Come dice il titolo, in questo libro, la cui ossatura è costituita da un corso di lezioni tenute nel 1920-21 a Göttingen, redatte con modifiche e aggiunte da Stefan Cohn-Vossen, Hilbert espone gli argomenti della geometria per mezzo di concetti intuitivi e della diretta esperienza spaziale delle forme, senza servirsi dell’analisi matematica neppure per quelle parti della geometria per cui si usa ricorrere esclusivamente al calcolo. Completa il volume il contributo di Pavel S. Aleksandrov su "I primi fondamenti della topologia", appositamente scritto nel 1932.
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 The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen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.
Constance Reid, in Chapter VII, recounts the creation of the Zahlbericht, known as Die Theorie der algebraischen Zahlkörper. In 1893, the Deutsche Mathematiker-Vereinigung invited Hilbert and Minkowski to report on the state of number theory, with a two-year deadline. They agreed that Minkowski would cover rational number theory while Hilbert focused on algebraic number theory. By early 1896, Hilbert had nearly completed his section, but Minkowski had made little progress and decided to withdraw. Hilbert then finished his report on algebraic number fields, which his wife carefully transcribed before sending it to the printers. The proofs were meticulously reviewed by Minkowski, with assistance from Hurwitz, ensuring both mathematical clarity and proper typesetting. At Minkowski's suggestion, Hilbert included a note of gratitude to his wife. Reid notes that the report exceeded the expectations of the Mathematical Society; instead of a simple summary, they received a masterpiece that elegantly integrated recent complex developments into a cohesive theory.
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 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. It lays the groundwork for his later work with Bernays. 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.
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.
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.
