B. Articles in periodicals






Articles in Festschriften, proceedings-volumes and other anthologies.



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.



“Double Regge Analysis and the Extended Dolen-Horn-Schmid Duality Applied to the Processes  pp‑>Δ++πp  and  pp‑>ppω”. Nuclear Physics B 11 (1969), 428438.



with Else Høyrup. Matematikundervisning – hvorfor?Matematik 1:3 (1973), 19–24; 1:4 (1973), 20–26.


“Matematikundervisning: Reformer, formål og bivirkninger”. Dansk Pædagogisk Tidsskrift 22 (1974), 345–363.


with Bernhelm Booß. “From Kepler's Planetary Motion to the ‘Quark Confinement’ in Elementary Particle Physics. Empirical Investigations in the Problem of Model Transfer and Analogy. Fable with a Moral” presented to the meeting on “Mathematical Economics”, Oberwolfach, January 1979. Materialien des Universitätsschwerpunkt Mathematisierung der Einzelwissenschaften, Universität Bielefeld 14 (1979), 211–242.



“Influences of Institutionalized Mathematics Teaching on the Development and Organization of Mathematical Thought in the Pre-Modern Period. Investigations into an Aspect of the Anthropology of Mathematics”. Materialien und Studien. Institut für Didaktik der Mathematik der Universität Bielefeld 20 (1980), 7–137.



“Om teoretisk og praktisk videnskab; om grundforskning og målforskning; om tværfaglighed, videnskabelige discipliner og problemorientering”. Filosofi og videnskabsteori på Roskilde Universitetscenter 2 (1981), 31–55.



“Investigations of an Early Sumerian Division Problem, c. 2500 B.C.”. Historia Mathematica 9 (1982), 19–36. The original publication is available at http://www.sciencedirect.com/science/journal/03150860.



“Sixth-Century Intuitive Probability: The Statistical Significance of a Miracle”. Historia Mathematica 10 (1983), 80–84. The original publication is available at http://www.sciencedirect.com/science/journal/03150860.



“Erkendelsesteoretiske, historiske og andre bemærkninger til offentlighedsegrebet”. Filosofi og Videnskabsteori på Roskilde Universitetscenter 4 (1984), 136–168.



“Varieties of Mathematical Discourse in Pre-Modern Socio-Cultural Contexts: Mesopotamia, Greece, and the Latin Middle Ages”. Science & Society 49 (1985), 4–41. Included in A:10.



“Al-Khwârizmî, Ibn Turk, and the Liber Mensurationum: on the Origins of Islamic Algebra”. Erdem 2 (Ankara 1986), 445–484. In A:12 vol.  II.



“Hârezmî, Ibn Türk, ve Liber Mensurationum: Islâm Cebirinin Kökenleri Üzerine”. Erdem 2 (1986), 485–526. Turkish translation of B:12.


“The Formation of «Islamic Mathematics». Sources and Conditions”. Science in Context 1 (1987), 281–329. Included in A:10. Manuscript of preprint. In A:12 vol.  II.



“Filozofija: slučaj, epifenomen ili sinergijski uzrok promjene trendova u matematici. Obriz razvitka od dvanaestoga do šesnaestoga stoljeća”. Godišnjam za povijest filozofije 5 (Zagreb 1987), 210–274. Croatian translation of A:6.



“Naturvidenskaben anno 1988. Overvejelser i anledning af en ny populærvidenskabelig serie”. Tiden 49:5 (1988), 4–13.


“Jordanus de Nemore, 13th Century Mathematical Innovator: an Essay on Intellectual Context, Achievement, and Failure”. Archive for History of Exact Sciences 38 (1988), 307–363.



“Jordanus de Nemore: A Case Study on 13th Century Mathematical Innovation and Failure in Cultural Context”. Philosophica 42 (Gent, 1988), 43–77. Abridged version of B:17 provided with an extra chapter. Included in A:10. Manuscript.



Zur Frühgeschichte algebraischer Denkweisen”. Mathematische Semesterberichte 36 (1989), 1–46. In A:12 vol.  II.


“Algebra and Naive Geometry. An Investigation of Some Basic Aspects of Old Babylonian Mathematical Thought”. Altorientalische Forschungen 17 (1990), 27–69, 262–354. In A:12 vol.  II.



“Sub-Scientific Mathematics. Observations on a Pre-Modern Phenomenon”. History of Science 28 (1990), 63–86. Included in A:10. In A:12 vol.  II.


“Dýnamis, the Babylonians, and Theaetetus 147c7 – 148d7”. Historia Mathematica 17 (1990), 201–222. The original publication is available at http://www.sciencedirect.com/science/journal/03150860. Manuscript. I A:12 vol.  II.



“Θεσμoπoιησεις τες διδασκαλιασ τωv μαθηματικωv και o χαρακτηρας τoυ μαθηματικoυ ΄logou΄”. Ομιλoς για τηv Iστoρια τωv Μαθηματικωv No 41 (May 1990). Greek translation of B:11.



“On Parts of Parts and Ascending Continued Fractions”. Centaurus 33 (1990), 293–324. In A:12 vol.  II. Manuscript of preprint.


“Matematika kao socijalni fenomen” (ed. Rajka Rusan). Treći Program Hrvatskog Radija 29 (Zagreb 1990; printed 1991), 5–32.


[Croatian translation of “Platonism or Archimedism: On the Ideology and Self-Imposed Model of Renaissance Mathematicians (1400 to 1600)”]. Godišnjak za povijest filozofije 8 (1990), 114–149. English text included in A:10.



Anfänge von Wissenschaft im Kontext der frühmesopotamischen «städtischen Revolution». Berichte zur Wissenschaftsgeschichte 15 (1992), 7597.



Sumerian: The Descendant of a Proto-Historical Creole? An Alternative Approach to the «Sumerian Problem». AIΩN. Annali del Dipartimento di Studi del Mondo Classico e del Mediterraneo Antico. Sezione linguistica. Istituto Universitario Orientale, Napoli 14 (1992; publ. 1994), 2172, Figs. 13. Also, possibly easier to get hold of, as ROLIG-Papir No 51 (Roskilde University, 1993).



“Mathematical Susa Texts VII and VIII. A Reinterpretation. Altorientalische Forschungen 20 (1993), 245260. In A:12 vol.  II.


«Remarkable Numbers» in Old Babylonian Mathematical Texts: A Note on the Psychology of Numbers”. Journal of Near Eastern Studies 52 (1993), 281–286. I A:12 vol.  II.



“Algebra in the Scribal School – Schools in Babylonian Algebra?” NTM. Schriftenreihe für Geschichte der Naturwissenschaften, Technik und Medizin, N. S. 4 (1993), 201218.



“On Subtractive Operations, Subtractive Numbers, and Purportedly Negative Numbers in Old Babylonian Mathematics”. Zeitschrift für Assyrio–logie und Vorderasiatische Archäologie 83 (1993), 42–60.



“A Note on an Anomalous Area Measurement from Ur III (with a Remark about Confidence in Experts)”. Altorientalische Forschungen 22 (1995), 8486.



Linee larghe. Un'ambiguità geometrica dimenticata. Bollettino di Storia delle Scienze Matematiche 15 (1995), 314.

Text with English translation.



“Changing Trends in the Historiography of Mesopotamian Mathematics: An Insider's View”. History of Science 34 (1996), 132. Preprint.


 Sulla posizione della «formula di Erone» nei Metrica (con una nota platonica)”. Bollettino di Storia delle Scienze Matematiche 17 (1997), 3–11. Text with English translation (6 October 2011).



Barocco e scienza secentesca: un legame inesistente?Analecta Romana Instituti Danici 25 (1997), 141172. Preprint. Republished with minor corrections in B:60.



“A Note on Water-Clocks and on the Authority of Texts”. Archiv für Orientforschung 44–45 (1997–98), 192–194.




 “Textos de procedimientos matemáticos de la antigua Babilonia. Una selección de problemas ‘algebraicos’ y relacionados con un analisi conciso / Old Babylonian Mathematical Procedure Texts. A Selection of ‘Algebraic’ and Related Problems with Concise Analysis”. Mathesis 13:3 (Mexico, 1997), 224–253.Preprint (only English, not the Castilian translation).



“A New Art in Ancient Clothes. Itineraries Chosen between Scholasticism and Baroque in Order to Make Algebra Appear Legitimate, and Their Impact on the Substance of the Discipline”. Physis, n.s. 35 (1998), 11–50. Preprint.



“Om matematikkens historiografi: et summarisk essay”. Slagmark nr. 28–29 (1999), 105–122. Manuscript.


ed., trans., Jacobus de Florentia, Tractatus algorismi (1307), the Chapter on Algebra (Vat. Lat. 4826, fols 36v–45v). Centaurus 42 (2000), 21–69. Slightly revised preprint.



“Geometrical Patterns in the Pre-classical Greek Area. Prospecting the Borderland Between Decoration, Art, and Structural Inquiry”. Revue d'Histoire des Mathématiques 6 (2000), 5–58.



“On a Collection of Geometrical Riddles and Their Role in the Shaping of Four to Six «Algebras»”. Science in Context 14 (2001), 85–131. Preprint.




Lasciti sotto-scientifici alla matematica d'abbaco: quasi algebra ed altre strane specie / The Sub-Scientific Heritage in `abbaco´-Mathematics: Quasi-Algebra and Other Queer Species”. L'educazione matematica 22 (2001), 23-39, 94-103, 149-158.



“A Note on Old Babylonian Computational Techniques”. Historia Mathematica 29 (2002), 193–198. The original publication is available at http://www.sciencedirect.com/science/journal/03150860. Preprint.



“Existence, Substantiality, and Counterfactuality. Observations on the Status of Mathematics According to Aristotle, Euclid, and Others”. Centaurus 44 (2002), 1–31. Preprint.



“Pedro Nuñez: Innovateur bloqué, et dernier témoin d'une tradition millénaire”. Gazeta de Matemática no 143 (Julho 2002), 5259. Manuscript.


with Bernhelm–Booß-Bavnbek. “Mathematics and War”. European Mathematical Society. Newsletter, Issue 46 (December 2002), 20–22.


“A Note to Kazuo Muroi, ‘Inheritance Problems in the Susa Mathematical Text No. 26’. Historia Scientiarum 13:1 (2003), 5458.


“Matematica e guerra”. Quaderni di ricerca in didattica N. 13 (Palermo, G.R.I.M., 2003), 152–162 (Web-journal, http://math.unipa.it/~grim/menuquad_mat.htm).



“Mathematics and War: An Invitation to Revisit”. The Mathematical Intelligencer 25:3 (Summer 2003), 12–25.


Matematica e guerra. Lettera matematica pristem 47 (2003), 512.


“Conceptual Divergence – Canons and Taboos – and Critique: Reflections on Explanatory Categories”. Historia Mathematica 31 (2004), 129–147. Preprint. The original publication is available at http://www.sciencedirect.com/science/journal/03150860, or directly.



“Leonardo Fibonacci and Abbaco Culture: a Proposal to Invert the Roles”. Revue d'Histoire des Mathématiques 11 (2005), 23–56. Errata.


“Jacopo da Firenze and the Beginning of Italian Vernacular Algebra”. Historia Mathematica 33 (2006), 4–42, doi: 10.1016/j.hm.2005.03.001. Preprint. The original publication is available at http://www.sciencedirect.com/science/journal/03150860, or directly.



“Artificial Language in Ancient Mesopotamia – a Dubious and a Less Dubious Case”. Journal of Indian Philosophy 34 (2006), 57–88, doi: 10.1007/s10781-005-8169-4. Preprint. The original publication is available at www.springerlink.com.




 “The Roles of Mesopotamian Bronce Age Mathematics: Tool for State Formation and Administration - Carrier of Teachers' Professional Intellectual Autonomy”. Educational Studies in Mathematics 66 (2007), 257–271. Manuscript.



“Generosity  – No Doubt, but at Times Excessive and Delusive”. Journal of Indian Philosophy 35 (2007), 469–485, doi: 10.1007/s10781-007-9028-2. Preprint. The original publication is available at www.springerlink.com.




 The 'Unknown Heritage': trace of a forgotten locus of mathematical sophistication. Archive for history of Exact Sciences 62 (2008), 613-654. DOI 10.1007/s00407-008-0025-y. Preprint.





 Baroque Mind-set and New Science: A Dialectic of Seventeenth-Century High Culture. Sarton Chair Lecture. Sartoniana 22 (2009), 4773.




 State, ‘Justice’, Scribal Culture and Mathematics in Ancient Mesopotamia. Sartoniana 22 (2009), 1345.




 “`Proportions' in and around the Italian Abbacus Tradition”. Physis 46 (2009; published 2011), 55110. Preprint.




 “Barocco e scienza secentesca: un legame inesistente?” Il Covile 12:694 (2012), 1–40. (New Edition of B:37).




Old Babylonian Algebra, and What It Teaches Us about Possible Kinds of Mathematics”. Ganita Bhārati32 (2010; actually 2012), 87110. Preprint (much longer than the published version).




“A Hypothetical History of Old Babylonian Mathematics: Places, Passages, Stages, Development. Ganita Bhārati34 (2012; actually 2014), 1–23.





 “Sanskrit-Prakrit Interaction in Elementary Mathematics as Reflected in Arabic and Italian Formulations of the Rule of Three – and Something more on the Rule Elsewhere. Ganita BhāratÌ 34 (2012; actually 2014), 144172.




 Fibonacci Protagonist or Witness? Who Taught Catholic Christian Europe about Mediterranean Commercial Arithmetic?. Journal of Transcultural Medieval Studies 1 (2014), 219247.




 Embedding: Another Case of Stumbling Progress in the History of Algebra. Physis, nuova series 50 (2015), 1–38.




 Which kind of mathematics was known and referred to by those who wanted to integrate mathematics in «Wisdom» –Neopythagoreans and others?. AIMS Mathematics 1 (2016), 77–95.




 ASeleucid, Demotic and Mediterranean Mathematics versus Chapters VIII and IX of the Nine Chapters: Accidental or significant Similarities?. Studies in the History of Natural Sciences 35 (2016), 463476.




 What Is `Geometric Algebra', and What Has It Been in Historiography?. AIMS Mathematics 2 (2017), 128160.




 Archimedes  Knowledge and Lore from Latin Antiquity to the Outgoing European Renaissance. Ganita Bharati  39 (2017), 122.




When is the Algorithm Concept Pertinent – and When Not? Thoughts about Algorithms and Paradigmatic Examples, and about Algorithmic and Non-Algorithmic Mathematical Cultures. AIMS Mathematics 3 (2018), 211–232. 




 On Old Babylonian Mathematical Terminology and its Transformations in the Mathematics of Later Periods. Ganita Bharati 40 (2018), 5399.




 Explicit and Less Explicit Algorithmic Thinking, 1200-1500. Jordanus de Nemore, and the Contrast between Barthelemy de Romans et Chuquet. Bollettino di Storia delle Scienze Matematiche 28 (2018), 930




Hippocrates of Chios – His Elements and His Lunes: A critique of circular reasoning. AIMS Mathematics 5 (2019), 158–184



 “Reinventing or Borrowing Hot Water: Early Latin and Tuscan Algebraic Operations with Two Unknowns”. Gaṇita Bhāratī 41 (2019; published 2021), 115–159.



 Booß-Bavnbek, Bernhelm, & Jens Høyrup, 2021. “Fachwissenschaften und Leitung der Gesellschaft”. Forum Wissenschaft 38:3 (2021), 55–58.



 Fifteenth-century Italian symbolic algebraic calculation with four or five unknowns Gaṇita Bhāratī 42 (2020, published 2022), 161–192.



 “Peeping into Fibonacci’s Study Room”. Gaṇita Bhāratī 43 (2021), 1–70.


B :76

 “Where and How Did Archimedes Get In? Oblique and Labyrinthine Reflections”. Interdisciplinary Science Reviews 47 (2022), 391–403.





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