Jens Hoyrup is Professor in the Department of Languages and Culture at Roskilde University in Denmark.

"Jens Hoyrup deals forthrightly with the most important question now facing historians of science: what is the relation between ideas and socioeconomic life? His conclusions are persuasive and stimulating. They go a long way to refuting the currently fashionable relativist view that science has been nothing but a collection of prejudices, conventions, and practical compromises. In this book one finds a welcome social history of science composed by a philologically sophisticated, technically informed scholar." — Lewis Pyenson, Universite de Montreal

• 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 Mathematics2. Greek Mathematics: From Open, Reasoned Discourse to Closed Axiomatics3. The Latin Middle Ages: A Discourse of Relics4. Perspectives 2. Subscientific Mathematics: Observations on a Pre-Modern Phenomenon Introduction 1. The Concepts2. The Character and Structure of Subscientific Mathematics3. Traditions and Index Fossils4. Practical Geometry5. Algebra6. 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 State2. The Early State and Its Origin3. The Rise of States in Southern Mesopotamia4. City-States and Centralization5. Breakdown and Apogee6. Mathematics7. From Tokens to Mathematics8. Trends in Third-Millenniium Mathematics9. The Paramount Accomplishment of Bureaucracy10. The Culmination of Babylonian Mathematics11. Devolution12. Supplementary Comparative Observations 4. The Formation of "Islamic Mathematics": Sources and Conditions IntroductionBiographical Cues 1. Introducing the Problem2. Scientific Source Traditions: The Greeks3. Scientific Source Traditions: India4. Subscientific Source Traditions: Commercial Calculation5. Subscientific Source Traditions: Practical Geometry6. Algebra and Its Alternative7. Reception and Synthesis8. "Melting Pot" and Tolerance9. Competition?10. Institutions or Sociocultural Conditions?11. Practical Fundamentalism12. Variations of the Islamic Pattern13. The Importance of General Attitudes: The Mutual Relevance of Theory and Practice14. The Institutionalized Cases: (1) Madrasah and Arithmetical Textbook15. The Institutionalized Cases: (2) Astronomy and Pure Geometry16. A Warning17. 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 Century2. The Thirteenth Century3. The Fourteenth Century4. The Early Renaissance5. 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 Principles2. Jordanus de Nemore: Who, When, What?3. The "Latin Quadrivium"4. "Christian " Quadrivium and "Christian" Learning5. The Wider Context of Mathematics6. Jordanus and Illegitimacy. The Jordanian Corpus7. Arithmetic8. Geometry9. Perspective10. Science of Stars11. Science of Weights12. Science of Ingenuities13. Algorism Revisited14. Jordanus's Achievement15. Failure and Its Reasons16. Epilogue: Epistemology 7. Platonism or Archimedism: On the Ideology and Self-Imposed Model of Renaissance Mathematicians (1400 to 1600) Introduction 1. The Question of Platonism2. Renascent Mathematics3. The Mature Italian Renaissance4. Northern Humanism5. The New Philosophies6. 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 PotentialsWritten in collaboration with Bernhelm Booss-Bavnbek Introduction 1. The Past2. The Implications of History3. Nineteenth-Century Prelude4. The Era of the World Wars5. Our Present Situation6. What Can - and What Should - Be Done? Notes Abbreviations and Bibliography Index

Jens Hoyrup is Professor in the Department of Languages and Culture at Roskilde University in Denmark.

"Jens Hoyrup deals forthrightly with the most important question now facing historians of science: what is the relation between ideas and socioeconomic life? His conclusions are persuasive and stimulating. They go a long way to refuting the currently fashionable relativist view that science has been nothing but a collection of prejudices, conventions, and practical compromises. In this book one finds a welcome social history of science composed by a philologically sophisticated, technically informed scholar." — Lewis Pyenson, Universite de Montreal

• 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 Mathematics2. Greek Mathematics: From Open, Reasoned Discourse to Closed Axiomatics3. The Latin Middle Ages: A Discourse of Relics4. Perspectives 2. Subscientific Mathematics: Observations on a Pre-Modern Phenomenon Introduction 1. The Concepts2. The Character and Structure of Subscientific Mathematics3. Traditions and Index Fossils4. Practical Geometry5. Algebra6. 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 State2. The Early State and Its Origin3. The Rise of States in Southern Mesopotamia4. City-States and Centralization5. Breakdown and Apogee6. Mathematics7. From Tokens to Mathematics8. Trends in Third-Millenniium Mathematics9. The Paramount Accomplishment of Bureaucracy10. The Culmination of Babylonian Mathematics11. Devolution12. Supplementary Comparative Observations 4. The Formation of "Islamic Mathematics": Sources and Conditions IntroductionBiographical Cues 1. Introducing the Problem2. Scientific Source Traditions: The Greeks3. Scientific Source Traditions: India4. Subscientific Source Traditions: Commercial Calculation5. Subscientific Source Traditions: Practical Geometry6. Algebra and Its Alternative7. Reception and Synthesis8. "Melting Pot" and Tolerance9. Competition?10. Institutions or Sociocultural Conditions?11. Practical Fundamentalism12. Variations of the Islamic Pattern13. The Importance of General Attitudes: The Mutual Relevance of Theory and Practice14. The Institutionalized Cases: (1) Madrasah and Arithmetical Textbook15. The Institutionalized Cases: (2) Astronomy and Pure Geometry16. A Warning17. 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 Century2. The Thirteenth Century3. The Fourteenth Century4. The Early Renaissance5. 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 Principles2. Jordanus de Nemore: Who, When, What?3. The "Latin Quadrivium"4. "Christian " Quadrivium and "Christian" Learning5. The Wider Context of Mathematics6. Jordanus and Illegitimacy. The Jordanian Corpus7. Arithmetic8. Geometry9. Perspective10. Science of Stars11. Science of Weights12. Science of Ingenuities13. Algorism Revisited14. Jordanus's Achievement15. Failure and Its Reasons16. Epilogue: Epistemology 7. Platonism or Archimedism: On the Ideology and Self-Imposed Model of Renaissance Mathematicians (1400 to 1600) Introduction 1. The Question of Platonism2. Renascent Mathematics3. The Mature Italian Renaissance4. Northern Humanism5. The New Philosophies6. 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 PotentialsWritten in collaboration with Bernhelm Booss-Bavnbek Introduction 1. The Past2. The Implications of History3. Nineteenth-Century Prelude4. The Era of the World Wars5. Our Present Situation6. What Can - and What Should - Be Done? Notes Abbreviations and Bibliography Index

Jens Hoyrup is Professor in the Department of Languages and Culture at Roskilde University in Denmark.

"Jens Hoyrup deals forthrightly with the most important question now facing historians of science: what is the relation between ideas and socioeconomic life? His conclusions are persuasive and stimulating. They go a long way to refuting the currently fashionable relativist view that science has been nothing but a collection of prejudices, conventions, and practical compromises. In this book one finds a welcome social history of science composed by a philologically sophisticated, technically informed scholar." — Lewis Pyenson, Universite de Montreal

• 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 Mathematics2. Greek Mathematics: From Open, Reasoned Discourse to Closed Axiomatics3. The Latin Middle Ages: A Discourse of Relics4. Perspectives 2. Subscientific Mathematics: Observations on a Pre-Modern Phenomenon Introduction 1. The Concepts2. The Character and Structure of Subscientific Mathematics3. Traditions and Index Fossils4. Practical Geometry5. Algebra6. 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 State2. The Early State and Its Origin3. The Rise of States in Southern Mesopotamia4. City-States and Centralization5. Breakdown and Apogee6. Mathematics7. From Tokens to Mathematics8. Trends in Third-Millenniium Mathematics9. The Paramount Accomplishment of Bureaucracy10. The Culmination of Babylonian Mathematics11. Devolution12. Supplementary Comparative Observations 4. The Formation of "Islamic Mathematics": Sources and Conditions IntroductionBiographical Cues 1. Introducing the Problem2. Scientific Source Traditions: The Greeks3. Scientific Source Traditions: India4. Subscientific Source Traditions: Commercial Calculation5. Subscientific Source Traditions: Practical Geometry6. Algebra and Its Alternative7. Reception and Synthesis8. "Melting Pot" and Tolerance9. Competition?10. Institutions or Sociocultural Conditions?11. Practical Fundamentalism12. Variations of the Islamic Pattern13. The Importance of General Attitudes: The Mutual Relevance of Theory and Practice14. The Institutionalized Cases: (1) Madrasah and Arithmetical Textbook15. The Institutionalized Cases: (2) Astronomy and Pure Geometry16. A Warning17. 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 Century2. The Thirteenth Century3. The Fourteenth Century4. The Early Renaissance5. 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 Principles2. Jordanus de Nemore: Who, When, What?3. The "Latin Quadrivium"4. "Christian " Quadrivium and "Christian" Learning5. The Wider Context of Mathematics6. Jordanus and Illegitimacy. The Jordanian Corpus7. Arithmetic8. Geometry9. Perspective10. Science of Stars11. Science of Weights12. Science of Ingenuities13. Algorism Revisited14. Jordanus's Achievement15. Failure and Its Reasons16. Epilogue: Epistemology 7. Platonism or Archimedism: On the Ideology and Self-Imposed Model of Renaissance Mathematicians (1400 to 1600) Introduction 1. The Question of Platonism2. Renascent Mathematics3. The Mature Italian Renaissance4. Northern Humanism5. The New Philosophies6. 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 PotentialsWritten in collaboration with Bernhelm Booss-Bavnbek Introduction 1. The Past2. The Implications of History3. Nineteenth-Century Prelude4. The Era of the World Wars5. Our Present Situation6. What Can - and What Should - Be Done? Notes Abbreviations and Bibliography Index