Curriculum Vitae: Full Name: Jens Egede Høyrup. Born: Copenhagen

Total Page:16

File Type:pdf, Size:1020Kb

Curriculum Vitae: Full Name: Jens Egede Høyrup. Born: Copenhagen Curriculum vitae: Full name: Jens Egede Høyrup. Born: Copenhagen, 1943. “Studentereksamen” (corresponds to French baccalauréat/German Abitur) 1962. Studies of physics with mathematics as a second subject, University of Copenhagen, Niels Bohr Institute, 1962–1965, 1966–1969. 1965–66, French bourse d’état, with studies of physics at Institut Henri Poincaré, Paris. 1969, cand. scient. (dissertation in particle physics). 1969–1970, conscientious objector’s civil service. 1971–1973, assistant lecturer in physics at Danmarks Ingeniørakademi. 1973–1989 “lektor” (corresponds to British “senior lecturer”), since 1989 “docent” (corresponds to British “reader”) at Roskilde University, 1973–1978 in the Department of Social Sciences, 1978–1992 in the Institute of Educational Research, Media Studies and Philosophy of Science, 1992–1997 in the Department of Languages and Culture, since 1997 in the Section for Philosophy and Science Studies. Since 2005 emeritus. Jan. 1990 Gast-Dozent, Karl-Marx-Universität Leipzig. Sept. 1994 – Jan. 1995 guest researcher at Max-Planck-Institut für Wissenschaftsgeschichte, Berlin. Many shorter stays since then. December 2016 to December 2019, visiting scholar (not in permanent residence). 1995 Dr. phil. (corresponds approximately to French Doctorat d’état/German Habilitation). 2008/2009, George Sarton Memorial Chair, University of Ghent. 26.4.2013, Awarded Zhu Kezhen Visiting Professorship, Institute for History of Natural Science of the Chinese Academy of Science, and appointed permanent Honorary Research Fellow at the Institute for the History of Natural Science, Chinese Academy of Sciences. 26.7.2013, awarded Kenneth O. May Medal and Prize “for outstanding contributions to the history of mathematics”. April – June 2019, visiting professor, Department of the History of Science, Tsinghua University, Beijing. Field of teaching before retiring: History of natural, human and social science in the specialization cycle of philosophy and science studies, occasionally also philosophical topics; philosophy, history of ideas, history of sciences in the cycle of general humanities. Field of research: History of science, especially the history of mathematics in pre- and early Modern cultures (emphasizing Babylonia and the pre-Modern practitioners’ traditions in their interaction with Babylonian, ancient Greek, and medieval Islamic, Latin and Romance vernacular cultures; in recent years the Italian abbacus tradition and it Arabic background); secondary interest in social and societal aspects of modern science. Also publications in linguistics and in the Philosophy of science. Since 1983 reviewer for history and sociology of mathematics in Zentralblatt für Mathematik, and since 1984 in Mathematical Reviews. Associate editor of Historia Mathematica; until 2017 member of the Editorial Committee of Revue d’Histoire des Mathématiques; associate editor of Bollettino di Storia delle Scienze Matematiche; member of editorial board, AIMS Mathematics; advisory editor for Isis; regularly referee for most of these, for Annals of Science, for Centaurus, for The Mathematical Intelligencer, and for various other journals and publishers. Full member, Académie Internationale d’Histoire des Sciences; member of various other professional organizations and networks. -1- Member of the Danish National Committee for the History and Philosophy of the Sciences 1998-2006. As long as they lasted (1983 to publication of summary quasi-proceedings in 2001, for which I was responsible together with Peter Damerow) member of the planning committee for the workshops on Concept Development in Mesopotamian Mathematics held at Altorientalisches Seminar, Freie Universität Berlin. Major publications since 1994: books Selected Essays on Pre- and Early Modern Mathematical Practice. Cham etc.: Springer, 2019 Algebra in Cuneiform: Introduction to an Old Babylonian Geometrical Technique. Berlin: Edition Open Access, 2017. L’algèbre au temps de Babylone : Quand les mathématiques s’écrivaient sur de l’argile. Paris: Vuibert & Adapt-SNES, 2010. Jacopo da Firenze’s Tractatus Algorismi and Early Italian Abbacus Culture. (Science Networks. Historical Studies, 34). Basel etc.: Birkhäuser, 2007. (ed., with Bernhelm Boos-Bavnbek) Mathematics and War. Basel etc.: Birkhäuser, 2003. Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. (Studies and Sources in the History of Mathematics and Physical Sciences). New York: Springer, 2002. (ed., with Peter Damerow) Changing Views on Ancient Near Eastern Mathematics. (Berliner Beiträge zum Vorderen Orient, 19). Berlin: Dietrich Reimer, 2001. Human Sciences: Reappraising the Humanities through History and Philosophy. Albany, New York: State University of New York Press, 2000. Algebra på lertavler. København: Matematiklærerforeningen, 1998. In Measure, Number, and Weight. Studies in Mathematics and Culture. New York: State University of New York Press, 1994. articles “Euclid: Reception in the Renaissance”,in M. Sgarbi (ed.), Encyclopedia of Renaissance Philosophy. Online, https://doi.org/10.1007/978-3-319-02848-4_918-1. “Gua¯nyú yo¯uxia¯n, cuòwù hé zhèngquè – ga¯o dé nà, “ga¯o dé nà”, Wú Wénjùn, yˇijí suànfˇa” [“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 shˇi yèjı¯ [On Wu Wenjun’s Achievements in History of Mathematics]. Shanghai: Shanghai Jiaotong University Press, 2019. “Archimedes: Reception in the Renaissance”, in M. Sgarbi (ed.), Encyclopedia of Renaissance Philosophy. Online, https://doi.org/10.1007/978-3-319-02848-4_892-1. “What Is a Number? What Is a Concept? Who Has a Number Concept”, pp. 23–27 in Jürgen Renn & Matthias Schemmel (eds), Culture and Cognition: Essays in Honor of Peter Damerow. Berlin: Edition Open Access, 2019. “From the Practice of Explanation to the Ideology of Demonstration: An Informal Essay”, pp. 27–46 in Gert Schubring (ed.), Interfaces between Mathematical Practices and Mathematical Education. Cham etc.: Springer, 2019. “On Old Babylonian Mathematical Terminology and Its Transformations in the Mathematics of Later Periods”. Ganita Bha¯ratı¯ 40 (2018; published 2019), 53–99. “Mesopotamian Mathematics”, pp. 58–72 in Alexander Jones & Liba Taub (eds), The Cambridge History of Science.I.Ancient Science. Cambridge: Cambridge University Press, 2018. -2- “Egyptian Mathematics”, pp. 144–159 in Alexander Jones & Liba Taub (eds), The Cambridge History of Science.I.Ancient Science. Cambridge: Cambridge University Press, 2018. “Computational Techniques and Computational Aids in Ancient Mesopotamia”, pp. 49–63 in Alexei Volkov & Viktor Freiman (eds), Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators. Cham etc.: Springer, 2018. “The Summit of Ancient Latin Mathematical Competence: Apuleius and Augustine”, pp. 157–170 in Actes du XIIIe Colloque Maghrébin sur l’Histoire des Mathématiques Arabes, Tunis, 30–31 mars e 1er avril 2018 (COMHISMA13). Tunis: 2018. “Spengler and Mathematics in a Mesopotamian Mirror”, pp. 207–224 in Sebastian Fink & Robert Rollinger (eds), Oswald Spenglers Kulturmorphologie: Eine multiperspektivische Annäherung. Wiesbaden: Springer, 2018. “Mesopotamian Mathematics”, pp. 11–24 in Paul T. Keyser and John Scarborough (eds), Oxford Handbook of Science and Medicine in the Classical World. Oxford & New York: Oxford University Press, 2018. “Explicit and Less Explicit Algorithmic Thinking, 1200-1500: Jordanus de Nemore, and the Contrast between Barthélemy de Romans et Chuquet.” Bollettino di Storia delle Scienze Matematiche 38 (2018), 9–30. “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. “Was Babylonian Mathematics Algorithmic?”, pp. 297–312 in Kristin Kleber, Georg Neumann & Susanne Paulus (eds), Grenzüberschretungen: Studien zur Kulturgeschichte des Alten Orients. Festschrift für Hans Neumann zum 65. Geburtstag am 9. Mai 2018. Münster: Zaphon, 2018. “The Indian Summer of al-Andalus Mathematics? An Expanded Addendum”, pp. 139–152 in Ezzaim Laabid (ed.), Actes du XIIe Coloque Maghrébin sur l’Histoire des Mathématiques Arabes. Marrakech, 26 au 28 mai 2016. Marrakech: École Normale Supérieure, 2018. “Abbacus School”, in M. Sgarbi (ed.), Encyclopedia of Renaissance Philosophy. Online, https://doi.org/10.1007/978-3-319-02848-4_1135-1. “Practitioners – School Teachers – ‘Mathematicians’: The Divisions of Pre-Modern Mathematics and Its Actors”, pp. 207–224 in John M. Steele & Mathieu Ossendrijver (eds), Studies on the Ancient Exact Sciences in Honor of Lis Brack-Bernsen. Berlin: Edition Topoi, 2017 “Archimedes – Knowledge and Lore from Latin Antiquity to the Outgoing European Renaissance”. Ganita Bha¯ratı¯ 39 (2017), 1–22 “What Is Mathematics: Perspectives Inspired by Anthropology”, pp. 179–196 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 “What Is ‘Geometric Algebra’, and What Has It Been in Historiography?”. AIMS Mathematics 2 (2017), 128-160. “Seleucid, 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), 463–476. “Embedding: Multi-purpose
Recommended publications
  • Early-Dynastic Tables from Southern Mesopotamia, Or the Multiple Facets of the Quantification of Surfaces (Preprint)
    Mathematics, Administrative and Economic Activities in the Ancient Worlds C. Michel & K. Chemla (eds) Springer 2020 Chapter 9 Christine Proust 1 Early-Dynastic Tables from Southern Mesopotamia, or the Multiple Facets of the Quantification of Surfaces (preprint) Abstract How were surfaces evaluated before the invention of the sexagesimal place value notation in Mesopotamia? This chapter examines a group of five tablets containing tables for surfaces of squares and rectangles dated to the Early Dynastic period (ca. 2600-2350 BCE) and unearthed in southern Mesopotamia. In order to capture the methods used by ancient scribes to quantify surfaces, special attention is paid to the layout and organization of the tables, as well as to the way in which measurement values are written down. It is argued that these methods vary according to the dimensions of the squares or rectangles concerned: the quantification of small surfaces does not use the same mathematical tools as the quantification of large parcels of land. The chapter shows a reciprocal influence between the metrological systems adopted by the ancient scribes and the methods of calculation of surface they implemented. Some methods may reflect ancient land-surveying practices, and others may testify the emergence of new mathematical concepts applied to all kinds of surfaces, large or small. Ultimately, several different conceptualizations of the notion of surface emerge from the examination of these tables. Introduction2 This contribution is an attempt to understand how surfaces were quantified in southern Mesopotamia during the Early Dynastic period (ca. 2600-2350 BCE – see chronology in Appendix 9.B), that is, before the invention of the sexagesimal place value notation.
    [Show full text]
  • Tablettes Mathématiques De Nippur.1Er Partie:Reconstitution Du Cursus Scolaire. 2Me Partie
    Tablettes mathématiques de Nippur. 1er partie: Reconstitution du cursus scolaire. 2me partie: Édition des tablettes conservées au Musée Archéologique d’Istanbul, avec la collaboration de Veysel Donbaz et de Asuman Dönmez, translittération des textes lexicaux et littéraires par Antoine Cavigneaux by Christine Proust Varia Anatolica 18. Paris: Institut Français d’Études Anatoliennes Georges-Dumezil, 2007. Pp. 356 + 49 plates, CD-ROM. ISBN 978--2-- 906053--92--9.Paper ¤ 75.00 Reviewed by Duncan J. Melville St Lawrence University [email protected] The decipherment of cuneiform and the recovery of Mesopotamian mathematics, and especially that of the Old Babylonian period, open- ed an exciting early chapter in the history of mathematics. The pi- oneering work of Neugebauer, Thureau-Dangin, and others revealed a complex algorithmic and algebraic body of mathematics involv- ing often ingenious constructions and presenting a sustained interest in quadratic mathematics more than 1000 years before Pythagoras. Inevitably, in this reconstruction, the fundamental problem texts doc- umenting the extent and depth of the mathematical knowledge of the period took center stage. A key characteristic of Mesopotamian mathematics is that the sources are principally from an educational context: the tablets are school tablets produced by students and their teachers, and they derive from the business of teaching and learning mathematics. It is only comparatively recently that scholars have turned their attention from establishing the boundaries of Old Baby- lonian mathematical knowledge to determining how, and how much of, that mathematics was learned by students of the time. Proust’s volume fits squarely into this current trend in understanding ancient pedagogy.
    [Show full text]
  • PLIMPTON 322: a UNIVERSAL CUNEIFORM TABLE for OLD BABYLONIAN MATHEMATICIANS, BUILDERS, SURVEYORS and TEACHERS Introduction
    Ø Ñ ÅØÑØÐ ÈÙ ÐØÓÒ× DOI: 10.1515/tmmp-2016-0027 Tatra Mt. Math. Publ. 67 (2016), 1–40 PLIMPTON 322 : A UNIVERSAL CUNEIFORM TABLE FOR OLD BABYLONIAN MATHEMATICIANS, BUILDERS, SURVEYORS AND TEACHERS Rudolf Hajossy ABSTRACT. This article deals with the damaged and incomplete Old Babylo- nian tablet Plimpton 322 which contains 4 columns and 15 rows of a cuneiform mathematical text. It has been shown that the presumed original table with its 7 columns and 39 rows represented: a table of square roots of numbers from 0 to 2 for mathematicians; an earliest rudiments of a trigonometric table for builders and surveyors where angles are not measured as an arc in a unit circle but as a side of a unit right-angled triangle; a list of the 39 exercises on reciprocal pairs, unit and integer-side right triangles (rectangles), factorization and square num- bers for teachers. The article provides new arguments in favor of old disputes (squares of diag- onals or widths; mistakes in previous analysis of errors in P322). Contradictory ideas about P322 are discussed: Is it the table of triangle sides or factorization terms? Was it compiled by a parallel or independent factorization of the sides or of their squares? Are sides of an initial unit triangle enlarged or reduced by such a factorization? Does it contain two or four arithmetical errors? Time and dimensional requirements for calculation and writing of the complete tablet have been also estimated. Introduction The cuneiform clay tablet Plimpton 322 (P322 ) [1],[8],[10],[11], Fig. 1, is very likely the most famous mathematical product of Old Babylonian era (1900–1600 BCE), written probably in an ancient city Larsa (southern Iraq) several decades before the city was conquered (1762 BCE) by Hammurabi of Babylon.
    [Show full text]
  • The Algorithm of Factor Twelve
    The Algorithm of Factor 12: Generating the Information Carved on the Plimpton 322 Tablet. Fernando Qui˜nonez Abstract The right triangles represented in the Plimpton 322 data have integer sides (a, b, d) with a < b < d, by inspecting the data we propose b = MQM with M, QM positive integers. In this way we present a new data-driven family of algorithms in order to generate the whole content of the Plimpton-322 tablet. Each algorithm of the family corres- ponds to one given value of the bundling factor or mak¸sarum M. The algorithm with M = 12 arise naturally from data and is developed entirely through this work. We could generate the complete Plimpton 322 table by using three different schemes in the framework of the twelve factor algorithm. Finally we found by varying M in the general algorithm, we can be able to find all the Pythagorean Triples. Keywords: P322, Old Babylonian Trigonometry, 2000 MSC: 01A17 1. Introduction The 322nd clay tablet in the Plimpton collection of Columbia University in New York has wondered historian- mathematicians since (Neugebauer, 1935) and also (Otto Neugebauer and Abraham Sachs and A. Goetze, 1945) re- vealed this tablet contains carved information about fifteen right triangles. The Plimpton-322 tablet (P322) is an ancient artifact with rectangular shape of height 8.8 cm and width 12.7 cm, each rowhas a heightof 5 mm or 6 mm and are delimited by guide lines carved horizontally through the obverse of the entire tablet. As a matter of fact, there are not separation between the lines that delimit each row and some sexagesimal cuneiform numbers go out of its row field mostly invading the next row that comes above it.
    [Show full text]
  • Max Planck Institute for the History of Science a Hypothetical
    MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science 2012 PREPRINT 436 Jens Høyrup A hypothetical history of Old Babylonian mathematics: places, passages, stages, development A hypothetical history of Old Babylonian mathematics: places, passages, stages, development Jens Høyrup [email protected] http://ruc.dk/~jensh Contribution to the International Conference on History and Development of Mathematical Sciences Maharshi Dayanand University, Rohtak 21–24 November, 2012 To appear in the Proceedings Wilbur Knorr in memoriam Abstract Most general standard histories of mathematics speak indiscriminately of “Babylonian” mathematics, presenting together the mathematics of the Old Babylonian and the Seleucid period (respectively 2000–1600 and 300–100 BCE) and neglecting the rest. Specialist literature has always known there was a difference, but until recently it has been difficult to determine the historical process within the Old Babylonian period. It is still impossible to establish the details of this process with certainty, but a rough outline and some reasoned hypotheses about details can now be formulated. That is what I am going to present during the talk. Non-history of Mesopotamian mathematics in general histories of mathematics . 1 What is known to those who care about the historical development of Mesopotamian mathematics ................................................... 2 Old Babylonian political history in rough outline .......................... 5 Old Babylonian mathematics, and mathematics teaching .................... 6 Theend.......................................................... 17 References ........................................................ 18 Kort her Non-history of Mesopotamian mathematics in general histories of mathematics General histories of mathematics often begin with or contain a chapter on “Babylonian mathematics”, or perhaps a chapter mixing up Babylonian matters with early literate mathematics in broader generality.
    [Show full text]
  • INTERPRETATION of REVERSE ALGORITHMS in SEVERAL MESOPOTAMIAN TEXTS Christine Proust
    INTERPRETATION OF REVERSE ALGORITHMS IN SEVERAL MESOPOTAMIAN TEXTS Christine Proust To cite this version: Christine Proust. INTERPRETATION OF REVERSE ALGORITHMS IN SEVERAL MESOPOTAMIAN TEXTS. Karine Chemla. The History of Mathematical Proof in Ancient Tra- ditions, 2012. hal-01139635 HAL Id: hal-01139635 https://hal.archives-ouvertes.fr/hal-01139635 Submitted on 7 Apr 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Preprint of Proust 2012, in The History of Mathematical Proof in Ancient Traditions, ed. K. Chemla, CUP INTERPRETATION OF REVERSE ALGORITHMS IN SEVERAL MESOPOTAMIAN TEXTS Christine Proust (Laboratory SPHERE, CNRS & University Paris Diderot) Is it possible to discuss proofs in texts which contain only numbers and no verbal element? I propose to analyze a Mesopotamian tablet containing a long series of reciprocal calculations, written as numeric data in sexagesimal place value notation. The provenance of this tablet, which today is conserved at the University Museum in Philadelphia under the number CBS 1215, is not documented, but there are numerous parallels from the scribal schools of southern Mesopotamia, notably Nippur and Ur, all from the Old Babylonian period (beginning two millennia before the Christian era).
    [Show full text]
  • Further Reading General Otto Neugebauer, the Exact Sciences in Antiquity. 2Nd Edition. Providence, Brown University Press, 1957
    Further reading General Otto Neugebauer, The Exact Sciences in Antiquity. 2nd edition. Providence, Brown University Press, 1957. Reprinted by Dover Publications, 1969. Eleanor Robson, Mathematics in Ancient Iraq: A Social History. Princeton, Princeton University Press, 2008. Victor J. Katz, editor, The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton, Princeton University Press, 2007. C. B. F. Walker, Cuneiform. Reading the Past 3. Berkeley, University of California Press/British Museum, 1987. Numerals, metrology, and calculations Asger Aaboe, Episodes from the Early History of Mathematics. Washington D.C., Mathematical Association of America, 1964. Marvin Powell, "The Antecedents of Old Babylonian Place Notation and the Early History of Babylonian Mathematics." Historia Mathematica 3, 1976, 417- 439. Robert M. Whiting, "More Evidence for Sexagesimal Calculations in the Third Millennium B.C." Zeitschrift für Assyriologie 74, 1984, 59-66. Jöran Friberg, "On the Alleged Counting with Sexagesimal Place Value Numbers in Mathematical Cuneiform Texts from the Third Millennium BC." Cuneiform Digital Library Journal 2005:2. http://cdli.ucla.edu/pubs/cdlj/2005/cdlj2005_002.html Christine Proust, "Quantifier et calculer: usages des nombres à Nippur." Revue d'Histoire des Mathématiques 14.2, 2008, 143-209. Christine Proust, "Mesopotamian metrological lists and tables: Forgotten sources," in F. Bretelle-Establet et al., eds., Looking at it from Asia: The Processes that Shaped the Sources of History of Science. Boston Studies in the Philosophy of Science 265. New York, Springer, 2010. 245-276. Scribal training Karen Rhea Nemet-Nejat, "Systems for Learning Mathematics in Mesopotamian Scribal Schools." Journal of Near Eastern Studies 54, 1995, 241-260.
    [Show full text]
  • International Studies in the History of Mathematics and Its Teaching
    International Studies in the History of Mathematics and its Teaching Series Editors Alexander Karp Teachers College, Columbia University, New York, NY, USA Gert Schubring Universität Bielefeld, Bielefeld, Germany Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil [email protected] The International Studies in the History of Mathematics and its Teaching Series creates a platform for international collaboration in the exploration of the social history of mathematics education and its connections with the development of mathematics. The series offers broad perspectives on mathematics research and education, including contributions relating to the history of mathematics and mathematics education at all levels of study, school education, college education, mathematics teacher education, the development of research mathematics, the role of mathematicians in mathematics education, mathematics teachers' associations and periodicals. The series seeks to inform mathematics educators, mathematicians, and historians about the political, social, and cultural constraints and achievements that influenced the development of mathematics and mathematics education. In so doing, it aims to overcome disconnected national cultural and social histories and establish common cross-cultural themes within the development of mathematics and mathematics instruction. However, at the core of these various perspectives, the question of how to best improve mathematics teaching and learning always remains the focal issue informing the series.
    [Show full text]
  • INTERPRETATION of REVERSE ALGORITHMS in SEVERAL MESOPOTAMIAN TEXTS Christine Proust
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Hal-Diderot INTERPRETATION OF REVERSE ALGORITHMS IN SEVERAL MESOPOTAMIAN TEXTS Christine Proust To cite this version: Christine Proust. INTERPRETATION OF REVERSE ALGORITHMS IN SEVERAL MESOPOTAMIAN TEXTS. Karine Chemla. The History of Mathematical Proof in Ancient Traditions, 2012. <hal-01139635> HAL Id: hal-01139635 https://hal.archives-ouvertes.fr/hal-01139635 Submitted on 7 Apr 2015 HAL is a multi-disciplinary open access L'archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destin´eeau d´ep^otet `ala diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publi´esou non, lished or not. The documents may come from ´emanant des ´etablissements d'enseignement et de teaching and research institutions in France or recherche fran¸caisou ´etrangers,des laboratoires abroad, or from public or private research centers. publics ou priv´es. Preprint of Proust 2012, in The History of Mathematical Proof in Ancient Traditions, ed. K. Chemla, CUP INTERPRETATION OF REVERSE ALGORITHMS IN SEVERAL MESOPOTAMIAN TEXTS Christine Proust (Laboratory SPHERE, CNRS & University Paris Diderot) Is it possible to discuss proofs in texts which contain only numbers and no verbal element? I propose to analyze a Mesopotamian tablet containing a long series of reciprocal calculations, written as numeric data in sexagesimal place value notation. The provenance of this tablet, which today is conserved at the University Museum in Philadelphia under the number CBS 1215, is not documented, but there are numerous parallels from the scribal schools of southern Mesopotamia, notably Nippur and Ur, all from the Old Babylonian period (beginning two millennia before the Christian era).
    [Show full text]
  • Plimpton 322 : a Universal Cuneiform Table for Old Babylonian Mathematicians, Builders, Surveyors and Teachers
    Ø Ñ ÅØÑØÐ ÈÙ ÐØÓÒ× DOI: 10.1515/tmmp-2016-0027 Tatra Mt. Math. Publ. 67 (2016), 1–40 PLIMPTON 322 : A UNIVERSAL CUNEIFORM TABLE FOR OLD BABYLONIAN MATHEMATICIANS, BUILDERS, SURVEYORS AND TEACHERS Rudolf Hajossy ABSTRACT. This article deals with the damaged and incomplete Old Babylo- nian tablet Plimpton 322 which contains 4 columns and 15 rows of a cuneiform mathematical text. It has been shown that the presumed original table with its 7 columns and 39 rows represented: a table of square roots of numbers from 0 to 2 for mathematicians; an earliest rudiments of a trigonometric table for builders and surveyors where angles are not measured as an arc in a unit circle but as a side of a unit right-angled triangle; a list of the 39 exercises on reciprocal pairs, unit and integer-side right triangles (rectangles), factorization and square num- bers for teachers. The article provides new arguments in favor of old disputes (squares of diag- onals or widths; mistakes in previous analysis of errors in P322). Contradictory ideas about P322 are discussed: Is it the table of triangle sides or factorization terms? Was it compiled by a parallel or independent factorization of the sides or of their squares? Are sides of an initial unit triangle enlarged or reduced by such a factorization? Does it contain two or four arithmetical errors? Time and dimensional requirements for calculation and writing of the complete tablet have been also estimated. Introduction The cuneiform clay tablet Plimpton 322 (P322 ) [1],[8],[10],[11], Fig. 1, is very likely the most famous mathematical product of Old Babylonian era (1900–1600 BCE), written probably in an ancient city Larsa (southern Iraq) several decades before the city was conquered (1762 BCE) by Hammurabi of Babylon.
    [Show full text]
  • Christine PROUST
    Christine PROUST Née le 19 octobre 1953 Docteur en épistémologie et histoire des sciences (thèse soutenue en 2004) Membre de l’Unité SPHERE (UMR 7219, CNRS & Université Diderot Paris 7) Adresse personnelle : 18 rue de Turbigo, 75 002 Paris Tel : (0033) (0)1 42 33 41 37 Courriels : [email protected], [email protected] SOMMAIRE A - CURRICULUM VITAE ......................................................................... 2 B - RECHERCHE ...................................................................................... 5 C - COMMUNICATIONS ........................................................................... 6 D - PUBLICATIONS ............................................................................... 10 Toutes les publications (thèse, articles et ouvrages) sont téléchargeables à l’adresse http://pagesperso-orange.fr/christine.proust/CV.htm 1 A - CURRICULUM VITAE Christine PROUST Née le 19 octobre 1953 à Nîmes (Gard), France Nationalité française, deux enfants Adresse personnelle : 18 rue de Turbigo, 75002 Paris, tel (00 33) 1 42 33 41 37 Adresse professionnelle (postale uniquement) : Université Diderot Paris 7, Case courrier 7064, 2 place Jussieu, 75251 Paris cedex 05, tel (00 33) 1 57 27 63 24 Courriel : [email protected] Page web personnelle : http://www.rehseis.univ-paris-diderot.fr/spip.php?article228 Publications téléchargeables sur http://pagesperso-orange.fr/christine.proust/CV.htm (page non publique) Situation professionnelle actuelle Enseignante du secondaire détachée, agrégée de mathématiques. Membre de l’Institute for Advanced Study (Princeton, USA) de septembre à décembre 2009. Chercheur invité par l’Institute for the Study of the Ancient World (Université de New York, USA) et par l’Unité Mixte Internationale 3199 (CNRS / NYU) de janvier à juin 2010. Collaborations 2003-2007 Membre du groupe de chercheurs réuni autour de l’ACI "Jeunes chercheurs" :"Corpus de textes scientifiques : Histoire et perspectives théoriques", dir.
    [Show full text]
  • Otto Neugebauer and the Exploration of Ancient Near Eastern Mathematics
    Roskilde University Otto Neugebauer and the Exploration of Ancient Near Eastern Mathematics Høyrup, Jens Published in: Max-Planck-Institut für Wissenschaftsgeschichte. Preprint Publication date: 2017 Document Version Publisher's PDF, also known as Version of record Citation for published version (APA): Høyrup, J. (2017). Otto Neugebauer and the Exploration of Ancient Near Eastern Mathematics. Max-Planck- Institut für Wissenschaftsgeschichte. Preprint, (488). General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain. • You may freely distribute the URL identifying the publication in the public portal. Take down policy If you believe that this document breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 02. Oct. 2021 MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science 2017 PREPRINT 488 Jens Hµyrup Otto Neugebauer and the Exploration of Ancient Near Eastern Mathematics Abstract The exploration of Mesopotamian mathematics took its beginning together with the decipherment of the cuneiform script around 1850. Until the 1920s, “mathematics in use” (number systems, metrology, tables and some practical calculations of areas) was the object of study – only very few texts dealing with more advanced matters were approached before 1929, and with quite limited results.
    [Show full text]