Jeremy Gray

José Ferreirós Domínguez

Aimed at both students and researchers in philosophy, mathematics and the history of science, this edited volume, authored by leading scholars, highlights foremost developments in both the philosophy and history of modern mathematics.

Essays in History and Philosophy

The Architecture of Modern Mathematics

John Fauvel

The History of Mathematics, a Reader. Edited by John Fauvel and Jeremy Gray

Robin Wilson

Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.

Selections from The Mathematical Intelligencer

Mathematical Conversations

David Hilbert was arguably the leading mathematician of his generation. He was among the few mathematicians who could reshape mathematics, and was able to because he brought together an impressive technical power and mastery of detail with a vision of where the subject was going and how it should get there. This was the unique combination which he brought to the setting of his famous 23 Problems. Few problems in mathematics have the status of those posed by David Hilbert in 1900. Mathematicians have made their reputations by solving individual ones such as Fermat's last theorem, and several remain unsolved including the Riemann hypotheses, which has eluded all the great minds of this century. A hundred years on, it is timely to take a fresh look at the problems, the man who set them, and the reasons for their lasting impact on the mathematics of the twentieth century. In this fascinating new book, Jeremy Gray and David Rowe consider what has made this the pre-eminent collection of problems in mathematics, what they tell us about what drives mathematicians, and the nature of reputation, influence and power in the world of modern mathematics. The book is written in a clear and lively manner and will appeal both to the general reader with an interest in mathematics and to mathematicians themselves.

The Hilbert Challenge

Vagn Lundsgaard Hansen

History of Mathematics is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on History of Mathematics discusses: Mathematics in Egypt and Mesopotamia; History of Trigonometryto 1550; Mathematics in Japan; The Mathematization of The Physical Sciences-Differential Equations of Nature; A Short History of Dynamical Systems Theory:1885-2007; Measure Theories and Ergodicity Problems; The Number Concept and Number Systems; Operations Research and Mathematical Programming: From War to Academia - A Joint Venture; Elementary Mathematics From An Advanced Standpoint; The History and Concept of Mathematical Proof; Geometry in The 20th Century; Bourbaki: An Epiphenomenon in The History of Mathematics This volume is aimed at the following five major target audiences: University and College Students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers, NGOs and GOs.

History of Mathematics

Reuben Acciano

The crakling energy of Rotterdam's nightlife, Friesland's golden sands and shimmering lakes, Amsterdam's museums ans art galleries - the Netherlands is more than canals, clogs and coffeeschops! This inspiring guide takes you beyond the tourist honeypots to uncover the real Netherlands. Pedal power - our special section on cycling tells you need to know about biking the byways. Be inspired - full-colour highlights and preplanning sections give you the lowdown on this Low Country before you leave home. Know your way - packed with user-friendly maps. Stay in style - bustling hostels or boutique hotels, canalsides or countryside: whatever you taste, we've got it covered. Find the fun - from cool cafés to fabulous festivals, our experts bring you the best reviews.

The Netherlands

From beerhalls and Bratwurst to Glockenspiels and gardens, this comprehensive guide to the Bavarian capital is an indispensible companion for any traveller. -- 16 pages of colour maps, including a public transport map -- the latest on clubs, bars and live music venues -- invaluable language section -- detailed information on excursions to Nuremberg and Salzburg -- all museums covered, from Picasso to porcelain, BMWs to Botticelli

Munich

Old World charm and New World chic collide in this historic town with a young attitude. Take this guide and explore Montréal - it's jazz heaven, architecture nirvana, restaurant cloud nine, all with a French twist on good ol' Canadian hospitality. 18 full-color, detailed maps ; restaurant listings to impress every palate and budget ; auberge de jeunesse or gîte du passant ? Accommodations options in detail ; walking tour of Vieux Montréal, Downtown and Quartier Latin ; Coverage of gay & lesbian Montréal, as well as the international Jazz Festival, North America's biggest ; très handy French Language section and glossary.

Lonely Planet Montreal

Nikki Hall

Designed for the discerning, short-term visitor, Lonely Planet Condensed captures the best a destination has to offer and presents it in a compact, portable package. Each informative and entertaining guide provides selective information in typical Lonely Planet style: from specifics on top sites to opinionated reviews of where to eat, stay, and have fun. Detailed fold-out maps are located inside front and back covers. Each guide is a convenient, essential resource for the focused traveller.

Amsterdam Condensed

Catherine Goldstein

Jim Ritter

Une image courante des mathématiques en fait une discipline née en Europe et se répandant ensuite dans le monde entier. L'histoire récente des sciences récuse ce récit simpliste en montrant les formations mathématiques et les interactions en jeu, tant à l'intérieur qu'à l'extérieur de l'Europe. Synthétisant ces résultats, l'ouvrage va plus loin et cherche à comprendre la raison d'être et les modalités du récit usuel, ainsi que la constitution concrète des mathématiques européennes. De l'Extrême-Orient aux centres fluctuants de l'Europe géographique, de l'Antiquité classique aux nations modernes, la recherche de l'Europe mathématique mène à la réflexion sur les rapports entre sciences et sociétés.

Histoires, mythes, identités

L' Europe mathématique/Mathematical Europe

Waldo Dunnington

Gauss: Titan of Science

This book presents a history of differential equations, both ordinary and partial, as well as the calculus of variations, from the origins of the subjects to around 1900. Topics treated include the wave equation in the hands of d'lembert and Euler; Fourier solutions to the heat equation and the contribution of Kovalevskaya; the work of Euler, Gauss, Kummer, Riemann, and Poincaré on the hypergeometric equation; Green's functions, the Dirichlet principle, and Schwarz's solution of the Dirichlet problem; minimal surfaces; the telegraphists' equation and Thomson's successful design of the trans-Atlantic cable; Riemann's paper on shock waves; the geometrical interpretation of mechanics; and aspects of the study of the calculus of variations from the problems of the catenary and the brachistochrone to attempts at a rigorous theory by Weierstrass, Kneser, and Hilbert. Three final chapters look at how the theory of partial differential equations stood around 1900, as they were treated by Picard and Hadamard. There are also extensive, new translations of original papers by Cauchy, Riemann, Schwarz, Darboux, and Picard. The first book to cover the history of differential equations and the calculus of variations in such breadth and detail, it will appeal to anyone with an interest in the field. Beyond secondary school mathematics and physics, a course in mathematical analysis is the only prerequisite to fully appreciate its contents. Based on a course for third-year university students, the book contains numerous historical and mathematical exercises, offers extensive advice to the student on how to write essays, and can easily be used in whole or in part as a course in the history of mathematics. Several appendices help make the book self-contained and suitable for self-study.

A History of Differential Equations to 1900

Change and Variations

Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method--debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.

The Modernist Transformation of Mathematics

Plato's Ghost

This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.

From Algebraic Equations to Modern Algebra

A History of Abstract Algebra

G. Waldo Dunnington

Fritz-Egbert Dohse

Classic biography of Gauss, updated with new introduction, bibliography and new material.

Titan of Science

Carl Friedrich Gauss

guida città

Amsterdam

June Barrow-Green

The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the first volume of the two-volume set, takes readers from the beginning of counting in prehistory to 1600 and the threshold of the discovery of calculus. It is notable for the extensive engagement with original—primary and secondary—source material. The coverage is worldwide, and embraces developments, including education, in Egypt, Mesopotamia, Greece, China, India, the Islamic world and Europe. The emphasis on astronomy and its historical relationship to mathematics is new, and the presentation of every topic is informed by the most recent scholarship in the field. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.

Jeremy Gray

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