Contents -- List of Figures and Tables -- Preface -- ONE Introduction -- CONVENTION -- THE FIELDS OF TOPOLOGY -- STRATEGY AND STRUCTURE -- ANALOGY AND SYZYGY -- TWO Convention: How Means and Variances are Entrenched as Statistics -- I -- CONVENTION AND CULTURE IN MATHEMATICS -- THE CENTRAL LIMIT THEOREM -- II -- THE ESTABLISHMENT OF MEANS AND VARIANCES -- JUSTIFYING MEANS AND VARIANCES -- EXCEPTIONS AND ALTERNATIVES TO MEANS-VARIANCE ANALYSIS -- III -- THEOREMS FROM PROBABILITY AS JUSTIFICATIONS FOR MEANS-VARIANCE ANALYSIS -- ITO LEVY AND KHINCHIN: A TECHNICAL INTERLUDE -- DEFENDING RANDOMNESS FROM IMPOSSIBLE LONGSHOTS AND COINCIDENCES -- IV -- MAKING VARIANCES REAL BY IDENTIFYING THEM WITH ENDURING OBJECTS AND OTHER FEATURES OF THE WORLD -- VARIANCES AS THE CANONICAL ACCOUNT OF FLUCTUATION -- NOISE -- EINSTEIN AND FISHER -- V -- THREE Subject: The Fields of Topology -- I -- ANALYSIS AND ALGEBRA -- THE SUBJECTS OF TOPOLOGY -- PREVIEW -- II -- BEFORE THE BIRTH: STORIES OF NINETEENTH-CENTURY PRECURSORS -- III -- GENERAL TOPOLOGY: EXAMPLES AND COUNTEREXAMPLES DIAGRAMS AND CONSTRUCTIONS -- PARTS IN ANALYSIS -- ALGEBRAIC TOPOLOGY AS PLAYING WITH BLOCKS -- IV -- OPEN SETS AS THE CONTINUITY OF NEIGHBORHOODS -- DIMENSION AND HOMOLOGY AS BRIDGING CONCEPTS -- V -- THE TENSIONS IN PRACTICE: THE LOCAL AND THE GLOBAL -- THE TENSION IN ANALYSIS: THE HARD AND THE SOFT -- HARD ANALYSIS: THE ISING MODEL OF FERROMAGNETISM AND THE STABILITY OF MATTER -- VI -- KEEPING TRACK OF UNSMOOTHNESS AND DISCONTINUITY -- KEEPING TRACK OF THE SHAPE OF OBJECTS -- VII -- DIAGRAMMATICS AND MACHINERY -- PICTURES AND DIAGRAMS AS WAYS OF KEEPING TRACK OF FLOWS AND SYSTEMIC RELATIONSHIPS -- THE RIGHT PARTS -- NATURALITY -- VIII -- THE TENSIONS AND THE LESSONS -- Appendix: The Two-Dimensional Ising Model of a Ferromagnet.

SOME OF THE SOLUTIONS TO THE TWO-DIMENSIONAL ISING MODEL -- FOUR Calculation: Strategy Structure and Tactics in Applying Classical Analysis -- I -- DECIPHERING STRATEGY TACTICS AND STRUCTURE IN MATHEMATICS PAPERS -- II -- RIGOROUS AND EXACT MATHEMATICAL PHYSICS -- C.N. YANG ON THE SPONTANEOUS MAGNETIZATION OF THE ISING LATTICE -- FIGURING OUT SOME OF YANG'S PAPER -- STRATEGY AND STRUCTURE IN PROOFS OF THE STABILITY OF MATTER -- SOME OF THE MATHEMATICS AND THE PHYSICS -- MATHEMATICAL TECHNIQUES -- III -- STAGING SEQUENCING DEMONSTRATING -- WHY ALL THESE DETAILS? -- NEW IDEAS AND NEW SEQUENCES: THE ELLIOTT LIEB-WALTER THIRRING PROOF -- IV -- CHARLES FEFFERMAN'S CLASSICAL ANALYSIS -- 1. THE STABILITY OF MATTER -- 2. MATTER AS A GAS -- 3. STABILITY OF MATTER WITH A GOOD CONSTANT -- MORE ON FEFFERMAN-SECO -- THE FEFFERMAN-SECO ARGUMENT: A TECHNICAL INTERLUDE -- V -- "WHY ARE THESE MATHEMATICAL OBJECTS USEFUL IN DESCRIBING THIS SYSTEM?" -- TACTICS ASCENDANT: UNAVOIDABLE ALGEBRAIC MANIPULATION AND LENGTHY COMPUTATIONAL PROOFS -- THE WU-MCCOY-TRACY-BAROUCH PAPER -- WHY WIENER-HOPF AND TOEPLITZ? -- VI -- FIGURING OUT MORE OF WHAT IS REALLY GOING ON -- CLUES ALONG THE WAY: IDENTIFYING THE FORMAL AND THE ABSTRACT WITH SUBSTANTIVE MEANING -- FIVE Analogy: A Syzygy Between a Research Program in Mathematics and a Research Program in Physics -- I -- ANALOGY IN MATHEMATICAL WORK -- THE MATHEMATICAL ANALOGY HISTORICALLY -- THE ANALOGY IN PRACTICE -- II -- A SYZYGY BETWEEN FIELDS OF MATHEMATICS EXPRESSED IN VARIOUS WAYS -- THE ONSAGER PROGRAM IN LANGLANDS-PROGRAM TERMS -- THE ONSAGER PROGRAM AND THE LANGLANDS PROGRAM -- III -- THE IMPORT OF THE ANALOGIES AND THE SYZYGY -- PRIME FACTORIZATIONS AND ELEMENTARY EXCITATIONS -- THE ANALOGY MADE CONCRETE.

How THESE IDEAS CAME TO BE SEEN AS AN INTERRELATED COMPLEX -- IV -- ANDRE WEIL'S ROSETTA STONE LEARNING RIEMANNIAN AND TRANSLATING -- V -- SYZYGY AND FUNCTORIALITY -- THE PROGRAMS IN PRACTICE -- Six In Concreto: The City of Mathematics -- I -- RIEMANN AND MAXWELL AS AN EPITOME -- "WHAT IS REALLY GOING ON" IN THE MATHEMATICS -- II -- MATHEMATICS AND THE CITY IN THE NINETEENTH CENTURY -- III -- ORDER AND STRUCTURE -- CENTER AND PERIPHERY -- PROCESS PATTERN AND PALIMPSEST -- IV -- EMPLOYING YOUR BODY TO PROVE A THEOREM: THE SNAKE LEMMA OF ALGEBRAIC TOPOLOGY -- TRAIN TRACKS AND PAIRS OF PANTS -- V -- GOD'S TRANSCENDENCE AS ANALOGIZED TO MATHEMATICAL NOTIONS -- ASCENT TO THE ABSOLUTE -- SETS AS MODELS OF GOD'S INFINITUDE -- VI -- THE CITY OF MATHEMATICS -- Epilog -- APPENDICES -- A:The Spontaneous Magnetization of a Two-Dimensional Ising Model" -- B:On the Dirac and Schwinger Corrections to the Ground-State Energy of an Atom -- C:Sur la forme des espaces topologiques et sur les points fixes des representations -- D:Une lettre a Simone Weil -- Notes -- Bibliography -- Index.