This book is a collection of research papers published in the prestigious journal Mathematische Annalen. It features groundbreaking work by prominent mathematicians such as David Hilbert and Albert Einstein, spanning topics from geometry to number theory.
Founded by celebrated mathematician Carl Neumann in 1868, Mathematische Annalen is one of the world's most prestigious mathematical journals. Featuring groundbreaking articles by luminaries like Albert Einstein, David Hilbert, and Félix Klein, this collection offers a window into the cutting-edge of mathematical research and exploration. A must-read for anyone passionate about mathematics.
Mathematische Annalen is a seminal mathematics journal that has published many groundbreaking papers and provided a venue for the most important mathematical discoveries of the past century. This anthology contains some of the most important papers published in the journal and includes contributions from luminaries such as David Hilbert, Albert Einstein, and Felix Klein. With its rigorous analysis and groundbreaking insights, this book is an essential resource for anyone interested in the history and development of the most important mathematical ideas of the 20th century.
Mathematische Annalen is a scientific journal dedicated to mathematics published by Springer-Verlag. This book is a compilation of articles published in Mathematische Annalen from the years 1869 to 1949, written by some of the most prominent mathematicians of the time, including Albert Einstein and David Hilbert. It is a must-read for anyone interested in the history of mathematics.
This book presents a systematic approach to geometry by establishing a simple and complete set of independent axioms. It aims to logically derive key geometrical theorems, highlighting the significance of various axiom groups and the implications of each individual axiom. Through this method, the text seeks to clarify the foundational principles that underpin geometric concepts, making it a valuable resource for understanding the logical structure of geometry.
Culturally significant, this work offers a faithful reproduction of an original artifact, preserving its authenticity with original copyright references and library stamps. It serves as a valuable resource for understanding the knowledge base of civilization, reflecting the historical context and importance of the material housed in major libraries worldwide.
Selected for its cultural significance, this work preserves the integrity of the original artifact, including copyright references and library stamps. It serves as a vital component of the knowledge base of civilization, offering readers a glimpse into historical context and scholarly importance. The reproduction aims to maintain authenticity, making it a valuable resource for those interested in the preservation of cultural heritage.
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.
Focusing on the contributions of David Hilbert, this work highlights his significant influence on mathematics in the 19th and early 20th centuries. Born in Prussia, Hilbert is celebrated for his groundbreaking ideas in invariant theory and the axiomatization of geometry, as well as for formulating the theory of Hilbert spaces, which became foundational in functional analysis. The book is republished with a new introductory biography that provides context to his remarkable achievements.
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.