In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isom…
This biography sheds light on all facets of the life and the achievements of Ernst Zermelo (1871-1953). Zermelo is best-known for the statement of the axiom of choice and his axiomatization of set theory. However, he also worked in applied mathematics and mathematical physics. His dissertation, for example, promoted the calculus of variations, and he created the pivotal method in the theory of …
This book presents an account of selected topics from key mathematical works of medieval Islam, based on the Arabic texts themselves. Many of these works had a great influence on mathematics in Western Europe. Topics covered in the first edition include arithmetic, algebra, geometry, trigonometry, and numerical approximation; this second edition adds number theory and combinatorics. Additionall…
Joseph W. Dauben, a leading authority on the history of mathematics in Europe, China, and North America, has played a pivotal role in promoting international scholarship over the last forty years. This Festschrift volume, showcasing recent historical research by leading experts on three continents, offers a global perspective on important themes in this field.
This book provides the first critical edition of Ibn al-Haytham’s On the Shape of the Eclipse with English translation and commentary, which records the first scientific analysis of the camera obscura. On the Shape of the Eclipse includes pioneering research on the conditions of formation of the image, in a time deemed to be committed to aniconism. It also provides an early attempt to merge t…
The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with arch…
This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen I” will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of example…
The son of a prominent Japanese mathematician who came to the United States after World War II, Ken Ono was raised on a diet of high expectations and little praise. Rebelling against his pressure-cooker of a life, Ken determined to drop out of high school to follow his own path. To obtain his father’s approval, he invoked the biography of the famous Indian mathematical prodigy Srinivasa Raman…
“Modern Logic, 1850–1950, East and West is a memorial volume for the respected historian of logic Irving H. Anellis … . an excellent job identifying the distinctive features of this work in accessible terms and is able to reflect on its historical importance and broader social context from firsthand experience. … an excellent starting point for any historical study of this avenue of mat…