John W. Dawson Knihy

This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different. While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems. The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice. He then outlines various purposes that alternative proofs may serve. Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues’ Theorem, the Prime Number Theorem, and the proof of the irreducibility of cyclotomic polynomials. Why Prove It Again? will appeal to a broad range of readers, including historians and philosophers of mathematics, students, and practicing mathematicians.  Additionally, teachers will find it to be a useful source of alternative methods of presenting material to their students.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface.We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Delving into the relationship between the natural world and biblical teachings, this collection of lectures offers insights from December 1874 in New York. The text explores how nature reflects divine principles and enhances spiritual understanding, providing a thoughtful examination of faith and the environment. This reprint retains the original's quality, making it a valuable resource for those interested in the intersection of science and religion.

Focusing on the Pleistocene geology of Canada, this book offers in-depth notes on the era's unique life forms and climatic conditions. It serves as a valuable resource for understanding the geological history of Canada during the Ice Age, providing insights into the environmental factors that shaped the region. This high-quality reprint of the original 1894 edition preserves the detailed observations and analyses of the time, making it a significant contribution to the study of Canadian geology and paleontology.

The book offers a faithful reprint of the original 1894 edition, presenting key scientific insights into Earth science. It delves into various aspects of the planet's structure and processes, reflecting the scientific understanding of the time. This unchanged edition serves as a valuable resource for those interested in historical perspectives on Earth science.

The book is a facsimile reprint of an original antiquarian text, preserving its historical significance despite potential imperfections like marks and flawed pages. It aims to promote and protect cultural literature by providing an affordable, high-quality modern edition that remains true to the original work.

The book offers a faithful reprint of the original 1888 edition, exploring the intersection of modern science and biblical history. It delves into the discoveries and advancements in scientific understanding as they relate to the geographical and cultural contexts of biblical lands. This work aims to bridge the gap between ancient texts and contemporary scientific insights, providing readers with a unique perspective on the historical significance of these regions.

This work explores the intersections between religious revelation and natural science, offering insights into how these two realms can inform and enrich one another. Originally published in 1885, it provides a historical perspective on the dialogue between faith and empirical understanding, making it a valuable resource for those interested in the philosophical implications of science and religion. The reprint maintains the quality and integrity of the original text, preserving its significance for contemporary readers.

Der österreichische Mathematiker Kurt Gödel (1906–1978) ist einer der herausragendsten Logiker des 20. Jahrhunderts. Seine Resultate sind von allerhöchster Bedeutung für die Mathematik, und zunehmend werden auch die Auswirkungen auf unser modernes Weltbild sichtbar. Mit dem Erscheinen von Douglas Hofstadters Buch „Gödel, Escher, Bach“ wurde Gödels Werk einem breiten Publikum bekannt gemacht. John W. Dawson jr., Professor für mathematische Logik und Nachlaßverwalter von Gödel, zeichnet in dieser Biographie das Bild eines Mannes, dessen Werk allgemein für abstrus gehalten wurde und dessen Leben Elemente der Rationalität und der Psychopathologie vereinigt. Die lang erwartete Gödel-Biographie ergründet den Mythos des Mathematikers, indem sie gleichermaßen seine Ideen und Arbeit verständlich aufbereitet, als auch die Person zu erfassen vermag.