C. Articles in Festschriften, proceedings-volumes and other anthologies





Articles in periodicals.


Articles in encyclopaediae and encyclopaedic works.


Book reviews.


Lecture notes and teaching compendia.


Preprints etc. which have not or not yet given rise to a proper publication


NB: Links, when present, are mostly to preprint or manuscript versions, which may differ more or less

radically from the published version, and whose paginations are in any case quite different.



“Kan du regne”, pp. 33–36 in Palle Rasmussen (ed.), Skolen i klassesamfundet. København: Politisk Revy, 1975.


“Historien om den nye matematik i Danmark – En skitse”, pp. 49–65 in P. Bollerslev (ed.), Den nye matematik i Danmark – en essaysamling. (Gyldendals Matematikbibliotek). København: Gyldendal, 1979.



“’Videnskabens antropologi’ – et essay om ‘ydre’ og ‘indre’ årsager og deres sammenhæng”, pp. 29–46 in Helge Kragh (ed.), Bidrag til videnskabshistoriens teori. København: Akademisk Forlag, 1982.



“Naturvidenskaben i 1980ernes slutning”, pp. 139–154 in Jens Høyrup, Brynja Svane & Ib Thiersen (eds), Humanistisk Årbog Nr. 3. (Årbog for humanistisk forskning, bind 3). Roskilde: Roskilde Universitetscenter, 1989 (=A:7).



“On Mathematics and War”, pp. 30–32 in Christine Keitel, Peter Damerow, Alan Bishop & Paulus Gerdes (eds), Mathematics, Education, and Society. (Science and Technology Education. Document Series No. 35).



“Algebraic Traditions Behind Ibn Turk and Al-Khwârizmî”, pp. 247–268 in Acts of the International Symposium on Ibn Turk, Khwârezmî, Fârâbî, and Ibn Sînâ (Ankara, 9–12 September, 1985). (Atatürk Culture Center Publications, No: 41. Series of Acts of Congresses and Symposiums, No: 1). Ankara: Atatürk Supreme Council for Culture, Language and History, 1990.



Archimedism, not Platonism: on a Malleable Ideology of Renaissance Mathematicians (1400 to 1600), and on its Role in the Formation of Seventeenth-Century Philosophies of Science”, pp. 81–110 in Corrado Dollo (ed.), Archimede. Mito Tradizione Scienza. (Biblioteca di Nuncius. Studi e testi IV). Firenze: Leo S. Olschki, 1992.



“Matematik og krig”, pp. 49–96 in Jens Høyrup, Mogens Niss, Ib Thiersen & Hans Hedal, Teknologi og Historie. Fire artikler. (Tekster fra IMFUFA, 228). Roskilde: IMFUFA, Roskilde Universitetscenter, 1992 (=A:9).



«Algèbre d'al-ğabr» et «algèbre d'arpentage» au neuvième siècle islamique et la question de l'influence babylonienne”, pp. 83–110 in Fr. Mawet & Ph. Talon (eds), D'Imhotep à Copernic. Astronomie et mathématiques des origines orientales au moyen âge. Actes du Colloque international, Université Libre de Bruxelles, 3‑4 novembre 1989. (Lettres Orientales, 2). Leuven: Peeters, 1992. In A:12 vol.  II.



“The Babylonian Cellar Text BM 85200 + VAT 6599. Retranslation and Analysis”, pp. 315–358 in Demidov et al (eds), Amphora. Festschrift für Hans Wussing zu seinem 65. Geburtstag. Basel etc.: Birkhäuser, 1992. In A:12 vol.  II.



nam‑lú‑ulù des scribes babyloniens. Un humanisme différent – ma non troppo, pp. 7380 in Inge Degn, Jens Høyrup & Jan Scheel (eds), Michelanea. Humanisme, litteratur og kommunikation. Festskrift til Michel Olsen i anledning af hans 60-årsdag den 23. april 1994. (Sprog og kulturmøde, 7). Aalborg: Center for Sprog og Interkulturelle Studier, Aalborg Universitetscenter, 1994.



«Les quatre côtés et l'aire» – sur une tradition anonyme et oubliée qui a engendré ou influencé trois grandes traditions mathématiques savantes”, pp. 507–531 in Histoire et épistémologie dans l'éducation mathématique. Actes de la première Université d'été européenne, Montpellier 10 au 13 juillet 1993. Montpellier: IREM de Montpellier, 1995. The publisher having omitted proof-reading, the article contains some 270 errors, including wrong formulae and skipped passages. Corrected republication pp. 192224 in E. Gallo, L. Giacardi & C. S. Roero (eds), Associazione Subalpina Mathesis. Seminario di Storia delle Matematiche Tullio Viola. Conferenze e Seminari 19951996. Torino: Associazione Subalpina Mathesis, 1996. Manuscript for the republication.



«The Four Sides and the Area». Oblique Light on the Prehistory of Algebra”, pp. 45–65 in Ronald Calinger (ed.), Vita mathematica. Historical Research and Integration with Teaching. Washington, DC: Mathematical Association of America, 1996. Contains upwards of 60 printing errors – the editor seems not to have realized that computer conversion should be followed by proof reading. Manuscript.



“The Formation of a Myth: Greek Mathematics – Our Mathematics”, pp. 103–119 in Catherine Goldstein, Jeremy Gray & Jim Ritter (eds), L'Europe mathématique. Mathematical Europe. Paris: Éditions de la Maison des sciences de l'homme, 1996. Manuscript.



“Sumerian: the Descendant of a Proto-Historical Creole? An Alternative Approach to the «Sumerian Problem»”, pp. 157–176 in Lars Heltoft & Hartmut Haberland (eds), Proceedings of the Thirteenth Scandinavian Conference of Linguistics. Roskilde: Roskilde University, Department of Languages and Culture, 1996.



“Hero, Ps.-Hero, and Near Eastern Practical Geometry. An Investigation of Metrica, Geometrica, and other Treatises, pp. 6793 in Klaus Döring, Bernhard Herzhoff & Georg Wöhrle (eds), Antike Naturwissenschaft und ihre Rezeption, Band 7. Trier: Wissenschaftlicher Verlag Trier, 1997. For obscure reasons, the publisher has changed into ~ and ⊏⊐ into ¤§ on p. 83 after having supplied correct proof sheets. Without this error pp. 93–116 in Tasoula Berggren (ed.), Third International Conference on Ancient Mathematics. Proceedings of the Third International Meeting, Delphi, Greece, July 30–August 3, 1996. Burnaby, British Columbia: Simon Fraser University, 1997.Corrected text. Preprint.



«Oxford» and «Gherardo da Cremona»: on the Relation between Two Versions of al-Khwārizmī's Algebra”, pp. 159–178 in Actes du 3me Colloque Maghrébin sur l'Histoire des Mathématiques Arabes, Tipaza (Alger, Algérie), 1–3 Décembre 1990, vol. II. Alger: Association Algérienne d'Histoire des Mathématiques, 1998. Preprint.



“Pythagorean ‘Rule’ and ‘Theorem’ – Mirror of the Relation Between Babylonian and Greek Mathematics”, pp. 393–407 in Johannes Renger (ed.), Babylon: Focus mesopotamischer Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne. 2. Internationales Colloquium der Deutschen Orient-Gesellschaft, 24.26. März 1998 in Berlin. Berlin: Deutsche Orient-Gesellschaft / Saarbrücken: SDV Saarbrücker Druckerei und Verlag. Manuscript.



“The Finer Structure of the Old Babylonian Mathematical Corpus. Elements of Classification, with some Results”, pp. 117–177 in Joachim Marzahn & Hans Neumann (eds), Assyriologica et Semitica. Festschrift für Joachim Oelsner anläßlich seines 65. Geburtstages am 18. Februar 1997. (Altes Orient und Altes Testament, 252). Münster: Ugarit Verlag, 2000. Preprint.



“The Old Babylonian Square Texts BM 13901 and YBC 4714. Retranslation and Analysis”, pp. 155–218 in Jens Høyrup & Peter Damerow (eds), Changing Views on Ancient Near Eastern Mathematics. (Berliner Beiträge zum Vorderen Orient, 19). Berlin: Dietrich Reimer, 2001.



“An Editor's Personal Reminiscences and Reflections”, pp. vii–xvi in Jens Høyrup & Peter Damerow (eds), Changing Views on Ancient Near Eastern Mathematics. (Berliner Beiträge zum Vorderen Orient, 19). Berlin: Dietrich Reimer, 2001.



“The Founding of Italian Vernacular Algebra”, pp. 129–156 in Commerce et mathématiques du moyen âge à la renaissance, autour de la Méditerranée. Actes du Colloque International du Centre International d'Histoire des Sciences Occitanes (Beaumont de Lomagne, 13–16 mai 1999). Toulouse: Éditions du C.I.H.S.O., 2001.



“Alchemy and Mathematics. Technical Knowledge Subservient to Ancient γvωσις”, pp. 38–54 in Vincent F. Hendricks & Jesper Ryberg (eds), Readings in Philosophy and Science Studies, vol. I. Roskilde: Department of Philosophy and Science Studies, 2001. Marred by numerous computer conversion errors. Preprint.



“Seleucid Innovations in the Babylonian «Algebraic» Tradition and Their Kin Abroad”, pp. 9–29 in Yvonne Dold-Samplonius et al (eds), From China to Paris: 2000 Years Transmission of Mathematical Ideas. (Boethius, 46). Stuttgart: Steiner, 2002. Preprint.



“How to Educate a Kapo, or, Reflections on the Absence of a Culture of Mathematical Problems in Ur III”, pp. 121–145 in John M. Steele & Annette Imhausen (eds), Under One Sky. Astronomy and Mathematics in the Ancient Near East. (Alter Orient und Altes Testament, 297). Münster: Ugarit-Verlag, 2002. Preprint.



“The Status of Theory and Practice in Ancient, Islamic and Medieval Latin Contexts”, pp. 1–17 in Raffaella Franci, Paolo Pagli & Annalisa Simi (eds), Il sogno di Galois. Scritti di storia della matematica dedicati a Laura Toti Rigatelli per il suo 60o compleanno. Siena: Centro Studi della Matematica Medioevale, Università di Siena, 2003. Manuscript.



with Bernhelm Booß-Bavnbek, “Introduction”, pp. 119 in Bernhelm Booß-Bavnbek & Jens Høyrup (eds), Mathematics and War. Basel etc.: Birkhäuser, 2003. The original publication is available at www.springerlink.com.



“Mahāvīra's Geometrical Problems: Traces of Unknown Links between Jaina and Mediterranean Mathematics in the Classical Ages”, pp. 83–95 in Ivor Grattan-Guinness & B. S. Yadav (eds), History of the Mathematical Sciences. New Delhi: Hindustan Book Agency. Manuscript.



“Mathematical Justification as Non-Conceptualized Practice: the Babylonian Example”, pp. 28–41 in HPM 2004: History and Pedagogy of Mathematics. Fourth Summer University History and Epistemology of Mathematics, ICME 10 Satellite Meeting, Uppsala July 12–17, 2004. Proceedings Uppsala: Universitetstryckeriet, 2004.



Tertium non datur: On Reasoning Styles in Early Mathematics”, pp. 91–121 in Paolo Mancosu et al (eds), Visualization, Explanation and Reasoning Styles in Mathematics. Dordrecht: Springer, 2005. Preprint.



“Questions to the Historiography of Arabic Mathematics Derived from Abbaco Mathematics”, pp. 217–232 in Actes du Huitième Colloque Maghrébin sur l'Histoire des Mathématiques Arabes, Tunis, le 18–19–20 Décembre 2004. Tunis: Association Tunisienne des Sciences Mathématiques, 2006.



“Pre-modern ‘Algebras’: a Concise Survey of That Which Was Shaped into the Technique and Discipline We Know”, pp. 1–15 in Henning Boje Andersen, Frederik Voetmann Christiansen, Klaus  Frovin Jørgensen & Vincent Hendricks (eds), The Way through Science and  Philosophy: Essays in Honour of Stig Andur Pedersen. London: College Publications, 2006.



Bronze Age Formal Science?, pp. 81-102 in Benedikt Löwe, Volker Peckhaus & Thoralf Räsch (eds), Foundations of the Formal Sciences IV. The History of the Concept of the Formal Sciences. (Studies in Logic, 3). London: College Publications, 2006. Preprint.



“Magten og de intellektuelle. En middelalderlig fabel med en upræcis morale”, pp. 83-96 in Robin Engelhardt, Camilla Mehlsen & Frederik Stjernfelt (eds), Tankestreger - tværvidenskabelige nybrud. København: Danmarks Pædagogiske Universitetsforlag, 2007.Manucript.



“Le origini”, pp. 11–36 in Claudio Bartocci & Piergiorgio Odifreddi (eds), La matematica. I: I luoghi e i tempi. Torino: Einaudi, 2007. Manuscript. NB: P. 15, lines 18–17 from bottom, the parenthesis “(cioè legati ... immediato)”, should be removed. It was inserted by the publisher or editors and says exactly the opposite of what should be said.



“The Rare Traces of Constructional Procedures in `Practical Geometries´”, pp. 213–220 in Horst Nowacki & Wolfgang Lefèvre (eds), “Creating Shapes in Civil and Naval Architecture”. Max-Planck-Institut für Wissenschaftsgeschichte. Preprint 338, vol. II. Preprint.


Les Lais: or, What Ever Became of Mesopotamian Mathematics”, pp. 11–36 in Micah Ross (ed.), From the Banks of the Euphrates. Studies in Honor of Alice Louise Slotsky. Winona Lake, Indiana: Eisenbrauns, 2007. Manuscript.



“The Algorithm Concept – Tool for Historiographic Interpretation or Red Herring”, pp. 261–272 in Arnold Beckmann, Costas Dimitracopoulos  & Benedikt Löwe (eds), Logic and Theory of Algorithms. 4th Conference on Computability in Europe, CiE 2008, Athens, Greece, June 15-20, 2008. Proceedings. (Lecture Notes in Computer Science, 5028). Berlin & Heidelberg: Springer, 2008. Camera-ready manuscript.





“The Tortuous Ways toward a New Understanding of Algebra in the Italian Abbacus School (14th–16th Centuries)”, pp. 1–15 in O. Figueras, J. L. Corina, S. Alatorre, T.Rojano, A. Sepúlveda (eds), Proceedings of the Joint Meeting of PME 32 and PME-NA XXX. Morelia, Mexico, July 17–21, 2008, vol. I. México: Cinvestav–UMSNH, 2008.




“What Did the Abbacus Teachers Aim At When They (Sometimes) Ended Up Doing Mathematics? An Investigation of the Incentives and Norms of a Distinct Mathematical Practice”, pp. 47–75 in Bart van Kerkhove (ed.), New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics. Singapore: World Scientific, 2009. Preprint.





“Les Origines”, pp. 13–40 in Claudio Bartocci & Piergiorgio Odifreddi (eds), La mathématique. Les lieux et les temps. Paris: CNRS Éditions, 2009. Translation of C:35. Since the publisher did not even react when I asked for information about the publication (I have received it since then privately from a colleague), I post it here.




“Translation and the Genesis of Mathematics in Greece”,  pp. 1117–1125 in Harald Kittel et al (eds), Übersetzung Translation Traduction. Ein Internationales Handbuch zur Übersetzungsforschung. An International Encyclopedia of Translation Studies. Encyclopédie internationale de la recherche sur la traduction. 2. Teilband. Berlin: de Gruyter, 2007. Manuscript.




“L'algèbre de Jacopo de Florence : un défi à l'historiographie de l'algèbre presque-moderne”, pp. 257–272 in Frank Daelemans et al (eds), Mélanges offerts à Hossam Elkhadem par ses amis et ses élèves. Bruxelles: Archives et Bibliothèques de Belgique/Archief- en Bibliotheekwezen in Belgie, 2007. Manuscript.


“How to transfer the conceptual structure of Old Babylonian Mathematics: solutions and inherent problems. With an Italian Parallel”, pp. 385–117 in Annette Imhausen & Tanja Pommerening (eds), Writings of Early Scholars in the Ancient Near East, Egypt, Rome and Greece: Translating Ancient Scientific Texts. (Beiträge zur Altertumskunde, 296). Berlin & New York: De Gruyter, 2010. Preprint.





“A Diluted al-Karaji in Abbacus Mathematics”, pp. 187197 in Actes du 10ième Colloque Maghrébin sur l'Histoire des mathématiques Arabes, Tunis, 29–30–31 mai, 2010. Tunis: Publications de l'Association Tunisiennes des Sciences mathématiques, 2011. Preprint.






“Hesitating progress: the slow development toward algebraic symbolization in abbacus-and related manuscripts, c. 1300 to c. 1550”, pp. 356 in Albrecht Heeffer & Maarten Van Dyck (eds), Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics. (Studies in Logic, 26). London: College Publications, 2010.




“«Proportions» in the Liber abbaci”, pp. 83–100 in Sabine Rommevaux, Philippe Vendrix & Vasco Zara (eds), Proportions: Science – Musique – Peinture & Architecture. Actes du LIe Colloque International d'Études Humanistes, 30 juin – 4 juillet 2008. Turnhout: Brepols, 2011. Brepols does not allow web diffusion of the preprint, but if you need it you may ask for it by email (jensh@ruc.dk).





“Was Babylonian Mathematics Created by ‘Babylonian Mathematicians’?”, pp. 105-119 in  Hans Neumann & Susanne Paulus (eds), Wissenskultur im Alten Orient: Weltanschauung, Wissenschaften, Techniken, Technologien. 4. Internationales Colloquium der Deutschen Orient-Gesellschaft, 20.–22. Februar 2002, Münster. Wiesbaden: Harrassowitx Verlag, 2012.





Written Mathematical Traditions in Ancient Mesopotamia: Knowledge, Ignorance, and Reasonable Guesses, pp. 189-213 in Daliah Bawanypeck & Annette Imhausen (eds), Traditions of Written Knowledge in Ancient Egypt and Mesopotamia. Proceedings of Two Workshops Held at Goethe-University, Frankfurt/Main in December 2011 and May 2012. Münster: Ugarit Verlag, 2014.



Mathematics Education in the European Middle Ages, pp. 109124 in Alexander Karp & Gert Schubring (eds), Handbook on the History of Mathematics Education. New York etc.: Springer, 2014.




Brede linier--En glemt geometrisk begrebsstruktur, in AIGIS Supplementum III Marisnus 80: Festskrift for Christian MarinusTaisbak – 80 År. København: Saxo Instituttet, Københavns Universitet, 2014. http://aigis.igl.ku.dk/CMT80/JH-bred.pdf.




“As the Outsider Walked in: the Historiography of Mesopotamian Mathematics Until Neugebauer”, pp. 165195 in Alexander Jones, Christine Proust & John M. Steele (eds), A Mathematician’s Journeys: Otto Neugebauer and Modern Transformations of Ancient Science. Cham etc.: Springer Verlag, Verlag, 2014..



Spengler and Mathematics in a Mesopotamian Mirror”, pp. 207–224 in Sebastian Fink & Robert Rollinger (eds), Oswald Spenglers Kulturmorphologie: Eine multiperspektivische Annäherung. Wiesbaden: Springer VS, 2018.




Mesopotamian Mathematics, Seen `from the Inside' (by Assyriologists) and `from the Outside' (by Historians of Mathematics), pp. 5378 in Volker R. Remmert, Martina Schneider & Henrik Kragh Sørensen (eds), Historiography of Mathematics in the 19th and 20th Centuries. Basel: Birkhäuser, 2016.




What Is Mathematics: Perspectives Inspired by Anthropology, pp. 179196 in John W. Adams, Patrick Barmby & Alex Mesoudi (eds), The Nature and Development of Mathematics: Cross Disciplinary Perspectives on Cognition, Learning and Culture. London & New York: Routledge, 2017.




Practitioners  School Teachers  `Mathematicians´: The Divisions of Pre-Modern Mathematics and Its Actors, pp. 207224 in John M. Steele & Mathieu Ossendrijver (eds), Studies on the Ancient Exact Sciences in Honor of Lis Brack-Bernsen. Berlin: Edition Topoi, 2017.




The Indian Summer of al-Andalus Mathematics - an Expanded Addendum, pp. 139-152 in Ezzaim Laabid (ed.), Actes du XIIe Colloque Maghrebin sur l'Histoire des Mathematiques Arabes, Marrakech 26-28 mai 2016. Marrakech: Universite Cadi Ayyad, Ecole Normale Superieure, 2018.



Was Babylonian Mathematics Algorithmic?, pp. 297312 in Kristin Kleber, Georg Neumann und Susanne Paulus (eds), Grenzüberschreitungen: Studien zur Kulturgeschichte des Alten Orients. Festschrift für Hans Neumann zum 65. Geburtstag am 9. Mai 2018. Münster: Zaphon, 2018.



Computational Techniques and Computational Aids in Ancient Mesopotamia, pp. 4963 in A. Volkov and V. Freiman (eds.), Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators. Cham: Springer, 2018.



From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay, pp. 2746 in G. Schubring (ed.), Interfaces between Mathematical Practices and Mathematical Education. Cham: Springer, 2018.



The Summit of Ancient Latin Mathematical Competence: Apuleius and Augustine, pp. 157170 in Actes du 13e colloque maghrébin sur l’histoire des mathématiques arabes, Tunis 2018. Tunis, 2018.



What Is a Number? What Is a Concept? Who Has a Number Concept?, pp. 2327 in Jürgen Renn and Matthias Schemmel (eds.), Culture and Cognition. Essays in Honor of Peter Damerow. Berlin: Edition Open Access, 2019.





Guānyú yōuxiān, cuòwù hé zhèngquè – gāo dé nà, gāo dé nà, Wú Wénjùn, yǐjí suànfǎ [On Being First, Being Wrong and Being Right: Knuth, ‘Knuth’, Wu Wenjun, and Algorithms; Chinese translation by Zheng Fanglei], pp. 82–92 in JI Yungang & XU Khanlin,(eds), Lùn Wú Wénjùn de shùxué shǐ yèjī [On Wu Wenjun’s Achievements in History of Mathematics]. Shanghai: Shanghai Jiaotong University Press, 2019. English manuscript.




3.2. Mathematische Texte”, pp. 65–71 in Bernd Janowski &Daniel Schwermer (eds), Texte zur Wissenskultur. (Texte aus der Umwelt des Alten Testaments, Neue Folge 9). Gütersloh: Gütersloher Verlagshaus, 2020.




“Advanced Arithmetic from Twelfth-Century Al-Andalus, Surviving Only (and Anonymously) in Latin Translation? A Narrative That Was Never Told”, pp. 33–61 in Sonja Brentjes and Alexander Fidora (eds), Premodern Translation: Comparative Approaches to Cross-Cultural
. Turnhout: Brepols, 2021. Manuscript.




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