Eugène Charles Catalan made his famous conjecture – that 8 and 9 are the only two consecutive perfect powers of natural numbers – in 1844 in a letter to the editor of Crelle’s mathematical journal. One hundred and fifty-eight years later, Preda Mihailescu proved it. Catalan’s Conjecture presents this spectacular result in a way that is accessible to the advanced undergraduate. The author dissects both Mihailescu’s proof and the earlier work it made use of, taking great care to select streamlined and transparent versions of the arguments and to keep the text self-contained. Only in the proof of Thaine’s theorem is a little class field theory used; it is hoped that this application will motivate the interested reader to study the theory further. Beautifully clear and concise, this book will appeal not only to specialists in number theory but to anyone interested in seeing the application of the ideas of algebraic number theory to a famous mathematical problem.

The historical relationship between the Catalan and Occitan languages had a definitive impact on the linguistic identity of the powerful Crown of Aragon and the emergent Spanish Empire. Drawing upon a wealth of historical documents, linguistic treatises and literary texts, this book offers fresh insights into the political and cultural forces that shaped national identities in the Iberian Peninsula and, consequently, neighboring areas of the Mediterranean during the Middle Ages and the Early Modern Period. The innovative textual approach taken in these pages exposes the multifaceted ways in which the boundaries between the region’s most prestigious languages were contested, and demonstrates how linguistic identities were linked to ongoing struggles for political power. As the analysis reveals, the ideological construction of Occitan would play a crucial role in the construction of a unified Catalan, and Catalan would, in turn, give rise to a fervent debate around ‘Spanish’ language that has endured through the present day. This book will appeal to students and scholars of historical linguistics, sociolinguistics, Hispanic linguistics, Catalan language and linguistics, anthropological linguistics, Early Modern literature and culture, and the history of the Mediterranean.

This is a book about how Catalans use their past, real and imagined, in the construction of their present and future. Michael A. Vargas inventories the significant people, signal events, and familiar icons that constitute the Catalan collective memory, from Wilfred the Hairy and Sant Jordi to the mountain monastery of Montserrat, red peasant caps, and human towers in town squares. He then considers how that inventory is employed to posit a brilliant political heritage at the forefront of modern European democracy—and for some, to build a powerful independence movement. As the future of Catalonia remains fraught, this book offers a lively and engaging exploration of how we draw upon history to confront contemporary challenges.

The Splendor and Opulence of the Past traces the career of Jaume Caresmar (1717–1791), a church historian and a key figure of the Catalan Enlightenment who transcribed tens of thousands of parchments to preserve and glorify Catalonia's medieval past in the face of its diminishing autonomy. As Paul Freedman shows, Caresmar's books, essays, and transcriptions—some only recently discovered—provide fresh insights into the Middle Ages as remembered in modern Catalonia and illustrate how a nation's past glories and humiliations can inform contemporary politics and culture. From the ninth to the sixteenth centuries, Catalonia was a thriving, independent set of principalities within what would become modern Spain. In the wake of the dismantling of its autonomy by the eighteenth-century Spanish state, Catalan scholars looked to the region's medieval independence and wealth as a means of maintaining a distinct Catalan identity and resisting Castilian hegemony. Through their writings and archival investigations, Caresmar and the canons at Santa Maria de Bellpuig de les Avellanes, where Caresmar was abbot, laid the foundations for not only the scholarly exploration of the Middle Ages but also the development of Catalan national sentiment. Although the eighteenth century is often regarded as a low point for the Catalan language and culture, The Splendor and Opulence of the Past emphasizes the importance of this period's antiquarians to Catalan projects of modernization and economic progress and links their historiography of the Middle Ages to struggles over Catalonia's relationship to the Spanish state over two centuries.

The Symposium on the Current State and Prospects of Mathematics was held in Barcelona from June 13 to June 18, 1991. Seven invited Fields medalists gavetalks on the development of their respective research fields. The contents of all lectures were collected in the volume, together witha transcription of a round table discussion held during the Symposium. All papers are expository. Some parts include precise technical statements of recent results, but the greater part consists of narrative text addressed to a very broad mathematical public. CONTENTS: R. Thom: Leaving Mathematics for Philosophy.- S. Novikov: Role of Integrable Models in the Development of Mathematics.- S.-T. Yau: The Current State and Prospects of Geometry and Nonlinear Differential Equations.- A. Connes: Noncommutative Geometry.- S. Smale: Theory of Computation.- V. Jones: Knots in Mathematics and Physics.- G. Faltings: Recent Progress in Diophantine Geometry.