Articles

Unpublished

"How Useful is the Term ‘Modernism’ for Understanding the History of Early Twentieth-Century Mathematics?", planned to appear in Moritz Epple and Falk Mueller (eds.) Modernism in the Sciences, ca. 1900-1940, Berlin, Akademie Verlag (Forthcoming).

2021

 Israel y COVID-19: Cómo se escribirá en el futuro la historia de la epidemia en este país? In: Revista História, Ciências, Saúde – Manguinhos (Blog), 14 April 2021.

2017-2020

"Five Years as Dean - Texts and Thoughts",(English and Hebrew) רוח וצלצולים מבחר טקסטים ודברי ברכה - עם תום תקופה של חמש שנים בתפקיד דקאן הפקולטה למדעי הרוח

 

"Mie’s Electromagnetic Theory of Matter and the Background to Hilbert’s Unified Foundations of Physics" in Joseph Kouneiher (ed.) Foundations of Mathematics and Physics One Century After Hilbert - New Perspectives, New York, Springer (2018): 75-96. (Parts of this article appeared in my previous work on Hilbert.)

 

"Hilbert's 6th Problem: Between the Foundations of Geometry and the Axiomatization of Physics", Philosophical Transactions of the Royal Society (A), 376 (2018); 28 April 2018.

 

"Creating a Modern Hebrew Language for Mathematics", Nitsa Movshovitz-Hadar (ed.) K-12 Mathematics Education in Israel. Issues and Innovations (2018), pp. 319-326.

2011-2016

"Steht es alles wirklich schon bei Dedekind? Ideals and factorization between Dedekind and Noether", in Katrin Scheel, Thomas Sonar and Peter Ullrich (eds.) In Memoriam Richard Dedekind (1831-1916) Münster, Verlag für wissenschaftliche Texte und Medien (2017), pp. 134-159.

 

"From the Universal Turing Machine to Turing's Analog Computer: Father of the Modern Computer?", Communications of the ACM Vol. 60 (8), August 2017, pp. 50-58.

"Some distributivity-like results in the the medieval arithmetic of Jordanus Nemorarius and Campanus de Novara", Historia Mathematica 43 (2016), 310–331. 

 

"Mathematical Fiction and the Prosaic Dangers of Salgarism", in M. Emmer, M. Abate, M. Falcone, M. Villarreal (eds.) Imagine Maths 5, Unione Matematica Italiana, UMI, Bologna and Istituto Veneto di Scienze, Lettere ed Arti, Venice (2016), pp. 57-73.

 

"And the prize for supporting role goes to ... mathematics", Alaxon (June 2015) ובתפקיד המשנה: המתמטיקה  אלכסון (Hebrew)

 

"Geometry and Arithmetic in the Medieval Traditions of Euclid's Elements: a View from Book II", Archive for History of Exact Sciences, 67(6) (2013): 637-705. READ HERE A REVIEW

"Berechnungen zur Grenze der poetischen Freiheit. Fiktionales Erzählen und die Geschichte der Mathematik", in Andrea Albrecht et al (eds.) Zahlen, Zeichen und Figuren Mathematische Inspirationen in Kunst und Literatur, Berlin: De Gruyter (2011), pp. 564-59. (German Translation of "Calculating the Limits of Poetic License: Fictional Narrative and the History of Mathematics", Configurations 15 (3) (2007), 195-226.)

2009-2010

"Science in an Israeli Context: Case Studies. Introduction", (with Tal Golan) Science in Context, 23 (4) (2010): 393-394.

 

"Zionist Internationalism through Number Theory: Edmund Landau at the Opening of the Hebrew University in 1925", (with Norbert Schappacher) Science in Context, 23 (4) (2010): 427-471.

 

"Hunting Prime Numbers from Human to Electronic Computers", The Rutherford Journal - The New Zealand Journal for the History and Philosophy of Science and Technology (rutherfordjournal.org), Vol. 3 (2010). 

 

"On the History of Fermat’s Last Theorem: Fresh Views on an Old Tale", Mathematische Semesterberichte 57 (1)  (2010): 123-138. 

 

"Mathematical Motifs in Borges' Writings: On the Uses and Abuses of Interpretation", Odissey (Hebrew) Vol. 4 (2009)  מוטיבים מתמטיים ביצירתו של בורחס – על פרשנות והפרזותיה  אודיסאה - מסע בין רעיונות

 

"Writing the Ultimate Mathematical Textbook: Nicolas Bourbaki’s Éléments de mathématique", in Eleanor Robson et al (eds.) Handbook of the History of Mathematics, Oxford, Oxford University Press (2009), 565-587.

2007-2008

"The Development of the Idea of Proof up to 1900". In: Tim Gowers (ed.) The Princeton Companion to Mathematics, Princeton, Princeton University Press (2008), 129-142.

 

"Number Crunching vs. Number Theory: Computers and FLT from Kummer to SWAC (1850-1960), and beyond", Archive for History of Exact Science 62(1) (2008): 393-455.

 

"FLT Meets SWAC: Vandiver, the Lehmers, Computers and Number Theory (1930-1956)", Annals of the History of Computing 30 (1) (2008): 38-49. READ HERE A REVIEW

 

"Calculating the Limits of Poetic License: Fictional Narrative and the History of Mathematics", Configurations 15 (3) (2007), 195-226.  HTML VERSION HERE.
(German translation: "Berechnungen zur Grenze der poetischen Freiheit. Fiktionales Erzählen und die Geschichte der Mathematik", in Andrea Albrecht et al (eds.) Zahlen, Zeichen und Figuren Mathematische Inspirationen in Kunst und Literatur, Berlin: De Gruyter (2011), pp. 564-599.)

 

"Axiomatics between Hilbert and the New Math: Diverging Views on Mathematical Research and their Consequences on Education", International Journal for the History of Mathematics Education 2 (2): (2007): 21-37.

 

"On Borges and Fritz Mauthner", Preface to the Hebrew Edition of Siete Noches, by Jorge Luis Borges (Hebrew Translation and Comments by Ori Preuss) - שבעה לילות Tel-Aviv, Hakibbutz Hameuhad (2007).

 

"A Clash of Mathematical Titans in Austin: Robert Lee Moore and Harry Schultz Vandiver (1924-1974)”, Mathematical Intelligencer 29 (4), 62-74 (2007).

 

"Fermat Comes to America: Harry Schultz Vandiver and FLT (1914-1964)”, Mathematical Intelligencer 29 (3), 30-40 (2007). 

 

"Albert Einstein and Relativity: One Hundred Years of History - One Hundred years of Historiography" (Hebrew), Zmanim - Quarterly Journal of History, Tel-Aviv, 71 (2007): 58-69 אלברט אינשטיין ותורת היחסות: מאה שנים של היסטוריה - מאה שנים של היסטוריוגרפיה,  זמנים

 

"From Algebra (1895) to Moderne Algebra (1930): Changing Conceptions of a Discipline. A Guided Tour Using the Jahrbuch über die Fortschritte der Mathematik", in J. Gray and K.H. Parshall (eds.), Episodes in the History of Modern Algebra, Providence, American Mathematical Society / London Mathematical Society (2007), 80-105.

2004-2006

"El Teorema de Fermat y sus Historias", Gaceta de la Real Sociedad Matemática Española 9 (2), 387-424 (2006).

 

"On the Origins of Hilbert’s 6th Problem: Physics and the Empiricist Approach to Axiomatization". In Marta Sanz-Solé et al (eds.), Proceedings of the International Congress of Mathematicians, Madrid 2006, Vol. 3, Zurich, European Mathematical Society (2006), 1679-1718.

 

"The Origin of Hilbert's Axiomatic Method". In: Jürgen Renn et  al (eds.). The Genesis of General Relativity, Vol. 4 Theories of Gravitation in the Twilight of Classical Physics: The Promise of Mathematics and the Dream of a Unified Theory, New York, Springer (2006), 139-236.

 

"Axiomatics, Empiricism, and Anschauung in Hilbert´s Conception of Geometry: Between Arithmetic and General Relativity". In: Jeremy Gray and José Ferreirós (eds.) The Architecture of Modern Mathematics: Essays in History and Philosophy, Oxford, Oxford University Press (2006), 155-176.

 

"History of Algebra". In: Encyclopaedia Britannica (2005). 

 

"Jorge Borges: Author of 'The Name of the Rose", in Nicholas Gane and Mike Gane (eds.), in Umberto Eco (3 Vols.), London, Sage (Masters in Modern Social Thought Series) (2005), Vol. 2: 389-406. [Originally published in Poetics Today 13: 425-445 (1992)]

 

"Science in Latin-American Contexts. An Introduction", Science in Context 18 (2): 174-17 (2005).

 

"The Emergence of the Structural Conception in Algebra", in Sandro Petruccioli (ed.) Storia della scienza, Roma, Istituto della Encyclopedia Italiana (2004), Vol. VIII, 193-198.

 

"Fermat's Last Theorem: How Does a Marginal Remark Turn into an Important Mathematical Question? Or Does it?", (Hebrew) Galileo. Israeli Journal for Science and Ecology (2004). "המשפט האחרון של פרמה". איך הופכת שאלה שבשוליים לבעיה מתמטית חשובה, ולרב-מכר עטור תהילה?

 

"The History of Modern Mathematics – Writing and Re-Writing", Science in Context 17 (1-2) (2004), 1-21.

 

"Heinrich Weber’s Lehrbuch der Algebra", in I. Grattan-Guinness et al. (eds.) Landmark Writings In Western Mathematics, 1640-1940, Amsterdam, Elsevier Science. (2004)ץ

2000-2003

"Algunas Ideas Científicas en la Obra de Jorge Luis Borges y su Contexto Histórico", in Borges en Jerusalén, Myrna Solotorevsky and Ruth Fine (eds.), Frankfurt am Main, Vervuert/Iberoamericana (2003), 49-74.

 

"Theory of Invariants", in Sandro Petruccioli (ed.) Storia della scienza, Roma, Istituto della Encyclopedia Italiana (2003), Vol. VII, 1025-1029.

 

"David Hilbert y su Filosofía Empiricista de la Geometría", Boletín de la Asociación Matemática Venezolana, 9 (1) (2002), 27-44.

 

"Mathematical Structures from Hilbert to Bourbaki: The Evolution of an Image of Mathematics", in A. Dahan and U. Bottazzini (eds.) Changing Images of Mathematics in History. From the French Revolution to the new Millenium, London, Harwood Academic Publishers (2001), 167-186.

 

Preface to the new Hebrew Edition of Flatland, E.E. Abbott (Hebrew Translation by Lia Nirgad)           - מישוריה   Tel-Aviv, Babel Publishers (2000).

 

"The Origins of the Definition of Abstract Rings", Gazette des Mathématiciens, 83 (Janvier 2000), 28-47. (Reprint: Modern Logic, 8 (1-2), 1998-2000: 5-27.)

 

"Relativity and Mathematics", in The History of Mathematics from Antiquity to the Present: A Selective Bibliography, Edited by Joseph W. Dauben, Revised Edition on CD-ROM, Albert C. Lewis in Cooperation with the International Comission on the History of Mathematics, Providence, The American Mathematical Society (2000).

 

"The Empiricist Roots of Hilbert’s Axiomatic Method", in Vincent F. Hendricks et al.  (eds.) Proof Theory: History and Philosophical Significance, Dordrecht, Kluwer (2000): 35-54.

1997-1999

"David Hilbert: Geometry and Physics: 1900-1915", in J.J. Gray (ed.) The Symbolic Universe: Geometry and Physics (1890-1930), Oxford, Oxford University Press (1999): 145-188.

 

"David Hilbert between Mechanical and Electromagnetic Reductionism, 1910-1913", Archive for History of Exact Sciences 53 (6): 489-527 (1999). Read here a REVIEW.

 

"From Mie's Electromagnetic Theory of Matter to Hilbert's Foundations of Physics" Studies in History and Philosophy of Modern Physics 30(2): 159-183 (1999). (Parts of this article are reprinted, within a broader context and with updates, in Joseph Kouneiher (ed.) Foundations of Mathematics and Physics One Century After Hilbert - New Perspectives, New York, Springer (2018): 75-96.)

 

"Jewish Mathematicians in Göttingen (1895-1933)" (Hebrew), Zmanim - Quarterly Journal of History, Tel-Aviv, 66: 91-101 -  מתמטיקאים יהודיים בגטינגן: 1895-1933 זמנים , 66: 91-101.

1998.

 

"Hilbert on Kinetic Theory and Radiation Theory (1912-1914)", Mathematical Intelligencer 20 (3): 52-58 (1998) 30(2): 159-183 (1999). 

 

"Einstein, Hilbert y la Teoría General de la Relatividad", Investigación y Ciencia 206 (Nov. 1998): 28-34.

 

"Los 23 Problemas de Hilbert y su Trasfondo Histórico", Boletín de la Asociación Matemática Venezolana 5 (2) (1998).

 

"The Influence of David Hilbert and Hermann Minkowski on Einstein's Views over the Interrelation between Physics and Mathematics", Endeavour 22(3): 95-97 (1998).

 

"The Origins of Eternal Truth in Modern Mathematics: Hilbert to Bourbaki and Beyond", Science in Context, 12: 137-183 (1998).

 

"Belated Decision in the Hilbert-Einstein Priority Dispute" (with Jürgen Renn and John Stachel), Science 278: 1270-1273 (Nov. 14, 1998).  

 

Hermann Minkowski and the Postulate of Relativity”, Archive for History of Exact Sciences 51: 281-314 (1997). Reprinted in: Vesselin Petkov (ed.), Minkowski Spacetime: A Hundred Years Later, New York, Springer (2010), pp. 3-42.

 

David Hilbert and the Axiomatization of Physics (1894-1905)”, Archive for History of Exact Sciences 51: 89-197 (1997). Read here a REVIEW.

1985-1996

Paradigms and Images in the History of Mathematics” in E. Ausejo and M. Hormigon (eds). Paradigms and Mathematics, Madrid, Siglo XXI (1996): 169-192.

 

Axiomática Moderna y Algebra Estructural en la Obra de David Hilbert”, Mathesis 12: 1-56 (1996). 

 

La Teoría de las Proporciones de Eudoxio Vista por Dedekind”, Mathesis 10: 35-68 (1994).

 

“Carpentier, Alejo”, Encyclopaedia Hebraica, Supplementary Vol. 3, p. 960 (1994) אלחו קרפנטייר", האנציקלופדיה העברית כרך מילואים ג - תשנ"ה"

 

“Vargas Llosa, Mario”, Encyclopaedia Hebraica, Supplementary Vol. 3, p. 365 (1994) מריו וארגס יוסה", האנציקלופדיה העברית כרך מילואים ג - תשנ"ה"

 

Kuhnian Issues, Scientific Revolutions and the History of Mathematics”, Studies in History and Philosophy of Science 24: 95-117 (1993).

 

Nicolas Bourbaki and the Concept of Mathematical Structure”, Synthese 92: 315-348 (1992). An elaborated version of this article appeared as Chapter 7 of my book Modern Algebra and the Rise of Mathematical Structures.    Read here a REVIEW.

 

Libros de Texto e Imágenes del Algebra en el Siglo XIX”, Llull 14: 7-30 (1991).

 

Reflexive Thinking in Mathematics: Formal and Non-formal Aspects”, in A. Diez et al (eds.) Proceedings of the Symposium on Structures in Mathematical Theories, San Sebastian (1990): 383-389.

 

Linearity and Reflexivity in the Growth of Mathematical Knowledge” Science in Context 3: 409-440 (1989).

 

The Splitting Data of Cohomology Classes”, Archiv der Mathematik 44: 418-423 (1985).