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| why is david hilbert important: 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 Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert’s intense, original, well-informed, and highly influential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. |
| why is david hilbert important: The Foundations of Geometry David Hilbert, 1902 |
| why is david hilbert important: 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. |
| why is david hilbert important: 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. |
| why is david hilbert important: 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. |
| why is david hilbert important: Geometry and the Imagination D. Hilbert, S. Cohn-Vossen, 2021-03-17 This remarkable book has endured as a true masterpiece of mathematical exposition. There are few mathematics books that are still so widely read and continue to have so much to offer—even after more than half a century has passed! 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. “Hilbert and Cohn-Vossen” is full of interesting facts, many of which you wish you had known before. It's also likely that you have heard those facts before, but surely wondered where they could be found. 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 R 3 R3. 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: π/4=1−1/3+1/5−1/7+−… π/4=1−1/3+1/5−1/7+−…. 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. Here, we see regular polyhedra again, from a different perspective. One of the high points of the chapter is the discussion of Schlafli's Double-Six, which leads to the description of the 27 lines on the general smooth cubic surface. As is true throughout the book, the magnificent drawings in this chapter immeasurably help the reader. A particularly intriguing section in the chapter on differential geometry is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? Many mathematicians are familiar with the plaster models of surfaces found in many mathematics departments. The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! 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. |
| why is david hilbert important: 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. |
| why is david hilbert important: The Foundations of Geometry David Hilbert, E. Townsend, 2014-12-11 The material contained in the following translation was given in substance by Professor Hilbert as a course of lectures on euclidean geometry at the University of G]ottingen during the winter semester of 1898-1899. The results of his investigation were re-arranged and put into the form in which they appear here as a memorial address published in connection with the celebration at the unveiling of the Gauss-Weber monument at G]ottingen, in June, 1899. In the French edition, which appeared soon after, Professor Hilbert made some additions, particularly in the concluding remarks, where he gave an account of the results of a recent investigation made by Dr. Dehn. These additions have been incorporated in the following translation. As a basis for the analysis of our intuition of space, Professor Hilbert commences his discussion by considering three systems of things which he calls points, straight lines, and planes, and sets up a system of axioms connecting these elements in their mutual relations. The purpose of his investigations is to discuss systematically the relations of these axioms to one another and also the bearing of each upon the logical development of euclidean geometry. Among the important results obtained, the following are worthy of special mention: 1. The mutual independence and also the compatibility of the given system of axioms is fully discussed by the aid of various new systems of geometry which are introduced. 2. The most important propositions of euclidean geometry are demonstrated in such a manner as to show precisely what axioms underlie and make possible the demonstration. 3. The axioms of congruence are introduced and made the basis of the definition of geometric displacement. 4. The significance of several of the most important axioms and theorems in the development of the euclidean geometry is clearly shown; for example, it is shown that the whole of the euclidean geometry may be developed without the use of the axiom of continuity; the significance of Desargues's theorem, as a condition that a given plane geometry may be regarded as a part of a geometry of space, is made apparent, etc. 5. A variety of algebras of segments are introduced in accordance with the laws of arithmetic. This development and discussion of the foundation principles of geometry is not only of mathematical but of pedagogical importance. Hoping that through an English edition these important results of Professor Hilbert's investigation may be made more accessible to English speaking students and teachers of geometry, I have undertaken, with his permission, this translation. In its preparation, I have had the assistance of many valuable suggestions from Professor Osgood of Harvard, Professor Moore of Chicago, and Professor Halsted of Texas. I am also under obligations to Mr. Henry Coar and Mr. Arthur Bell for reading the proof. |
| why is david hilbert important: Principia Mathematica Alfred North Whitehead, Bertrand Russell, 1927 The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century. |
| why is david hilbert important: 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. |
| why is david hilbert important: Emmy Noether's Wonderful Theorem Dwight E. Neuenschwander, 2017-04 Dwight E. Neuenschwander's introduction to the theorem's genesis, applications, and consequences artfully unpacks its universal importance and unsurpassed elegance. Drawing from over thirty years of teaching the subject, Neuenschwander uses mechanics, optics, geometry, and field theory to point the way to a deep understanding of Noether's Theorem. The three sections provide a step-by-step, simple approach to the less-complex concepts surrounding the theorem, in turn instilling the knowledge and confidence needed to grasp the full wonder it encompasses. Illustrations and worked examples throughout each chapter serve as signposts on the way to this apex of physics.--Publisher's description. |
| why is david hilbert important: Incompleteness Rebecca Goldstein, 2006-01-31 An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever--Provided by publisher. |
| why is david hilbert important: Elementary Concepts of Topology Paul Alexandroff, 2012-08-13 Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures. |
| why is david hilbert important: The Foundations of Geometry David Hilbert, 1902 |
| why is david hilbert important: The Pólya Picture Album: Encounters of a Mathematician George Pólya, 1987 Pólya was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for his work in heuristics and mathematics education. For many years mathematicians visiting Stanford enjoyed guided tours through pages of the Pólya photograph album, led by Pólya himself. This is a selection of the photographs accompanied by remarks taken from tapes of Pólya's conversations with his visitors. |
| why is david hilbert important: Philosophy of Mathematics Øystein Linnebo, 2017-05-30 A sophisticated, original introduction to the philosophy of mathematics from one of its leading contemporary scholars Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Written by Øystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Gödel, W. V. Quine, Paul Benacerraf, and Hartry H. Field. Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics. |
| why is david hilbert important: The Mathematics of Harmony Alexey Stakhov, 2009 Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science. |
| why is david hilbert important: Imaginary Philosophical Dialogues Kenneth Binmore, 2020-12-23 How would Plato have responded if his student Aristotle had ever challenged his idea that our senses perceive nothing more than the shadows cast upon a wall by a true world of perfect ideals? What would Charles Darwin have said to Karl Marx about his claim that dialectical materialism is a scientific theory of evolution? How would Jean-Paul Sartre have reacted to Simone de Beauvoir’s claim that the Marquis de Sade was a philosopher worthy of serious attention? This light-hearted book proposes answers to such questions by imagining dialogues between thirty-three pairs of philosophical sages who were alive at the same time. Sometime famous sages get a much rougher handling than usual, as when Adam Smith beards Immanuel Kant in his Konigsberg den. Sometimes neglected or maligned sages get a chance to say what they really believed, as when Epicurus explains that he wasn’t epicurean. Sometimes the dialogues are about the origins of modern concepts, as when Blaise Pascal and Pierre de Fermat discuss their invention of probability, or when John Nash and John von Neumann discuss the creation of game theory. Even in these scientific cases, the intention is that the protagonists come across as fallible human beings like the rest of us, rather than the intellectual paragons of philosophical textbooks. |
| why is david hilbert important: Principles of Mathematical Logic D. Hilbert, W. Ackermann, 2022-05-11 David Hilbert was particularly interested in the foundations of mathematics. Among many other things, he is famous for his attempt to axiomatize mathematics. This now classic text is his treatment of symbolic logic. This translation is based on the second German edition and has been modified according to the criticisms of Church and Quine. In particular, the authors' original formulation of Gödel's completeness proof for the predicate calculus has been updated. In the first half of the twentieth century, an important debate on the foundations of mathematics took place. Principles of Mathematical Logic represents one of Hilbert's important contributions to that debate. Although symbolic logic has grown considerably in the subsequent decades, this book remains a classic. |
| why is david hilbert important: David Hilbert's Lectures on the Foundations of Geometry 1891-1902 Michael Hallett, Ulrich Majer, 2004-01-01 |
| why is david hilbert important: The Mathematician's Brain David Ruelle, 2018-06-26 The Mathematician's Brain poses a provocative question about the world's most brilliant yet eccentric mathematical minds: were they brilliant because of their eccentricities or in spite of them? In this thought-provoking and entertaining book, David Ruelle, the well-known mathematical physicist who helped create chaos theory, gives us a rare insider's account of the celebrated mathematicians he has known-their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the sublime, inexpressible beauty of their most breathtaking mathematical discoveries. Consider the case of British mathematician Alan Turing. Credited with cracking the German Enigma code during World War II and conceiving of the modern computer, he was convicted of gross indecency for a homosexual affair and died in 1954 after eating a cyanide-laced apple--his death was ruled a suicide, though rumors of assassination still linger. Ruelle holds nothing back in his revealing and deeply personal reflections on Turing and other fellow mathematicians, including Alexander Grothendieck, René Thom, Bernhard Riemann, and Felix Klein. But this book is more than a mathematical tell-all. Each chapter examines an important mathematical idea and the visionary minds behind it. Ruelle meaningfully explores the philosophical issues raised by each, offering insights into the truly unique and creative ways mathematicians think and showing how the mathematical setting is most favorable for asking philosophical questions about meaning, beauty, and the nature of reality. The Mathematician's Brain takes you inside the world--and heads--of mathematicians. It's a journey you won't soon forget. |
| why is david hilbert important: Hilbert Constance Reid, 1996-04-01 |
| why is david hilbert important: Naming Infinity Loren Graham, Jean-Michel Kantor, 2009-03-31 In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity. |
| why is david hilbert important: Men Who Made a New Physics Barbara Lovett Cline, 1987-06-15 Cline recounts the development of quantum theory, capturing the atmosphere of argument and discovery among physicists in the 1920s. She explores the backgrounds of the major figures—Rutherford, Bohr, Planck, Einstein—separately, but draws them together as they begin to consider each other's questions about the nature of matter. |
| why is david hilbert important: Mathematical Lives CLAUDIO BARTOCCI, Renato Betti, Angelo Guerraggio, Roberto Lucchetti, 2010-10-01 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.’ |
| why is david hilbert important: Transcending Tradition: Jewish Mathematicians in German Speaking Academic Culture Birgit Bergmann, 2012-10-22 A companion publication to the international exhibition Transcending Tradition: Jewish Mathematicians in German-Speaking Academic Culture, the catalogue explores the working lives and activities of Jewish mathematicians in German-speaking countries during the period between the legal and political emancipation of the Jews in the 19th century and their persecution in Nazi Germany. It highlights the important role Jewish mathematicians played in all areas of mathematical culture during the Wilhelmine Empire and the Weimar Republic, and recalls their emigration, flight or death after 1933. |
| why is david hilbert important: From Kant to Hilbert Volume 1 William Bragg Ewald, William Ewald, 1999 This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics - algebra, geometry, number theory, analysis, logic, and set theory - with narratives to show how they are linked. |
| why is david hilbert important: Mathematicians under the Nazis Sanford L. Segal, 2014-11-23 Contrary to popular belief--and despite the expulsion, emigration, or death of many German mathematicians--substantial mathematics was produced in Germany during 1933-1945. In this landmark social history of the mathematics community in Nazi Germany, Sanford Segal examines how the Nazi years affected the personal and academic lives of those German mathematicians who continued to work in Germany. The effects of the Nazi regime on the lives of mathematicians ranged from limitations on foreign contact to power struggles that rattled entire institutions, from changed work patterns to military draft, deportation, and death. Based on extensive archival research, Mathematicians under the Nazis shows how these mathematicians, variously motivated, reacted to the period's intense political pressures. It details the consequences of their actions on their colleagues and on the practice and organs of German mathematics, including its curricula, institutions, and journals. Throughout, Segal's focus is on the biographies of individuals, including mathematicians who resisted the injection of ideology into their profession, some who worked in concentration camps, and others (such as Ludwig Bieberbach) who used the Aryanization of their profession to further their own agendas. Some of the figures are no longer well known; others still tower over the field. All lived lives complicated by Nazi power. Presenting a wealth of previously unavailable information, this book is a large contribution to the history of mathematics--as well as a unique view of what it was like to live and work in Nazi Germany. |
| why is david hilbert important: Consciousness and the Physical World Brian David Josephson, V. S. Ramachandran, 1980 |
| why is david hilbert important: Philosophy of Logic , 2006-11-29 The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter |
| why is david hilbert important: Challenging Modern Physics Al Kelly, 2005 Newton's Laws held for 300 years until Einstein developed the 'special theory of relativity' in 1905. Experiments done since then show anomalies in that theory. This book starts with a description of the special theory of relativity. It is shown that Einstein was not the first to derive the famous equation E = mc2, which has become synonymous with his name. Next, experimental evidence that cannot be explained by special relativity is given. In the light of this evidence, the two basic postulates of the special theory of relativity on the behaviour of light are shown to be untenable. A new theory (universal relativity) is developed, which conforms to the experimental evidence. The movement of a conductor near a pole of a magnet and the movement of that pole near the conductor does not always give the same result. It has been claimed that this contradicts relativity theory. Experiments described in this book show that it is not special relativity but another basic law of physics that is contradicted - Faraday's Law. The Big Bang theory of the beginning of the universe is questioned and an alternative proposed. The source of much of the mysterious missing 'dark matter' that has been sought for decades by astronomers is located. An explanation of the shapes of some galaxies is proffered. This book presents an alternative to Einstein's special theory of relativity, solves many problems left unanswered by special relativity, gives a better fit to many phenomena and experimental data and is more philosophically appealing. It is recommended to all people interested in fundamental issues of physics and cosmology. Professor Andre Assis, Brazil The book treats its subject properly, not just as an impersonal set of equations, but rather as a developing saga full of human triumph and failure. One learns from both experimental results and simple logical argument that all is not well with modern physics. Dr. Neal Graneau, Oxford University, U.K. Irish engineer solves the dark secrets of space. Sunday Times, U.K. Einstein got relativity theory wrong. Bangkok Post, Thailand |
| why is david hilbert important: From Frege to Gödel Jean van Heijenoort, 1967 Gathered together here are the fundamental texts of the great classical period in modern logic. A complete translation of Gottlob Frege’s Begriffsschrift—which opened a great epoch in the history of logic by fully presenting propositional calculus and quantification theory—begins the volume, which concludes with papers by Herbrand and by Gödel. |
| why is david hilbert important: 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. |
| why is david hilbert important: A Richer Picture of Mathematics David E. Rowe, 2018-02-13 Historian David E. Rowe captures the rich tapestry of mathematical creativity in this collection of essays from the “Years Ago” column of The Mathematical Intelligencer. With topics ranging from ancient Greek mathematics to modern relativistic cosmology, this collection conveys the impetus and spirit of Rowe’s various and many-faceted contributions to the history of mathematics. Centered on the Göttingen mathematical tradition, these stories illuminate important facets of mathematical activity often overlooked in other accounts. Six sections place the essays in chronological and thematic order, beginning with new introductions that contextualize each section. The essays that follow recount episodes relating to the section’s overall theme. All of the essays in this collection, with the exception of two, appeared over the course of more than 30 years in The Mathematical Intelligencer. Based largely on archival and primary sources, these vignettes offer unusual insights into behind-the-scenes events. Taken together, they aim to show how Göttingen managed to attract an extraordinary array of talented individuals, several of whom contributed to the development of a new mathematical culture during the first decades of the twentieth century. |
| why is david hilbert important: Development of Mathematics in the 19th Century Félix Klein, 1979 |
| why is david hilbert important: Euclid's Elements Euclid, Dana Densmore, 2002 The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary --from book jacket. |
| why is david hilbert important: Traveling at the Speed of Thought Daniel Kennefick, 2007-04-15 Since Einstein first described them nearly a century ago, gravitational waves have been the subject of more sustained controversy than perhaps any other phenomenon in physics. These as yet undetected fluctuations in the shape of space-time were first predicted by Einstein's general theory of relativity, but only now, at the dawn of the twenty-first century, are we on the brink of finally observing them. Daniel Kennefick's landmark book takes readers through the theoretical controversies and thorny debates that raged around the subject of gravitational waves after the publication of Einstein's theory. The previously untold story of how we arrived at a settled theory of gravitational waves includes a stellar cast from the front ranks of twentieth-century physics, including Richard Feynman, Hermann Bondi, John Wheeler, Kip Thorne, and Einstein himself, who on two occasions avowed that gravitational waves do not exist, changing his mind both times. The book derives its title from a famously skeptical comment made by Arthur Stanley Eddington in 1922--namely, that gravitational waves propagate at the speed of thought. Kennefick uses the title metaphorically to contrast the individual brilliance of each of the physicists grappling with gravitational-wave theory against the frustratingly slow progression of the field as a whole. Accessibly written and impeccably researched, this book sheds new light on the trials and conflicts that have led to the extraordinary position in which we find ourselves today--poised to bring the story of gravitational waves full circle by directly confirming their existence for the very first time. |
| why is david hilbert important: Birds and Frogs Freeman J Dyson, 2015-03-25 This book is a sequel to the volume of selected papers of Dyson up to 1990 that was published by the American Mathematical Society in 1996. The present edition comprises a collection of the most interesting writings of Freeman Dyson, all personally selected by the author, from the period 1990–2014. The five sections start off with an Introduction, followed by Talks about Science, Memoirs, Politics and History, and some Technical Papers. The most noteworthy is a lecture entitled Birds and Frogs to the American Mathematical Society that describes two kinds of mathematicians with examples from real life. Other invaluable contributions include an important tribute to C. N. Yang written for his retirement banquet at Stony Brook University, as well as a historical account of the Operational Research at RAF Bomber Command in World War II provocatively titled A Failure of Intelligence. The final section carries the open-ended question of whether any conceivable experiment could detect single gravitons to provide direct evidence of the quantization of gravity — Is a Graviton Detectable? Various possible graviton-detectors are examined. This invaluable compilation contains unpublished lectures, and surveys many topics in science, mathematics, history and politics, in which Freeman Dyson has been so active and well respected around the world. |
| why is david hilbert important: Mechanical Geometry Theorem Proving Shang-Ching Chou, 2001-11-30 Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the tree of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as experimental mathematics, CFD, completely integrable systems, chaos, synergetics and large-scale order, which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics. |
| why is david hilbert important: David Hilbert and the Axiomatization of Physics (1898–1918) L. Corry, 2014-03-14 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. |
"Why it is" vs "Why is it" - English Language & Usage Stack …
Nov 7, 2013 · The question: "Why is [etc.]" is a question form in English: Why is the sky blue? Why is it that children require so much attention? Why is it [or some thing] like that? When that …
How did the letter Z come to be associated with sleeping/snoring?
May 26, 2011 · See also Why Does ZZZ mean sleep? for another theory: The reason zzz came into being is that the comic strip artists just couldn’t represent sleeping with much. ... As the …
What's the proper way to handwrite a lowercase letter A?
Oct 31, 2017 · But why are there two different As? Back in ye olde days there were many ways to write a lower-case A. (The same went for other letters, for example þ was later written "y", …
Why is "pineapple" in English but "ananas" in all other languages?
Nov 7, 2013 · I don't think we are discussing whether "ananas" or "pineapple" was used first, but where it came from and why the English language does not use "ananas" today. I would say …
Reason for different pronunciations of "lieutenant"
Dec 6, 2014 · As to why present day usage is as it is: People can be contrary. It's possible the US adopted "Loo" because and only because the Brits said "Lef" -- or vice-versa. But it seems the …
The whys and the hows - English Language & Usage Stack …
Apr 13, 2017 · The rule on apostrophes on plurals applies if the word in question is a bona fide word as a plural. My dictionary shows the plural of "why" with a simple "s." Ditto other words …
terminology - Why use BCE/CE instead of BC/AD? - English …
Why do people use the latter terminology? For one thing, I find it confusing. It doesn't help that BCE is similar to BC. But moreover, there is only one letter of difference between the two …
etymology - Why "shrink" (of a psychiatrist)? - English Language ...
I'm afraid I have to disagree here. From my understanding, and a recent article in the Atlantic, derived from the new text Marketplace of the Marvelous: The Strange Origins of Modern …
Using hundreds to express thousands: why, where, when?
May 30, 2017 · Why change register half way through? [¶ Of course, even in the middle ages, educated professionals such as architects, military engineers and accountants would work to …
How did the word "beaver" come to be associated with vagina?
From "Why King George of England May Have to Lose His Beard: How the Game of 'Beaver' Which All England Is Playing Is So Threatening the Proper Reverence for the Throne That …
"Why it is" vs "Why is it" - English Language & Usage Stack …
Nov 7, 2013 · The question: "Why is [etc.]" is a question form in English: Why is the sky blue? Why is it that children require so much attention? Why is it [or some thing] like that? When that …
How did the letter Z come to be associated with sleeping/snoring?
May 26, 2011 · See also Why Does ZZZ mean sleep? for another theory: The reason zzz came into being is that the comic strip artists just couldn’t represent sleeping with much. ... As the …
What's the proper way to handwrite a lowercase letter A?
Oct 31, 2017 · But why are there two different As? Back in ye olde days there were many ways to write a lower-case A. (The same went for other letters, for example þ was later written "y", …
Why is "pineapple" in English but "ananas" in all other languages?
Nov 7, 2013 · I don't think we are discussing whether "ananas" or "pineapple" was used first, but where it came from and why the English language does not use "ananas" today. I would say …
Reason for different pronunciations of "lieutenant"
Dec 6, 2014 · As to why present day usage is as it is: People can be contrary. It's possible the US adopted "Loo" because and only because the Brits said "Lef" -- or vice-versa. But it seems the …
The whys and the hows - English Language & Usage Stack Exchange
Apr 13, 2017 · The rule on apostrophes on plurals applies if the word in question is a bona fide word as a plural. My dictionary shows the plural of "why" with a simple "s." Ditto other words …
terminology - Why use BCE/CE instead of BC/AD? - English …
Why do people use the latter terminology? For one thing, I find it confusing. It doesn't help that BCE is similar to BC. But moreover, there is only one letter of difference between the two …
etymology - Why "shrink" (of a psychiatrist)? - English Language ...
I'm afraid I have to disagree here. From my understanding, and a recent article in the Atlantic, derived from the new text Marketplace of the Marvelous: The Strange Origins of Modern …
Using hundreds to express thousands: why, where, when?
May 30, 2017 · Why change register half way through? [¶ Of course, even in the middle ages, educated professionals such as architects, military engineers and accountants would work to …
How did the word "beaver" come to be associated with vagina?
From "Why King George of England May Have to Lose His Beard: How the Game of 'Beaver' Which All England Is Playing Is So Threatening the Proper Reverence for the Throne That …
