TITLE -- COPYRIGHT -- CONTENTS -- INTRODUCTION -- CHAPTER 1 ANCIENT WESTERN MATHEMATICS -- ANCIENT MATHEMATICAL SOURCES -- MATHEMATICS IN ANCIENT MESOPOTAMIA -- THE NUMERAL SYSTEM AND ARITHMETIC OPERATIONS -- GEOMETRIC AND ALGEBRAIC PROBLEMS -- MATHEMATICAL ASTRONOMY -- MATHEMATICS IN ANCIENT EGYPT -- THE NUMERAL SYSTEM AND ARITHMETIC OPERATIONS -- GEOMETRY -- ASSESSMENT OF EGYPTIAN MATHEMATICS -- GREEK MATHEMATICS -- THE DEVELOPMENT OF PURE MATHEMATICS -- GEOMETRY IN THE 3RD CENTURY BCE -- LATER TRENDS IN GEOMETRY AND ARITHMETIC -- MATHEMATICS IN THE ISLAMIC WORLD (8TH-15TH CENTURY) -- ORIGINS -- MATHEMATICS IN THE 9TH CENTURY -- MATHEMATICS IN THE 10TH CENTURY -- OMAR KHAYYAM -- ISLAMIC MATHEMATICS TO THE 15TH CENTURY -- CHAPTER 2 EUROPEAN MATHEMATICS SINCE THE MIDDLE AGES -- EUROPEAN MATHEMATICS DURING THE MIDDLE AGES AND RENAISSANCE -- THE TRANSMISSION OF GREEK AND ARABIC LEARNING -- THE UNIVERSITIES -- THE RENAISSANCE -- MATHEMATICS IN THE 17TH AND 18TH CENTURIES -- THE 17TH CENTURY -- THE 18TH CENTURY -- OTHER DEVELOPMENTS -- MATHEMATICS IN THE 19TH AND 20TH CENTURIES -- PROJECTIVE GEOMETRY -- MAKING THE CALCULUS RIGOROUS -- FOURIER SERIES -- ELLIPTIC FUNCTIONS -- THE THEORY OF NUMBERS -- THE THEORY OF EQUATIONS -- GAUSS -- NON-EUCLIDEAN GEOMETRY -- RIEMANN -- RIEMANN'S INFLUENCE -- DIFFERENTIAL EQUATIONS -- LINEAR ALGEBRA -- THE FOUNDATIONS OF GEOMETRY -- THE FOUNDATIONS OF MATHEMATICS -- CANTOR -- MATHEMATICAL PHYSICS -- ALGEBRAIC TOPOLOGY -- DEVELOPMENTS IN PURE MATHEMATICS -- MATHEMATICAL PHYSICS AND THE THEORY OF GROUPS -- CHAPTER 3 SOUTH AND EAST ASIAN MATHEMATICS -- ANCIENT TRACES -- VEDIC NUMBER WORDS AND GEOMETRY -- THE POST-VEDIC CONTEXT -- INDIAN NUMERALS AND THE DECIMAL PLACE-VALUE SYSTEM -- THE "CLASSICAL" PERIOD -- THE ROLE OF ASTRONOMY AND ASTROLOGY -- CLASSICAL MATHEMATICAL LITERATURE.

THE CHANGING STRUCTURE OF MATHEMATICAL KNOWLEDGE -- MAHAVIRA AND BHASKARA II -- TEACHERS AND LEARNERS -- THE SCHOOL OF MADHAVA IN KERALA -- EXCHANGES WITH ISLAMIC AND WESTERN MATHEMATICS -- MATHEMATICS IN CHINA -- THE TEXTUAL SOURCES -- THE GREAT EARLY PERIOD, 1ST-7TH CENTURIES -- SCHOLARLY REVIVAL, 11TH-13TH CENTURIES -- FALL INTO OBLIVION, 14TH-16TH CENTURIES -- MATHEMATICS IN JAPAN -- THE INTRODUCTION OF CHINESE BOOKS -- THE ELABORATION OF CHINESE METHODS -- CHAPTER 4 THE FOUNDATIONS OF MATHEMATICS -- ANCIENT GREECE TO THE ENLIGHTENMENT -- ARITHMETIC OR GEOMETRY -- BEING VERSUS BECOMING -- UNIVERSALS -- THE AXIOMATIC METHOD -- NUMBER SYSTEMS -- THE REEXAMINATION OF INFINITY -- CALCULUS REOPENS FOUNDATIONAL QUESTIONS -- NON-EUCLIDEAN GEOMETRIES -- CANTOR -- THE QUEST FOR RIGOUR -- FORMAL FOUNDATIONS -- CATEGORY THEORY -- CHAPTER 5 THE PHILOSOPHY OF MATHEMATICS -- MATHEMATICAL PLATONISM -- TRADITIONAL PLATONISM -- NONTRADITIONAL VERSIONS -- MATHEMATICAL ANTI-PLATONISM -- REALISTIC ANTI-PLATONISM -- NOMINALISM -- LOGICISM, INTUITIONISM, AND FORMALISM -- MATHEMATICAL PLATONISM: FOR AND AGAINST -- THE FREGEAN ARGUMENT FOR PLATONISM -- THE EPISTEMOLOGICAL ARGUMENT AGAINST PLATONISM -- ONGOING IMPASSE -- GLOSSARY -- BIBLIOGRAPHY -- GENERAL SOURCES -- MATHEMATICS IN ANCIENT MESOPOTAMIA -- MATHEMATICS IN ANCIENT EGYPT -- GREEK MATHEMATICS -- MATHEMATICS IN THE ISLAMIC WORLD -- EUROPEAN MATHEMATICS DURING THE MIDDLE AGES AND RENAISSANCE -- MATHEMATICS IN THE 17TH AND 18TH CENTURIES -- MATHEMATICS IN THE 19TH AND 20TH CENTURIES -- SOUTH ASIAN MATHEMATICS -- EAST ASIAN MATHEMATICS -- FOUNDATIONS OF MATHEMATICS -- PHILOSOPHY OF MATHEMATICS -- INDEX -- BACK COVER.