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 Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert’s intense, original, well-informed, and highly influential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.

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.

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.

This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future developments of the field, highlighting a list of open problems. Graduate students and researchers working in physics, mathematics and mathematical physics will find this journey extremely fascinating. All those who want to benefit from a comprehensive description of all the latest advances in mathematics and mathematical physics, will find this book very useful too.

Quantum mechanics – the grandiose theory that describes nature down to the submicroscopic level – was first formulated in Göttingen in 1925. How did this come about and why is it that Göttingen became the pre-eminent location for a revolution in physics? This book is the first to investigate the wide range of factors that were pivotal for quantum physics to be established in Göttingen. These include the process of generational change of physics professors, the hopes of mathematicians seeking new fields of research, and a new understanding of the interplay of experiment, theory and philosophy.

This book offers fresh perspective on the role of phenomenology in the philosophy of physics which opens new avenues for discussion among physicists, "standard" philosophers of physics and philosophers with phenomenological leanings. Much has been written on the interrelations between philosophy and physics in the late 19th and early 20th century, and on the emergence of philosophy of science as an autonomous philosophical sub-discipline. This book is about the under-explored role of phenomenology in the development and the philosophical interpretation of 20th century physics. Part 1 examines questions about the origins and value of phenomenological approaches to physics. Does the work of classical phenomenologists such as Husserl, Merleau-Ponty or Heidegger contain elements of systematic value to both the practice and our philosophical understanding of physics? How did classical phenomenology influence “standard” philosophy of science in the Anglo-American and other traditions? Part 2 probes questions on the role of phenomenology in the philosophies of physics and science: - Can phenomenology help to solve “Wigner’s puzzle”, the problem of the "unreasonable effectiveness" of mathematics in describing, explaining and predicting empirical phenomena? - Does phenomenology allow better understanding of the principle of gauge invariance at the core of the standard model of contemporary particle physics? - Does the phenomenological notion of “Lifeworld” stand in opposition to the “scientific metaphysics” movement, or is there potential for dialogue? Part 3 examines the measurement problem. Is the solution outlined by Fritz London and Edmond Bauer merely a re-statement of von Neumann’s view, or should it be regarded as a distinctively phenomenological take on the measurement problem? Is phenomenology a serious contender in continuing discussions of foundational questions of quantum mechanics? Can other interpretational frameworks such as quantum Bayesianism benefit from implementing phenomenological notions such as constitution or horizonal intentionality?