Contributors
Graham Allan, late Reader in Mathematics, University of Cambridge
THE SPECTRUM [III.86]
Noga Alon, Baumritter Professor of Mathematics and Computer Science, Tel Aviv University
EXTREMAL AND PROBABILISTIC COMBINATORICS [IV.19]
George Andrews, Evan Pugh Professor in the Department of Mathematics, The Pennsylvania State University
SRINIVASA RAMANUJAN [VI.82]
Tom Archibald, Professor, Department of Mathematics, Simon Fraser University
THE DEVELOPMENT OF RIGOR IN MATHEMATICAL ANALYSIS [II.5], CHARLES HERMIT [VI.47]
Sir Michael Atiyah, Honorary Professor, School of Mathematics, University of Edinburgh
WILLIAM VALLANCE DOUGLAS HODGE [VI.90], ADVICE TO A YOUNG MATHEMATICIAN [VIII.6]
David Aubin, Assistant Professor, Institut de mathématiques de Jussieu
NICOLAS BOURBAKI [VI.96]
Joan Bagaria, ICREA Resecrch Professor, University of Barcelona
SET THEORY [IV.22]
Keith Ball, Astor Professor of Mathematics, University College London
THE EUCLIDEAN ALGORITHM AND CONTINUED FRACTIONS [III.22], OPTIMIZATION AND LAGRANGE MULTIPLIERS [III.64], HIGH-DIMENSIONAL GEOMETRY AND ITS PROBABILISTIC ANALOGUES [IV.26]
Alan F. Beardon, Professor of Complex Analysis, University of Ccmbridge
RIEMANN SURFACES [III.79]
David D. Ben-Zvi, Associate Professor of Mathematics, University of Texas, Austin
MODULI SPACES [IV.8]
Vitaly Bergelson, Professor of Mathematics, The Ohio State University
ERGODIC THEOREMS [III.9]
Nicholas Bingham, Professor, Mathematics Department, Imperial College London
ANDREI NIKOLAEVICH KOLMOGOROV [VI.88]
Béla Bollobás, Professor of Mathematics, University of Cambridge and University of Memphis
GODFREY HAROLD HARDY [VI.73],
JOHN EDENSOR LITTLEWOOD [VI.79],
ADVICE TO A YOUNG MATHEMATICIAN [VIII.6]
Henk Bos, Honorary Professor, Department of Science Studies, Aarhus University; Professor Emeritus, Department of Mathematics, Utrecht University
RENÉ DESCARTES [VI.11]
Bodil Branner, Emeritus Professor, Department of Mathematics, Technical University of Denmark
DYNAMICS [IV.14]
Martin R. Bridson, Whitehead Professor of Pure Mathematics, University of Oxford
GEOMETRIC AND COMBINATORIAL GROUP THEORY [IV.10]
John P. Burgess, Professor of Philosophy, Princeton, University
ANALYSIS, MATHEMATICAL AND PHILOSOPHICAL [VII.12]
Kevin Buzzard, Professor of Pure Mathematics, Impericl College London
L-FUNCTIONS [III.47], MODULAR FORMS [III.59]
Peter J. Cameron, Professor of Mathematics, Queen Mary, University of London
DESIGNS [III.14], GÖDEL’S THEOREM [III.15]
Jean-Luc Chabert, Professor, Laborntoire Amiénois de Mathemetique Fondamentale et Appliquée, Unveersité de Picardie
ALGORITHMS [II.4]
Eugenia Cheng, Lecturer, Department of Pure Mathematics, University of Sheffield
CATEGORIES [III.8]
Clifford Cocks, Chief Mathematician, Government Communications Headquarters, Cheltenham
MATHEMATICS AND CRYPTOGRAPHY [VII.7]
Alain Connes, Professor,
Collège de France, IHES, end Vanderbilt University
ADVICE TO A YOUNG MATHEMATICIAN [VIII.6]
Leo Corry, Director, The Cohn Institute for History and Philosophy of Science end Ideas, Tel Aviv University
THE DEVELOPMENT OF THE IDEA OF PROOF [II.6]
Wolfgang Coy, Professor of Computer Science, Humboldt-Universität zu Berlin
JOHN VON NEUMANN [VI.91]
Tony Crilly, Emeritus Reader in Mathematical Sciences, Department of Economics and Statistics, Middlesex University
ARTHUR CAYLEY [VI.46]
Serafina Cuomo, Lecturer in Roman History, School of History, Classics and Archaeology, Birkbeck College
PYTHAGORAS [VI.1], EUCLID [VI.2], ARCHIMEDES [VI.3], APOLLONIUS [VI.4]
Mihalis Dafermos, Reader in Mathematical Physics, University of Cambridge
GENERAL RELATIVITY AND THE EINSTEIN EQUATIONS [IV.13]
Partha Dasgupta, Frank Ramsey Professor of Economics, University of Cambridge
MATHEMATICS AND ECONOMIC REASONING [VII.8]
Ingrid Daubechies, Professor of Mathematics, Princeton University
WAVELETS AND APPLICATIONS [VII.3]
Joseph W. Dauben, Distinguished Professor, Herbert H Lehman College and City University of New York
GEORG CANTOR [VI.54], ABRAHAM ROBINSON [VI.95]
John W. Dawson Jr., Professor of Mathematics, Emeritus, The Pennsylvania State University
KURT GÖDEL [VI.92]
Francois de Gandt, Professeur d’Histoire des Sciences et de Philosophie, Université Charles de Gaulle, Lille
JEAN LE ROND D’ALEMBERT [VI.20]
Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University
MATHEMATICAL STATISTICS [VII.10]
Jordan S. Ellenberg, Associate Professor of Mathematics, University of Wisconsin
ELLIPTIC CURVES [III.21], SCHEMES [III.82], ARITHMETIC GEOMETRY [IV.5]
Lawrence C. Evans, Professor of Mathematics, University of California, Berkeley
VARIATIONAL METHODS [III.94]
Florence Fasanelli, Program Director,
American Association for the Advancement of Science
MATHEMATICS AND ART [VII.14]
Anita Burdman Feferman, Independent Scholar and Writer,
ALFRED TARSKI [VI.87]
Solomon Feferman, Patrick Suppes Family Professor of Humanities and Sciences and Emeritus Professor of Mathematics and Philosophy, Department of Mathematics, Stanford University
ALFRED TARSKI [VI.87]
Charles Fefferman, Professor of Mathematics, Princeton, University
THE EULER AND NAVIER-STOKES EQUATIONS [III.23], CARLESON’S THEOREM [III.5]
Della Fenster, Professor, Department of Mathematics and Computer Science, University of Richmond, Virginia
EMIL ARTIN [VI.86]
José Ferreirós, Professor of Logic and Philosophy of Science, University of Seville
THE CRISIS IN THE FOUNDATIONS OF MATHEMATICS [II.7], JULIUS WILHELM RICHARD DEDEKIND [VI.50], GIUSEPPE PEANO [VI.62]
David Fisher, Associate Professor of Mathematics, Indiana University, Bloomington
MOSTOW’S STRONG RIGIDITY THEOREM [III.23]
Terry Gannon, Professor,
Department of Mathematical Sciences, University of Alberta
VERTEX OPERATOR ALGEBRAS [IV.17]
A. Gardiner, Reader in Mathematics and Mathematics Education, University of Birmingham
THE ART OF PROBLEM SOLVING [VIII.1]
Charles C. Gillispie, Dayton-Stockton Professor of History of Science, Emeritus, Princeton University
PIERRE-SIMON LAPLACE [VI.23]
Oded Goldreich, Professor of Computer Science, Weizmann Institute of Science, Israel
COMPUTATIONAL COMPLEXITY [IV.20]
Catherine Goldstein, Directeur de Recherche, Institut de Mathématiques de Jussieu, CNRS, Paris
PIERRE FERMAI [VI.12]
Fernando Q. Gouvêa, Carter Professor of Mathematics, Colby College, Waterville, Maine
FROM NUMBERS TO NUMBER SYSTEMS [II.1],
LOCAL AND GLOBAL IN NUMBER THEORY [III.51]
Andrew Granville, Professor, Department of Mathematics and Statistics, Université de Montréal
ANALYTIC NUMBER THEORY [IV.2]
Ivor Grattan-Guinness, Emeritus Professor of the History of Mathematics and Logic, Middlesex University
ADRIEN-MARIE LEGENDRE [VI.24], JEAN-BAPTISTE JOSEPH FOURIER [VI.25], SIÉON-DENIS POISSON [VI.27], AUGUSTIN-LOUIS CAUCHY [VI.29], BERTRAND ARTHUR WILLIAM RUSSELL [VI.71], FRIGYES (FRÉDÉRIC) RIESZ [VI.74]
Jeremy Gray, Professor of History of Mathematics, The Open University
GEOMETRY [II.2], FUCHSIAN GROUPS [III.28], CARL FRIEDRICH GAUSS [VI.26], AUGUST FERDINAND MOBIUS [VI.30], NICOLAI IVANOVICH LOBACHEVSKII [VI.31], JÁNOS BOLYAI [VI.34], GEORG BERNHARD FRIEDRICH RJEMANN [VI.49], WILLIAM KINGDON CLIFFORD [VI.55], ÉLIE JOSEPH CARTAN [VI.69], THORALF SKOLEM [VI.81]
Ben Green, Herchel Smith Professor of Pure Mathematics, University of Cambridge
THE GAMMA FUNCTION [III.31], IRRATIONAL AND TRANSCENDENTAL NUMBERS [III.41], MODULAR ARITHMETIC [III.58], NUMBER FIELDS [III.63], QUADRATIC FORMS [III.73], TOPOLOGICAL SPACES [III.90], TRIGONOMETRIC FUNCTIONS [III.92]
Ian Grojnowski, Professor of Pure Mathematics, University of Cambridge
REPRESENTATION THEORY [IV.9]
Niccolò Guicciardini, Associate Professor of History of Science, University of Bergamo
ISAAC NEWTON [VI.14]
Michael Harris, Professor of Mathematics, Université Paris 7—Denis Diderot
“WHY MATHEMATICS?” YOU MIGHT ASK [VIII.2]
Ulf Hashagen, Doctor, Munich Center for the History of Science and Technology, Deutsches Museum, Munich
PETER GUSTAV LEJEUNE DIRICHLET [VI.36]
Nigel Higson, Professor of Mathematics, The Pennsylvania State University
OPERATOR ALGEBRAS [IV.15], THE ATIYAH–SINGER INDEX THEOREM [III.2]
Andrew Hodges, Tutorial Fellow in Mathematics, Wadham College, University of Oxford
ALAN TURING [VI.94]
F. E. A. Johnson, Professor of Mathematics, University College London
BRAID GROUPS [III.4]
Mark Joshi, Associate Professor,
Centre for Actuarial Studies, University of Melbourne
THE MATHEMATICS OF MONEY [VII.9]
Kiran S. Kedlaya, Associate Professor of Mathematics, Massachusetts Institute of Technology
FROM QUADRATIC RECIPROCITY TO CLASS FIELD THEORY [III.28]
Frank Kelly, Professor of the Mathematics of Systems and Master of Christ’s College, University of Cambridge
THE MATHEMATICS OF TRAFFIC IN NETWORKS [VII.4]
Sergiu Klainerman, Professor of Mathematics, Princeton University
PARTIAL DIFFERENTIAL EQUATIONS [IV.12]
Jon Kleinberg, Professor of Computer Science, Cornell University
THE MATHEMATICS OF ALGORITHM DESIGN [VII.5]
Israel Kleiner, Professor Emeritus,
Department of Mathematics and Statistics, York University
KARL WEIERSTRASS [VI.44]
Jacek Klinowski, Professor of Chemiccl Physics, University of Cambridge
MATHEMATICS AND CHEMISTRY [VII.1]
Eberhard Knobloch, Professor, Institute for Philosophy, History of Science and Technology, Technical University of Berlin
GOTTFRIED WILHELM LEIBNIZ [VI.15]
János Kollár, Professor of Mathematics, Princeton University
ALGEBRAIC GEOMETRY [IV.4]
T. W. Körner, Professor of Fourier Analysis, University of Cambridge
SPECIAL FUNCTIONS [III.85], TRANSFORMS [III.91], THE BANACH–TARSKI PARADOX [III.3], THE UBIQUITY OF MATHEMATICS [VIII.3]
Michael Krivelevich, Professor of Mathematics, Tel Aviv University
EXTREMAL AND PROBABILISTIC COMBINATORICS [IV.19]
Peter D. Lax, Professor, Courant Institute of Mathematical Sciences, New York University
RICHARD COURANT [VI.83]
Jean-François Le Gall, Professor of Mathematics, Université Paris-Sud, Orsay
STOCHASTIC PROCESSES [IV.24]
W. B. R. Lickoresh, Emeritus Professor of Geometric Topology, University of Cambridge
KNOT POLYNOMIALS [III.44]
Martin W. Liebeck, Professor of Pure Mathematics, Imperial College London
PERMUTATION GROUPS [III.68], THE CLASSIFICATION OF FINITE SIMPLE GROUPS [III.7], THE INSOLUBILITY OF THE QUINTIC [III.21]
Jesper Lützen, Professor, Department of Mathematical Sciences, University of Copenhagen
JOSEPH LIOUVILLE [VI.39]
Des MacHale, Associate Professor of Mathematics, University College Cork
GEORGE BOOLE [VI.43]
Alan L. Mackay, Professor Emeritus, School of Crystallography, Birkbeck College
MATHEMATICS AND CHEMISTRY [VII.1]
Shahn Majid, Professor of Mathematics, Queen Mary, University of London
QUANTUM GROUPS [III.75]
Lech Maligranda, Professor of Mathematics, Luleå University of Technology, Sweden
STEFAN BANACH [VI.84]
David Marker, Head of the Department of Mathematics, Statistics, and Computer Science, University of Illinois et Chiccgo
LOGIC AND MODEL THEORY [IV.23]
Jean Mawhin, Professor of Mathematics, Université Cctholique de Louvain
CHARLES-JEAN DE LA VALLÉE POUSSIN [VI.67]
Barry Mazur, Gerhard Gcde University Professor, Mathematics Department, Harvard University
ALGEBRAIC NUMBERS [IV.1]
Dusa McDuff, Professor of Mathematics, Stony Brook University and Barnard College
ADVICE TO A YOUNG MATHEMATICIAN [VIII.6]
Colin McLarty, Truman P. Handy Associate Professor of Philosophy and of Mathematics, Case Western Reserve University
EMMV NOETHER [VI.76]
Bojan Mohar, Canada Research Chair in Graph Theory, Simon Fraser University, Professor of Mathematics, University of Ljubljana
THE FOUR-COLOR THEOREM [III.12]
Peter M. Neumann, Fellow mnd Tutor in Mathematics, The Queen’s College, Oxford; University Lecturer in Mathematics, University of Oxford
NIELS HENRIK ABEL [VI.33], ÉVARISTE GALOIS [VI.41], FERDINAND GÉORG FROBENIUS [VI.58], WILLIAM BURNSIDE [VI.60]
Catherine Nolan, Associate Professor of Music, The University of Western Ontario
MATHEMATICS AND MUSIC [VII.13]
James Norris, Professor of Stochcstic Analysis, Stctisticcl Laboratory, University of Cambridge
PROBABILITY DISTRIBUTIONS [III.71]
Brian Osserman, Assistant Professor, Department of Mathematics, University of Cclifornic, Davis
THE WEIL CONJECTURES [III.35]
Richard S. Palais, Professor of Mathematics, University of Cclifornic, Irvine
LINEAR AND NONLINEAR WAVES AND SOLITONS [III.49]
Marco Panza, Directeur de Recherche, CNRS, Paris
JOSEPH LOUIS LAGRANGE [VI.22]
Karen Hunger Parshall, Professor of History and Mathematics, University of Virginic
THE DEVELOPMENT OF ABSTRACT ALGEBRA [II.3], JAMES JOSEPH SYLVESTER [VI.42]
Gabriel P. Paternain, Reader in Geometry and Dyncmics, University of Cambridge
SYMPLECTIC MANIFOLDS [III.88]
Jeanne Peiffer, Directeur de Recherche, CNRS, Centre Alexandre Koyré, Paris
THE BERNOULLIS [VI.18]
Birgit Petri, Ph.D. Candidate, Fcchbe reich? cthematik, Technische Universität Darmstadt
LÉOPOLD KRONECKER [VI.48], ANDRÉ WEIL [VI.93]
Carl Pomerance, Professor of Mathematics, Dartmouth College
COMPUTATIONAL NUMBER THEORY [IV.3]
Helmut Pulte, Professor, Ruhr-Universität Bochum
CARL GUSTAV JACOB JACOBI [VI.35]
Bruce Reed, Cianada Research Chcir in Graph Theory, McGill University
THE ROBERTSON–SEYMOUR THEOREM [III.32]
Michael C. Reed, Bishop-MacDermott Family Professor of Mathematics, Duke University
MATHEMATICAL BIOLOGY [VII.2]
Adrian Rice, Associate Professor of Mathematics, Randolph–Macon College, Virginia
A CHRONOLOGY OF MATHEMATICAL EVENTS [VIII.7]
Eleanor Robson, Senior Lecturer, Department of History and Philosophy of Science, University of Cambridge
NUMERACY [VIII.4]
Igor Rodnianski, Professor of Mathematics, Princeton University
THE HEAT EQUATION [III.36]
John Roe, Professor of Mathematics, The Pennsylvania State University
OPERATOR ALGEBRAS [IV.15], THE ATIYAH–SINGER INDEX THEOREM [III.2]
Mark Ronan, Professor of Mathematics, University of Illinois ct Chicago; Honorary Professor of Mathematics, University College London
BUILDINGS [III.5], LIE THEORY [III.48]
Edward Sandifer, Professor of Mathematics, Western Connecticut Stcte University
LEONHARD EULER [VI.19]
Peter Sarnak, Professor, Princeton University and Institute for Advrnced Study, Princeton
ADVICE TO A YOUNG MATHEMATICIAN [VIII.6]
Tilman Sauer, Doctor, Einstein Papers Project, Californic Institute of Technology
HERMANN MINKOWSKI [VI.64]
Norbert Schappacher, Professor, Institut de Recherche Mathématique Avancee, Strasbourg
LEOPOLD KRONECKER [VI.48], ANDRÉ WEIL [VI.93]
Andrzej Schinzel, Professor of Mathematics, Polish Academy of Sciences
WACŁAW SIERPIŃSKI [VI.77]
Erhard Scholz, Professor of History of Mathematics, Department of Mathematics and Natural Sciences, Universität Wuppertal
FELIX HAUSDORFF [VI.68], HERMANN WEYL [VI.80]
Reinhard Siegmund–Schultze, Professor, Faculty of Engineering and Science, University of Agder, Norway
HENRI LEBESGUE [VI.72], NORBERT WIENER [VI.85]
Gordon Slade, Professor of Mathematics, University of British Columbic
PROBABILISTIC MODELS OF CRITICAL PHENOMENA [IV.25]
David J. Spiegelhalter, Winton Professor of the Public Understmnding of Risk, University of Cambridge
MATHEMATICS AND MEDICAL STATISTICS [VII.11]
Jacqueline Stedall, Junior Research Fellow in Mathematics, The Queen’s College, Oxford
FRANCOIS VIÈTE [VI.9]
Arild Stubhaug, Freelance Writer, Oslo
SOPHUS LIE [VI.53]
Madhu Sudan, Professor of Computer Science and Engineering, Massachusetts Institute of Technology
RELIABLE TRANSMISSION OF INFORMATION [VII.6]
Terence Tao, Professor of Mathematics, University of Ctlifornk, Los Angeles
COMPACTNESS AND COMPACTIFICATION [III.9], DIFFERENTIAL FORMS AND INTEGRATION [III.16], DISTRIBUTIONS [III.18], THE FOURIER TRANSFORM [III.27], FUNCTION SPACES [III.29], HAMILTONIANS [III.35], RICCI FLOW [III.78], THE SCHRODINGER EQUATION [III.83], HARMONIC ANALYSIS [IV.11]
Jamie Tappenden, Associate Professor of Philosophy, University of Michigmn
GOTTLOB FREGE [VI.56]
C. H. Taubes, William Petschek Professor of Mathematics, Harvard University
DIFFERENTIAL TOPOLOGY [IV.7]
Rüdiger Thiele, Priνatdozent, Universität Leipzig
CHRISTIAN FELIX KLEIN [VI.57]
Burt Totaro, Lowndecrn Professor of Astronomy and Geometry, University of Ccm bridge
ALGEBRAIC TOPOLOGY [IV.6]
Lloyd N. Trefethen, Professor of Numerical Analysis, University of Oxford
NUMERICAL ANALYSIS [IV.21]
Dirk van Dalen, Professor, Department of Philosophy, Utrecht University
LUITZEN EGBERTUS JAN BROUWER [VI.75]
Richard Weber, Churchill Professor of Mathematics for Operntioncl Research, University of Ccm bridge
THE SIMPLEX ALGORITHM [III.84]
Dominic Welsh, Professor of Mathematics, Mathematical Institute, University of Oxford
MATROIDS [III.54]
Avi Wigderson, Professor in the School of Mathematics, Institute for Advcrnced Study, Princeton
EXPANDERS [III.24], COMPUTATIONAL COMPLEXITY [IV.20]
Herbert S. Wilf, Thomas A. Scott Professor of Mathematics, University of Pennsylvania
MATHEMATICS: AN EXPERIMENTAL SCIENCE [VIII.5]
David Wilkins, Lecturer in Mathematics, Trinity College, Dublin
WILLIAM ROWAN HAMILTON [VI.37]
Benjamin H. Yandell, Pasadena, Califomic (deceased)
DAVID HILBERT [VI.63]
Eric Zaslow, Professor of Mathematics, Northwestern University
CALABI–YAU MANIFOLDS [III.6], MIRROR SYMMETRY [IV.16]
Doron Zeilberger, Board of Governors Professor of Mathematics, Rutgers University
ENUMERATIVE AND ALGEBRAIC COMBINATORICS [IV.18]
Unattributed articles were written by the editors. In part III, Imre Leader wrote the articles THE AXIOM OF CHOICE [III.1], THE AXIOM OF DETERMINACY [III.2], CARDINALS [III.7], COUNTABLE AND UNCOUNTABLE SETS [III.11], GRAPHS [III.34], JORDAN NORMAL FORM [III.43], MEASURES [III.55], MODELS OF SET THEORY [III.57], ORDINALS [III.66], THE PEANO AXIOMS [III.67], RINGS, IDEALS, AND MODULES [III.81], and THE ZERMELO–FRAENKEL AXIOMS [III.99]. In part V, THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS [III.18] is by Imre Leader and TIm THREE–BODY PROBLEM [III.33] is by June Barrow–Green. In part VI, June Barrow–Green wrote all of the unattributed articles. All other unattributed articles throughout the book were written by Timothy Gowers.