Jens Hoyrup, recognized as the leading authority in social studies of pre-modern mathematics, here provides a social study of the changing mode of mathematical thought through history. His "anthropology" of mathematics is a unique approach to its history, in which he examines its pursuit and development as conditioned by the wider social and cultural context. Hoyrup moves from comparing features of Sumero-Babylonian, Mesopotamian, Ancient Greek, and Latin Medieval mathematics, to examining the character of Islamic practitioners of mathematics. He also looks at the impact of ideologies and philosophy on mathematics from Latin High Middle ages through the late Renaissance. Finally, he examines modern and contemporary mathematics, drawing out recurring themes in mathematical knowledge.

Table of Contents:
1. Varieties of Mathematical Discourse in Pre-Modern Sociocultural Contexts: Mesopotamia, Greece, and the Latin Middle Ages Introduction 1. Mesopotamia: Scribal Computation and Scribal School Mathematics 2. Greek Mathematics: From Open, Reasoned Discourse to Closed Axiomatics 3. The Latin Middle Ages: A Discourse of Relics 4. Perspectives 2. Subscientific Mathematics: Observations on a Pre-Modern Phenomenon Introduction 1. The Concepts 2. The Character and Structure of Subscientific Mathematics 3. Traditions and Index Fossils 4. Practical Geometry 5. Algebra 6. The End of Subscientific Mathematics 3. Mathematics and Early State Formation, or The Janus Face of Early Mesopotamian Mathematics: Bureaucratic Tool and Expression of Scribal Professional Autonomy Introduction 1. Mathematics and the Early State 2. The Early State and Its Origin 3. The Rise of States in Southern Mesopotamia 4. City-States and Centralization 5. Breakdown and Apogee 6. Mathematics 7. From Tokens to Mathematics 8. Trends in Third-Millenniium Mathematics 9. The Paramount Accomplishment of Bureaucracy 10. The Culmination of Babylonian Mathematics 11. Devolution 12. Supplementary Comparative Observations 4. The Formation of "Islamic Mathematics": Sources and Conditions Introduction Biographical Cues 1. Introducing the Problem 2. Scientific Source Traditions: The Greeks 3. Scientific Source Traditions: India 4. Subscientific Source Traditions: Commercial Calculation 5. Subscientific Source Traditions: Practical Geometry 6. Algebra and Its Alternative 7. Reception and Synthesis 8. "Melting Pot" and Tolerance 9. Competition? 10. Institutions or Sociocultural Conditions? 11. Practical Fundamentalism 12. Variations of the Islamic Pattern 13. The Importance of General Attitudes: The Mutual Relevance of Theory and Practice 14. The Institutionalized Cases: (1) Madrasah and Arithmetical Textbook 15. The Institutionalized Cases: (2) Astronomy and Pure Geometry 16. A Warning 17. The Moral of the Story 5. Philosophy: Accident, Epiphenomenon, or Contributory Cause of the Changing Trends of Mathematics - A Sketch of the Development from the Twelfth Through Sixteenth Century Introduction 1. The Twelfth Century 2. The Thirteenth Century 3. The Fourteenth Century 4. The Early Renaissance 5. Epilogue: Mathematics as Part of the Foundation of New Philosophies 6. Jordanus de Nemore: A Case Study on Thirteenth-Century Mathematical Innovation and Failure in Cultural Context Introduction 1. Preliminary Reflections on Principles 2. Jordanus de Nemore: Who, When, What? 3. The "Latin Quadrivium" 4. "Christian " Quadrivium and "Christian" Learning 5. The Wider Context of Mathematics 6. Jordanus and Illegitimacy. The Jordanian Corpus 7. Arithmetic 8. Geometry 9. Perspective 10. Science of Stars 11. Science of Weights 12. Science of Ingenuities 13. Algorism Revisited 14. Jordanus's Achievement 15. Failure and Its Reasons 16. Epilogue: Epistemology 7. Platonism or Archimedism: On the Ideology and Self-Imposed Model of Renaissance Mathematicians (1400 to 1600) Introduction 1. The Question of Platonism 2. Renascent Mathematics 3. The Mature Italian Renaissance 4. Northern Humanism 5. The New Philosophies 6. Generalizations 8. On Mathematics and War: An Essay on the Implications, Past and Present, of the Military Involvement of the Mathematical Sciences for Their Development and Potentials Written in collaboration with Bernhelm Booss-Bavnbek Introduction 1. The Past 2. The Implications of History 3. Nineteenth-Century Prelude 4. The Era of the World Wars 5. Our Present Situation 6. What Can - and What Should - Be Done? Notes Abbreviations and Bibliography Index