understand his physical activities in general. In particular, the now famous dialogue and interaction between Hilbert and Einstein, leading to the formulation in 1915 of the generally covariant field-equations of gravitation, is adequately explored here within the natural context of Hilbert’s overall scientific world-view. This book will be of interest to historians of physics and of mathematics, to historically-minded physicists and mathematicians, and to philosophers of science. |
| david hilbert: The Foundations of Geometry David Hilbert, 2015-05-06 This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis. |
| david hilbert: Geometry and the Imagination David Hilbert, Stephan Cohn-Vossen, 1999 This remarkable book endures as a true masterpiece of mathematical exposition. The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. Geometry and the Imagination is full of interesting facts, many of which you wish you had known before. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in $\mathbb{R}^3$. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $\pi/4 = 1 - 1/3 + 1/5 - 1/7 + - \ldots$. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is ``Projective Configurations''. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the pantheon of great mathematics books. |
| david hilbert: David Hilbert's Lectures on the Foundations of Physics 1915-1927 Tilman Sauer, Ulrich Majer, 2009-08-06 These documents do nothing less than bear witness to one of the most dramatic changes in the foundations of science. The book has three sections that cover general relativity, epistemological issues, and quantum mechanics. This fascinating work will be a vital text for historians and philosophers of physics, as well as researchers in related physical theories. |
| david hilbert: The Theory of Algebraic Number Fields David Hilbert, 2013-03-14 Constance Reid, in Chapter VII of her book Hilbert, tells the story of the writing of the Zahlbericht, as his report entitled Die Theorie der algebra is chen Zahlkorper has always been known. At its annual meeting in 1893 the Deutsche Mathematiker-Vereinigung (the German Mathematical Society) invited Hilbert and Minkowski to prepare a report on the current state of affairs in the theory of numbers, to be completed in two years. The two mathematicians agreed that Minkowski should write about rational number theory and Hilbert about algebraic number theory. Although Hilbert had almost completed his share of the report by the beginning of 1896 Minkowski had made much less progress and it was agreed that he should withdraw from his part of the project. Shortly afterwards Hilbert finished writing his report on algebraic number fields and the manuscript, carefully copied by his wife, was sent to the printers. The proofs were read by Minkowski, aided in part by Hurwitz, slowly and carefully, with close attention to the mathematical exposition as well as to the type-setting; at Minkowski's insistence Hilbert included a note of thanks to his wife. As Constance Reid writes, The report on algebraic number fields exceeded in every way the expectation of the members of the Mathemati cal Society. They had asked for a summary of the current state of affairs in the theory. They received a masterpiece, which simply and clearly fitted all the difficult developments of recent times into an elegantly integrated theory. |
| david hilbert: Methods of Mathematical Physics Harold Jeffreys, Bertha Jeffreys, 1999-11-18 This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical applications: this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the text: these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter. |
| david hilbert: Hilbert's Programs and Beyond Wilfried Sieg, 2013-01-24 Hilbert's Programs & Beyond presents the foundational work of David Hilbert in a sequence of thematically organized essays. They first trace the roots of Hilbert's work to the radical transformation of mathematics in the 19th century and bring out his pivotal role in creating mathematical logic and proof theory. They then analyze techniques and results of classical proof theory as well as their dramatic expansion in modern proof theory. This intellectual experience finally opens horizons for reflection on the nature of mathematics in the 21st century: Sieg articulates his position of reductive structuralism and explores mathematical capacities via computational models. |
| david hilbert: Axiomatic Thinking I Fernando Ferreira, Reinhard Kahle, Giovanni Sommaruga, 2022-10-13 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. Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com. |
| david hilbert: The World Formula Norbert Schwarzer, 2022-01-30 Surely the reader had come across situations where he would have given his life to get the “final answer”, the reason for our existence, a Theory of Everything, a true World Formula that contains it all... So did the author of this book. There was this deep-seated and forever unquenchable thirst for fundamental explanations on the one hand, and then there was this very special motivation from somebody else who needed this knowledge, on the other: “How to explain the world to my dying child?” Perhaps this provided the driving force to actually start this million-mile-long journey with the first small—and very tentative—step. Considering all the efforts taken, money spent, disputes fought, papers and books written, and conferences held, it is almost shocking to find that, in principle, the World Formula was already there. It was David Hilbert who wrote it down during World War I in November 1915. The complexity of the math involved was not the only thing that obscured what should have been obvious. This book explains why apparently only very few people had realized his immortal stroke of genius. |
| david hilbert: David Hilbert’s Lectures on the Foundations of Geometry 1891–1902 Michael Hallett, Ulrich Majer, 2004-05-17 This volume contains six sets of notes for lectures on the foundations of geometry held by Hilbert in the period 1891-1902. It also reprints the first edition of Hilbert’s celebrated Grundlagen der Geometrie of 1899, together with the important additions which appeared first in the French translation of 1900. The lectures document the emergence of a new approach to foundational study and contain many reflections and investigations which never found their way into print. |
| david hilbert: Beginning Functional Analysis Karen Saxe, 2013-04-17 This book is designed as a text for a first course on functional analysis for ad vanced undergraduates or for beginning graduate students. It can be used in the undergraduate curriculum for an honors seminar, or for a capstone course. It can also be used for self-study or independent study. The course prerequisites are few, but a certain degree of mathematical sophistication is required. A reader must have had the equivalent of a first real analysis course, as might be taught using [25] or [109], and a first linear algebra course. Knowledge of the Lebesgue integral is not a prerequisite. Throughout the book we use elementary facts about the complex numbers; these are gathered in Appendix A. In one spe cific place (Section 5.3) we require a few properties of analytic functions. These are usually taught in the first half of an undergraduate complex analysis course. Because we want this book to be accessible to students who have not taken a course on complex function theory, a complete description of the needed results is given. However, we do not prove these results. |
| david hilbert: Proof Theory Vincent F. Hendricks, Stig Andur Pedersen, Klaus Frovin Jørgensen, 2013-03-09 hiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math ematicians, logicians and historians of mathematics could exchange ideas pertaining to the historical and philosophical development of proof theory. Hence the conference was called Proof Theory: History and Philosophical Significance. To quote from the conference abstract: Proof theory was developed as part of Hilberts Programme. According to Hilberts Programme one could provide mathematics with a firm and se cure foundation by formalizing all of mathematics and subsequently prove consistency of these formal systems by finitistic means. Hence proof theory was developed as a formal tool through which this goal should be fulfilled. It is well known that Hilbert's Programme in its original form was unfeasible mainly due to Gtldel's incompleteness theorems. Additionally it proved impossible to formalize all of mathematics and impossible to even prove the consistency of relatively simple formalized fragments of mathematics by finitistic methods. In spite of these problems, Gentzen showed that by extending Hilbert's proof theory it would be possible to prove the consistency of interesting formal systems, perhaps not by finitis tic methods but still by methods of minimal strength. This generalization of Hilbert's original programme has fueled modern proof theory which is a rich part of mathematical logic with many significant implications for the philosophy of mathematics. |
| david hilbert: David Hilbert and the Axiomatization of Physics (1898–1918) L. Corry, 2004-11-01 David Hilbert (1862-1943) was the most influential mathematician of the early twentieth century and, together with Henri Poincaré, the last mathematical universalist. His main known areas of research and influence were in pure mathematics (algebra, number theory, geometry, integral equations and analysis, logic and foundations), but he was also known to have some interest in physical topics. The latter, however, was traditionally conceived as comprising only sporadic incursions into a scientific domain which was essentially foreign to his mainstream of activity and in which he only made scattered, if important, contributions. Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert’s intense, original, well-informed, and highly influential involvement with physics, that spanned his entire career and that constituted a truly main focus of interest in his scientific horizon. His program for axiomatizing physical theories provides the connecting link with his research in more purely mathematical fields, especially geometry, and a unifying point of view from which to understand his physical activities in general. In particular, the now famous dialogue and interaction between Hilbert and Einstein, leading to the formulation in 1915 of the generally covariant field-equations of gravitation, is adequately explored here within the natural context of Hilbert’s overall scientific world-view. This book will be of interest to historians of physics and of mathematics, to historically-minded physicists and mathematicians, and to philosophers of science. |
| david hilbert: Hilbert's Programs and Beyond Wilfried Sieg, 2013-03-07 David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations. |
| david hilbert: The Development of Modern Logic Leila Haaparanta, 2009-06-18 This edited volume presents a comprehensive history of modern logic from the Middle Ages through the end of the twentieth century. In addition to a history of symbolic logic, the contributors also examine developments in the philosophy of logic and philosophical logic in modern times. The book begins with chapters on late medieval developments and logic and philosophy of logic from Humanism to Kant. The following chapters focus on the emergence of symbolic logic with special emphasis on the relations between logic and mathematics, on the one hand, and on logic and philosophy, on the other. This discussion is completed by a chapter on the themes of judgment and inference from 1837-1936. The volume contains a section on the development of mathematical logic from 1900-1935, followed by a section on main trends in mathematical logic after the 1930s. The volume goes on to discuss modal logic from Kant till the late twentieth century, and logic and semantics in the twentieth century; the philosophy of alternative logics; the philosophical aspects of inductive logic; the relations between logic and linguistics in the twentieth century; the relationship between logic and artificial intelligence; and ends with a presentation of the main schools of Indian logic. The Development of Modern Logic includes many prominent philosophers from around the world who work in the philosophy and history of mathematics and logic, who not only survey developments in a given period or area but also seek to make new contributions to contemporary research in the field. It is the first volume to discuss the field with this breadth of coverage and depth, and will appeal to scholars and students of logic and its philosophy. |
| david hilbert: Genius Genes Michael Fitzgerald, Brendan O'Brien, 2007 Arguing that highly creative people are largely ?born and not made, ? the authors of Genius Genes: How Asperger Talents Changed the World present case studies of the lives of 21 famous individuals, tying their personalities, talents and lifestyles to the major characteristics of Asperger Syndrome. Subjects range from the well-known to some more obscure, including political/military figures (Thomas Jefferson, Thomas ?Stonewall? Jackson, Bernard Law Montgomery and Charles de Gaulle), mathematicians (Archimedes, Charles Babbage, Paul Erd?s, Norbert Wiener, David Hilbert, and Kurt G?del), scientists (Isaac Newton, Charles Darwin, Albert Einstein, Nikola Tesla, Henry Cavendish and Gregor Mendel), writers (Gerard Manley Hopkins and H. G. Wells), plus maverick aviator Charles Lindbergh, psychologist John Broadus Watson and sexologist Alfred C. Kinsey. |
| david hilbert: Global Bifurcation Theory and Hilbert’s Sixteenth Problem V. Gaiko, 2013-11-27 On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk Mathematical problems at the Second Interna tional Congress of Mathematicians in Paris. The talk covered practically all directions of mathematical thought of that time and contained a list of 23 problems which determined the further development of mathema tics in many respects (1, 119]. Hilbert's Sixteenth Problem (the second part) was stated as follows: Problem. To find the maximum number and to determine the relative position of limit cycles of the equation dy Qn(X, y) -= dx Pn(x, y)' where Pn and Qn are polynomials of real variables x, y with real coeffi cients and not greater than n degree. The study of limit cycles is an interesting and very difficult problem of the qualitative theory of differential equations. This theory was origi nated at the end of the nineteenth century in the works of two geniuses of the world science: of the Russian mathematician A. M. Lyapunov and of the French mathematician Henri Poincare. A. M. Lyapunov set forth and solved completely in the very wide class of cases a special problem of the qualitative theory: the problem of motion stability (154]. In turn, H. Poincare stated a general problem of the qualitative analysis which was formulated as follows: not integrating the differential equation and using only the properties of its right-hand sides, to give as more as possi ble complete information on the qualitative behaviour of integral curves defined by this equation (176]. |
| david hilbert: The Foundations of Geometry David Hilbert, 2023-10-01 The Foundations of Geometry by David Hilbert: The Foundations of Geometry is a groundbreaking work by mathematician David Hilbert that explores the fundamental principles and axioms of geometry. Hilbert presents a rigorous and comprehensive framework for understanding the logical foundations of geometry, laying the groundwork for further advancements in mathematical thinking. Key Aspects of the Book “The Foundations of Geometry”: Axiomatic Approach: Hilbert's work introduces an axiomatic approach to geometry, emphasizing the importance of precise definitions, logical deductions, and the systematic development of geometric concepts. He establishes a set of axioms and explores their implications, providing a solid foundation for the study of geometry and mathematical reasoning. Geometric Systems: The book delves into different geometric systems, such as Euclidean geometry, non-Euclidean geometries (like hyperbolic and elliptic geometries), and projective geometry. Hilbert explores the relationships between these systems, elucidating their distinctive properties, postulates, and implications for mathematical understanding. Logical Consistency: Hilbert's emphasis on logical consistency and rigor makes The Foundations of Geometry a seminal work in the field. He demonstrates the power of logical reasoning, the importance of clear definitions, and the significance of axiomatic systems in establishing a coherent and reliable mathematical framework. David Hilbert, a German mathematician, is widely regarded as one of the most influential mathematicians of the 20th century. Born in 1862, Hilbert made significant contributions to various branches of mathematics, including number theory, algebra, and mathematical logic. His groundbreaking work on the foundations of mathematics, known as Hilbert's program, had a profound impact on the field and set the stage for advancements in mathematical logic and computer science. Hilbert's rigorous approach to mathematical reasoning and his emphasis on precision and clarity continue to shape the discipline to this day. |
| david hilbert: Modern Mathematics Facts On File, Incorporated, 2006 During the first half of the 20th century, mathematics became an international discipline that led to major advances in science and technology. Modern Mathematics: 1900 to 1950 provides an eye-opening introduction to those five historic decades by analyzing the advancement of the field through the accomplishments of 10 significant mathematicians. From David Hilbert and Emmy Noether, who introduced the infinite dimensional vector spaces and algebraic rings that bear their names, to Norbert Wiener, the founder of cybernetics, this in-depth volume is an excellent choice for libraries aiming to provide a range of resources covering the history of mathematics. |
| david hilbert: Remarkable Mathematicians Ioan James, 2003-02-06 Ioan James introduces and profiles sixty mathematicians from the era when mathematics was freed from its classical origins to develop into its modern form. The subjects, all born between 1700 and 1910, come from a wide range of countries, and all made important contributions to mathematics, through their ideas, their teaching, and their influence. James emphasizes their varied life stories, not the details of their mathematical achievements. The book is organized chronologically into ten chapters, each of which contains biographical sketches of six mathematicians. The men and women James has chosen to portray are representative of the history of mathematics, such that their stories, when read in sequence, convey in human terms something of the way in which mathematics developed. Ioan James is a professor at the Mathematical Institute, University of Oxford. He is the author of Topological Topics (Cambridge, 1983), Fibrewise Topology (Cambridge, 1989), Introduction to Uniform Spaces (Cambridge, 1990), Topological and Uniform Spaces (Springer-Verlag New York, 1999), and co-author with Michael C. Crabb of Fibrewise Homotopy Theory (Springer-Verlag New York, 1998). James is the former editor of the London Mathematical Society Lecture Note Series and volume editor of numerous books. He is the organizer of the Oxford Series of Topology symposia and other conferences, and co-chairman of the Task Force for Mathematical Sciences of Campaign for Oxford. |
| david hilbert: On the Teaching of Linear Algebra J.-L. Dorier, 2005-12-27 This book presents the state-of-the-art research on the teaching and learning of linear algebra in the first year of university, in an international perspective. It provides university teachers in charge of linear algebra courses with a wide range of information from works including theoretical and experimental issues. |
| david hilbert: Logic's Lost Genius Eckart Menzler-Trott, 2007-01-01 Gerhard Gentzen (1909-1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called ''proof theory'' but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for ''German logic'', and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smorynski on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Godel; and its development up to the present day. Smorynski explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program. This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers. Information for our distributors: Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners. |
| david hilbert: Einstein's War Matthew Stanley, 2019-05-23 'Deeply researched and profoundly absorbing . . . Matthew Stanley traces one of the greatest epics of scientific history . . . An amazing story' Michael Frayn, author of Tony Award-winning Copenhagen In 1916, Arthur Eddington, a war-weary British astronomer, opened a letter written by an obscure German professor named Einstein. The neatly printed equations on the scrap of paper outlined his world-changing theory of general relativity. Until then Einstein's masterpiece of time and space had been trapped behind the physical and ideological lines of battle, unknown. Einstein's name is now synonymous with 'genius', but it was not an easy road. He spent a decade creating relativity and his ascent to global celebrity owed much to against-the-odds international collaboration, including Eddington's globe-spanning expedition of 1919 - two years before they finally met. We usually think of scientific discovery as a flash of individual inspiration, but here we see it is the result of hard work, gambles and wrong turns. Einstein's War is a celebration of what science can offer when bigotry and nationalism are defeated. Using previously unknown sources and written like a thriller, it shows relativity being built brick-by-brick in front of us, as it happened 100 years ago. 'Riveting . . . Stanley lets us share the excitement a hundred years later in this entertaining and gripping book. It's a must read if you ever wondered how Einstein became 'Einstein'' Manjit Kumar, author of Quantum |
| david hilbert: A History of Mathematics Carl B. Boyer, Uta C. Merzbach, 2011-01-25 The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it. |
| david hilbert: Logic Colloquium 2000 (hardcover) Rene Cori, Alexander Razborov, Stevo Todorcevic, Carol Wood, 2005-04-25 This compilation of papers presented at the 2000 European Summer Meeting of the Association for Symbolic Logic marks the centenial anniversery of Hilbert's famous lecture. Held in the same hall at La Sorbonne where Hilbert first presented his famous problems, this meeting carries special significance to the Mathematics and Logic communities. |
| david hilbert: Logic Colloquium 2000 René Cori, Alexander Razborov, Stevo Todorčević, Carol Wood, 2017-03-30 Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the nineteenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic, held in Paris, France in July 2000. This meeting marked the centennial anniversary of Hilbert's famous lecture and was held in the same hall at La Sorbonne where Hilbert presented his problems. Three long articles, based on tutorials given at the meeting, present accessible expositions of developing research in model theory, computability, and set theory. The eleven subsequent papers present work from the research frontier in all areas of mathematical logic. |
| david hilbert: James Joseph Sylvester Karen Hunger Parshall, 2013-01-10 In the folklore of mathematics, James Joseph Sylvester (1814-1897) is the eccentric, hot-tempered, sword-cane-wielding, nineteenth-century British Jew who, together with the taciturn Arthur Cayley, developed a theory and language of invariants that then died spectacularly in the 1890s as a result of David Hilbert's groundbreaking, 'modern' techniques. This, like all folklore, has some grounding in fact but owes much to fiction. The present volume brings together for the first time 140 letters from Sylvester's correspondence in an effort to establish the true picture. It reveals - through the letters as well as through the detailed mathematical and historical commentary accompanying them - Sylvester the friend, man of principle, mathematician, poet, professor, scientific activist, social observer, traveller. It also provides a detailed look at Sylvester's thoughts and thought processes as it shows him acting in both personal and professional spheres over the course of his eighty-two year life. The Sylvester who emerges from this analysis - unlike the Sylvester of the folkloric caricature - offers deep insight into the development of the technical and social structures of mathematics. |
| david hilbert: Mathematics Douglas M. Campbell, John C. Higgins, 1984 Based upon the principle that graph design should be a science, this book presents the principles of graph construction. The orientation of the material is toward graphs in technical writings, such as journal articles and technical reports. But much of the material is relevant for graphs shown in talks and for graphs in nontechnical publications. -- from back cover. |
| david hilbert: On the Nature of Ecological Paradox Michael Charles Tobias, Jane Gray Morrison, 2021-05-18 This work is a large, powerfully illustrated interdisciplinary natural sciences volume, the first of its kind to examine the critically important nature of ecological paradox, through an abundance of lenses: the biological sciences, taxonomy, archaeology, geopolitical history, comparative ethics, literature, philosophy, the history of science, human geography, population ecology, epistemology, anthropology, demographics, and futurism. The ecological paradox suggests that the human biological–and from an insular perspective, successful–struggle to exist has come at the price of isolating H. sapiens from life-sustaining ecosystem services, and far too much of the biodiversity with which we find ourselves at crisis-level odds. It is a paradox dating back thousands of years, implicating millennia of human machinations that have been utterly ruinous to biological baselines. Those metrics are examined from numerous multidisciplinary approaches in this thoroughly original work, which aids readers, particularly natural history students, who aspire to grasp the far-reaching dimensions of the Anthropocene, as it affects every facet of human experience, past, present and future, and the rest of planetary sentience. With a Preface by Dr. Gerald Wayne Clough, former Secretary of the Smithsonian Institution and President Emeritus of the Georgia Institute of Technology. Foreword by Robert Gillespie, President of the non-profit, Population Communication. |
| david hilbert: Richard Dedekind Stefan Müller-Stach, 2024-12-06 The two works titled What Are and What Should the Numbers Be? (1888) and Continuity and Irrational Numbers (1872) are Dedekind's contributions to the foundations of mathematics; therein, he laid the groundwork for set theory and the theory of real and natural numbers. These writings are indispensable in modern mathematics. However, Dedekind's achievements have not always been adequately acknowledged, and the content of these books is still little known to many mathematicians today. This volume contains not only the original texts but also a detailed analysis of the two writings and an interpretation in modern language, as well as a brief biography and a transcript of the famous letter to H. Keferstein. The extensive commentary offers a fascinating insight into the life and work of Dedekind's pioneering work and relates the latter to great contemporaries such as Cantor, Dirichlet, Frege, Hilbert, Kronecker, and Riemann. Researchers and students alike will find this work a valuable reference in the history of mathematics. |
| david hilbert: Analysis and Interpretation in the Exact Sciences Melanie Frappier, Derek Brown, Robert DiSalle, 2012-02-26 The essays in this volume concern the points of intersection between analytic philosophy and the philosophy of the exact sciences. More precisely, it concern connections between knowledge in mathematics and the exact sciences, on the one hand, and the conceptual foundations of knowledge in general. Its guiding idea is that, in contemporary philosophy of science, there are profound problems of theoretical interpretation-- problems that transcend both the methodological concerns of general philosophy of science, and the technical concerns of philosophers of particular sciences. A fruitful approach to these problems combines the study of scientific detail with the kind of conceptual analysis that is characteristic of the modern analytic tradition. Such an approach is shared by these contributors: some primarily known as analytic philosophers, some as philosophers of science, but all deeply aware that the problems of analysis and interpretation link these fields together. |
| david hilbert: David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933 William Ewald, Wilfried Sieg, 2013-06-03 The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics. |
| david hilbert: We, Programmers Robert C. Martin, 2024-12-05 The Journey of Programming and Its Pioneers: From the Birth of Code to the Rise of AI In We, Programmers, software legend Robert C. Martin--Uncle Bob--dives deep into the world of programming, exploring the lives of the groundbreaking pioneers who built the foundation of modern computing. From Charles Babbage and Ada Lovelace to Alan Turing, Grace Hopper, and Dennis Ritchie, Martin shines a light on the figures whose brilliance and perseverance changed the world. This memoir-infused narrative provides a rich human history filled with technical insights for developers, examining the coding breakthroughs that shaped computing at the bit and byte level. By connecting these technical achievements with the human stories behind them, Martin gives readers a rare glimpse into the struggles and triumphs of the people who made modern technology possible. Depression, failure, and ridicule--these pioneers faced it all, and their stories intertwine with the evolution of computing itself as the field evolved from its humble beginnings to the cloud-based AIs of today. With the rise of AI, Martin also explores how this technology is transforming the future of programming and the ethical challenges that come with it. Notable topics include Understanding programming's roots and how they shaped today's tech landscape The human side of coding pioneers--what drove them, and what they overcame Key programming breakthroughs, from the early days of assembly to the rise of object-oriented languages The pivotal role World War II played in advancing computer science Insights and predictions regarding the ethical considerations surrounding AI and the future of programming For programmers, coders, and anyone fascinated by the intersection of people and machines, this guide to the history, humanity, and technology behind the code that powers our world today is a fascinating and essential read. Register your book for convenient access to downloads, updates, and/or corrections as they become available. See inside book for details. |
| david hilbert: Landmark Writings in Western Mathematics 1640-1940 Ivor Grattan-Guinness, 2005-02-11 This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. - First book of its kind - Covers the period 1640-1940 of massive development in mathematics - Describes many of the main writings of mathematics - Articles written by specialists in their field |
| david hilbert: Modern Algebra and the Rise of Mathematical Structures Leo Corry, 2012-12-06 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. |
| david hilbert: Handbook of Philosophical Logic Dov M. Gabbay, Franz Guenthner, 2013-03-09 It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other. |
| david hilbert: Appraising Lakatos György Kampis, L. Kvasz, Michael Stöltzner, 2013-06-29 Imre Lakatos (1922-1974) was one of the protagonists in shaping the new philosophy of science. More than 25 years after his untimely death, it is time for a critical re-evaluation of his ideas. His main theme of locating rationality within the scientific process appears even more compelling today, after many historical case studies have revealed the cultural and societal elements within scientific practices. Recently there has been, above all, an increasing interest in Lakatos' philosophy of mathematics, which emphasises heuristics and mathematical practice over logical justification. But suitable modifications of his approach are called for in order to make it applicable to modern axiomatised theories. Pioneering historical research in England and Hungary has unearthed hitherto unknown facts about Lakatos' personal life, his wartime activities and his involvement in the political developments of post-war Europe. From a communist activist committed to Györgyi Lukács' thinking, Lakatos developed into a staunch anti-Marxist who found his intellectual background in Popper's critical rationalism. The volume also publishes for the first time a part of his Debrecen Ph.D. thesis and it is concluded by a bibliography of his Hungarian writings. |
| david hilbert: The Math Book Clifford A. Pickover, 2009 This book covers 250 milestones in mathematical history, beginning millions of years ago with ancient ant odometers and moving through time to our modern-day quest for new dimensions. |
| david hilbert: The Genesis of General Relativity Jürgen Renn, 2007-02-16 This four-volume work represents the most comprehensive documentation and study of the creation of general relativity. Einstein’s 1912 Zurich notebook is published for the first time in facsimile and transcript and commented on by today’s major historians of science. Additional sources from Einstein and others, who from the late 19th to the early 20th century contributed to this monumental development, are presented here in translation for the first time. The volumes offer detailed commentaries and analyses of these sources that are based on a close reading of these documents supplemented by interpretations by the leading historians of relativity. |
| david hilbert: Academic Genealogy of Mathematicians Sooyoung Chang, 2011 Burn for Burn |
David Hilbert - Wikipedia
David Hilbert (/ ˈhɪlbərt /; [3] German: [ˈdaːvɪt ˈhɪlbɐt]; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential …
David Hilbert | Facts, Contributions, & Biography | Britannica
David Hilbert, German mathematician who reduced geometry to a series of axioms and contributed substantially to the establishment of the formalistic foundations of mathematics. …
David Hilbert (1862 - 1943) - Biography - MacTutor History of ...
Jan 23, 2012 · Hilbert's work in geometry had the greatest influence in that area after Euclid. A systematic study of the axioms of Euclidean geometry led Hilbert to propose 21 such axioms …
David Hilbert - History of Math and Technology
David Hilbert (1862–1943) is widely regarded as one of the most influential mathematicians of the late 19th and early 20th centuries. His profound contributions to mathematics and science …
David Hilbert - Biography, Facts and Pictures - Famous Scientists
David Hilbert was one of the mathematical greats of the 19th and 20th centuries. Today, mathematics and physics are still powerfully influenced by his work and his vision. Early Life …
David Hilbert - The Foundations of Geometry - The Story of …
He has many mathematical terms named after him, including Hilbert space (an infinite dimensional Euclidean space), Hilbert curves, the Hilbert classification and the Hilbert …
David Hilbert Facts & Biography | Famous Mathematicians
David Hilbert was preeminent in numerous fields of mathematics, comprising axiomatic theory, algebraic number theory, invariant theory, class field theory as well as functional analysis.
David Hilbert Biography - Life of German Mathematician - Totally History
David Hilbert discovered the use of algebra and geometry and he came up with the idea of Hilbert spaces. Hilbert’s discovery in geometry had a huge influence in that time. The study of axioms …
David Hilbert (1862-1943) - University of Evansville
For many years, Hilbert held the position at the Mathematical Institute at the University of Göttingen that was recognized as the most prestigious mathematical position in Germany, and …
David Hilbert - Encyclopedia.com
May 14, 2018 · Hilbert was descended from a Protestant middleclass family that had settled in the seventeenth century near Freiberg, Saxony. His great-grandfather, Christian David, a surgeon, …
David Hilbert - Wikipedia
David Hilbert (/ ˈhɪlbərt /; [3] German: [ˈdaːvɪt ˈhɪlbɐt]; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential …
David Hilbert | Facts, Contributions, & Biography | Britannica
David Hilbert, German mathematician who reduced geometry to a series of axioms and contributed substantially to the establishment of the formalistic foundations of mathematics. …
David Hilbert (1862 - 1943) - Biography - MacTutor History of ...
Jan 23, 2012 · Hilbert's work in geometry had the greatest influence in that area after Euclid. A systematic study of the axioms of Euclidean geometry led Hilbert to propose 21 such axioms …
David Hilbert - History of Math and Technology
David Hilbert (1862–1943) is widely regarded as one of the most influential mathematicians of the late 19th and early 20th centuries. His profound contributions to mathematics and science …
David Hilbert - Biography, Facts and Pictures - Famous Scientists
David Hilbert was one of the mathematical greats of the 19th and 20th centuries. Today, mathematics and physics are still powerfully influenced by his work and his vision. Early Life …
David Hilbert - The Foundations of Geometry - The Story of …
He has many mathematical terms named after him, including Hilbert space (an infinite dimensional Euclidean space), Hilbert curves, the Hilbert classification and the Hilbert …
David Hilbert Facts & Biography | Famous Mathematicians
David Hilbert was preeminent in numerous fields of mathematics, comprising axiomatic theory, algebraic number theory, invariant theory, class field theory as well as functional analysis.
David Hilbert Biography - Life of German Mathematician - Totally History
David Hilbert discovered the use of algebra and geometry and he came up with the idea of Hilbert spaces. Hilbert’s discovery in geometry had a huge influence in that time. The study of axioms …
David Hilbert (1862-1943) - University of Evansville
For many years, Hilbert held the position at the Mathematical Institute at the University of Göttingen that was recognized as the most prestigious mathematical position in Germany, and …
David Hilbert - Encyclopedia.com
May 14, 2018 · Hilbert was descended from a Protestant middleclass family that had settled in the seventeenth century near Freiberg, Saxony. His great-grandfather, Christian David, a surgeon, …
