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