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Acerbi, F. Plato: Parmenides 149a7-c3: A Proof by Complete Induction?, Archive for History of Exact Sciences 55 (2000), 57–76. In Parmenides, Plato gives a full-ﬂedged example of proof by complete induction, indeed the only such example in the ancient mathematical corpus. Other alleged examples are untenable, suggesting that the generality of this proof technique, developed in a pre-Euclidean arithmetical context, was misunderstood. (JGF) #28.3.1

Aiton, Eric J. An Episode in the History of Celestial Mechanics and Its Utility in the Teaching of Applied Mathematics, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical Association of America, 1995, pp. 267–278. Considers the role of ﬁrst- and second-order inﬁnitesimals in late 17th- and early 18th-century studies of the dynamics of motion in a curve. (GVB) #28.3.2

Alberts, G. The Rise of Mathematical Modeling [in Dutch], Nieuw Archief voor Wiskunde 1 (2000), 59–67. “This is the ﬁrst of a series of four articles on the relations between mathematics and reality.” It includes a discussion of how modern Dutch modeling began in the 1930s with Tinbergen’s economic policy models. See the review by Eduard Glas in Mathematical Reviews 2001c:01003. (JA) #28.3.3

Alexiewicz, Andrzej; Barański,Feliks; and Koroński,Jan. The Mathematics–Physics Students Circle at the Jan Kazimierz University in Lwów[in Polish], Zeszty Naukowe Uniwerstetu Opole Matematyka 30 (1997), 9–42. The activities of the Mathematics-Physics Students Circle at the Polish university in Lvov for the 40 years

255 0315-0860/01 $35.00 Copyright C 2001 by Academic Press All rights of reproduction in any form reserved. 256 ABSTRACTS HMAT 28 from 1899 to 1939 are described. See the review by Jaroslav Zemanek in Mathematical Reviews 2001c:01043. (JA) #28.3.4 Ames-Lewis, Francis, ed. Sir Thomas Gresham and Gresham College, Aldershot: Ashgate, 1999, 272 pp., $74.95. A collection of papers emerging from a 1997 conference to celebrate the 400th anniversary of Gresham College. Some of the papers are abstracted separately. (GVB) #28.3.5 Amunategui, Godofredo Iommi. See #28.3.39. Applebaum, David. Dirac Operators—From Differential Calculus to the Index Theorem, The Mathematical Scientist 25 (2000), 63–71. The intriguing relationship between beautiful mathematics and physical applications may be illustrated through the Dirac equation for relativistic electrons, whose antecedents lie in 18th-century differential equations and 19th-century Clifford algebras, emerging into physics through the need to combine special relativity with quantum mechanics, and recently incarnated in index theory. (JGF) #28.3.6 Arcavi, Abraham. See #28.3.55, #28.3.90, and #28.3.206. Avital, Shmuel. History of Mathematics Can Help Improve Instruction and Learning, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson and Victor Katz, eds., Learn from the Masters, Washington: Mathematical Association of America, 1995, pp. 3–12. Educating teachers in the history of mathematics can help in at least four areas: giving insight into learning difficulties; improving modes of instruction; incorporating problem solving in lessons; drawing attention to emotional and affective factors in the creation and learning of mathematics. (JGF) #28.3.7 Bach, Craig N. Philosophy and Mathematics: Zermelo’s Axiomatization of Set Theory, Taiwanese Journal for Philosophy and History of Science 10 (1998), 5–31. This paper is a discussion of the early days of set theory; however, it contains historical inaccuracies. See the review by Leon Harkleroad in Mathematical Reviews 2001b:01016. (TBC) #28.3.8 Bagni, Giorgio T. See #28.3.9 and #28.3.188. Barański,Feliks. See #28.3.4. Barbin, Evelyne; Bagni, Giorgio T.; Grugnetti, Lucia; Kronfellner, Manfred; Lakoma, Ewa; and Menghini, Marta. Integrating History: Research Perspectives, in #28.3.59, pp. 63–90. Judging the effectiveness of integrating historical resources into mathematics teaching may not be susceptible to the research techniques of the quantitative experimental scientist. Research paradigms to explore and analyze include those developed by anthropologists. (JGF) #28.3.9 Barbin, Evelyne. See also #28.3.90. Barrantes, Hugo. See #28.3.167. Barrow-Green, June. See #28.3.133. Bartolini Bussi, Maria G. See #28.3.133 and #28.3.154. Bassalygo, L. A. From A. N. Kolmogorov to P. S. Aleksandrov [in Russian], Vestnik Rossiiskaya˘ Akademiya Nauk 69 (3) (1999), 245–255. Two letters written in 1942 from Kolmogorov to Aleksandrov show that their wartime separation did not prevent the interchange of scientific ideas and philosophical reflections. The article is accompanied by a comment on Kolmogorov by V. M. Tikhomirov; see #28.3.203. (GVB) #28.3.10 Batho, Gordon R. Thomas Harriot’s Manuscripts, in #28.3.70, pp. 286–297. Account drawing together recent studies on the fate and present whereabouts of Harriot’s manuscripts. (JGF) #28.3.11 Beckers, Danny J. Positive Thinking: Conceptions of Negative Quantities in the Netherlands and the Recep- tion of Lacroix’s Algebra Textbook, Revue d’Histoire des Mathematiques´ 6 (2000), 95–126. The beginning of the 19th century saw the emergence of several new approaches to negative numbers. In the early 19th-century Netherlands, Dutch mathematicians opted for an approach different from that of their contemporaries in Germany and France. The 1821 Dutch translation of Lacroix’s El´ emens´ d’Algebre` illustrates the Dutch notion of rigor. (JGF) #28.3.12 HMAT 28 ABSTRACTS 257

Beckers, Danny J. “Untiring Labor Overcomes All!” The History of the Dutch Mathematical Society in Comparison to its Various Counterparts in Europe, Historia Mathematica 28 (2001), 31–47. As in other countries, the Netherlands fostered several amateur mathematical societies during the 18th and early 19th centuries. One of these, the Amsterdam Mathematical Society, developed into the national professional society of today, Wiskundig Genootschap. (JGF) #28.3.13

Beckers, Danny J. Definitely Infinitesimal: Foundations of the Calculus in the Netherlands, 1840–1870, Annals of Science 58 (2001), 1–15. The foundations of analysis offered by Cauchy and Riemann were not immediately welcomed by the mathematical community. Before 1870 the foundations of mathematics were considered more or less a national affair. Mid-19th century Dutch mathematicians were aware of developments abroad but preferred the concept of infinitesimals as a foundation of mathematics. (JGF) #28.3.14

Beeley, Philip A. See #28.3.99. Bekken, Otto B. Wessel on Vectors, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical Association of America, 1995, pp. 207–213. Brieﬂy introduces Wessel’s work on multiplying vectors in the plane and 3-space, and relates it to today’s geometric representation of complex numbers. Also contains three exercises that greatly enhance the material. (SP) #28.3.15

Bekken, Otto B. See also #28.3.55, #28.3.90, and #28.3.154.

Bennett, J. A. Instruments, Mathematics, and Natural Knowledge: Thomas Harriot’s Place on the Map of Learn- ing, in #28.3.70, pp. 137–152. From the point of view of traditional history of astronomy, Harriot is disappointingly private, reluctant to share his insights. But our viewpoint may be wrong. Seeing Harriot as a professional mathematical practitioner yields a richer and more sympathetic picture. (JGF) #28.3.16

Bennett, Jim. Christopher Wren’s Greshamite History of Astronomy and Geometry, in #28.3.5, pp. 189–197. Wren’s inaugural lecture in 1657 as Gresham professor of astronomy gives interesting insights into his views on the status and role of mathematics and the history of astronomy, foreshadowing the theoretically informed practical mathematical direction that his work was later to take. (JGF) #28.3.17 Berger, Marcel. La Géométriede Riemann: Aper¸cuHistorique et RésultatsRécents, Cubo 3 (1) (2001), 13–36. Sections on the pioneering work of Gauss and of Riemann respectively are followed by a substantial account of modern developments, centering on the notion of a Riemann variety and including the work of Alexandrov- Toponogov (1950s) and of Gromov (1980s), among others. (HG) #28.3.18 Berggren, J. Lennart; and Van Brummelen, Glen R. The Role and Development of Geometric Analysis and Synthesis in Ancient Greece and Medieval Islam, in #28.3.193, pp. 1–31. A discussion and comparison of the logic, historical conceptions, and practice especially of analysis in ancient Greece and medieval Islam. (GVB) #28.3.19 Berggren, J. Lennart; and Van Brummelen, Glen R. Ab¯uSahl al-K¯uh¯ı on “Two Geometrical Questions,” Zeitschrift fur¨ Geschichte der Arabisch-Islamischen Wissenschaften 13 (2000), 165-187. A translation, with commentary, of a treatise by al-K¯uh¯ı(10th century A.D.) on two geometrical problems: the construction of a circle as a locus (a special case of a problem reportedly discussed in Apollonius), and a second unrelated problem, perhaps a fragment of another work. (JGF) #28.3.20 Bessot, Dider. Les Aspects Epistémologiquesde´ la PenséeDidactique de Desargues: L’Usage des Exemples Générique,in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 295–312. Bessot’s contribution concerns Desargues’s epistemological and didactic remarks which confirm, as the author has shown, the synthetic character of his thought. According to Bessot they also reveal that Desargues recognized the superiority of theory with respect to practice as the correctness of the artisan’s technique comes from the truth of theoretic bases, not from the success of the work. (AF) #28.3.21 Bianchini, Carlo. See #28.3.51. Biryukov, B. V. See #28.3.22. 258 ABSTRACTS HMAT 28

Biryukova, L. G.; and Biryukov, B. V. On the Axiomatic Sources of Fundamental Algebraic Structures: The Achievements of Hermann Grassmann and Robert Grassmann [in Russian], Modern Logic 7 (2) (1997), 131–159. The authors argue that Hermann Grassmann was the first to give axiomatizations for semi-groups, abelian groups, rings, fields, and various related structures. Not much is said about Robert Grassmann. See the review by E. Mendelson in Mathematical Reviews 2001b:01012. (TBC) #28.3.22 Bkouche, Rudolf. Desargues au XIXe Siècle: L’Influence d’un Livre non Lu, in Jean Dhombres and Joël Sakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 207–217. Bkouche analyzes the work by M. Chasles, Aperçu historique sur l’origine et le developpement´ des methodes´ en geom´ etrie´ (1837), in which the French geometer restored Desargues’ thought, having only an indirect knowledge of his major work, the Brouillon Project (1639). According to the author, the interest of the geometers of the 19th century in Desar- gues’s mathematical work was connected with the progressive ideas of the Age of Enlightenment; moreover, the projective conception never died between Desargues and Monge. (AF) #28.3.23 Boero, Paolo. See #28.3.154. Booth, A. D. See #28.3.216. Bottazzini, Umberto. See #28.3.34. Brackenridge, J. Bruce. Newton’s Dynamics: The Diagram as a Diagnostic Device, in #28.3.44, pp. 71–102. Newton developed three methods for solving direct problems of orbital motion, the least well-recognized of which might be called a curvature method, where an element of the continuous orbit is represented by a vanishingly small arc of the circle of curvature. Newton developed this measure of the rate of bending of curves before he began his analysis of orbital motion. (JGF) #28.3.24 Brigaglia, Aldo. The Rediscovery of Analysis and the Apollonian Problems [in Italian], in Marco Panza and Clara Silvia Roero, eds., Geometry, Fluxions and Differentials [in Italian], Naples: La Cittàdel Sole, 1995, pp. 221–269. This paper discusses certain problems of Apollonius that were analyzed in Pappus’s Collection, Book VII, and then were reformulated in algebraic language between 1659 (Descartes’s Geometry) and the 1680s (Newton’s treatise on geometry). See the review by William R. Shea in Mathematical Reviews 2001c:01013. (JA) #28.3.25 Bueno, Otávio. Empiricism, Scientific Change and Mathematical Change, Studies in the History and Philosophy of Science 31 (2000), 269–296. A unified account of scientific and mathematical change in a thoroughly empiricist setting may be illustrated through examining the early history of formulating set theory (in particular, the works of Cantor, Zermelo, and Skolem). (JGF) #28.3.26 Burn, Bob. Gregory of St. Vincent and the Rectangular Hyperbola, Mathematical Gazette 84 (2000), 480–485. One of the proofs by Gregory of St. Vincent (1584–1667) of the area under a rectangular hyperbola, which de Sarasa noticed has a logarithm-like property, has a remarkable similarity to Archimedes’s quadrature of the parabola. The proof is here given an analytical exposition. (JGF) #28.3.27 Burn, R. P. Alphonse Antonio de Sarasa and Logarithms, Historia Mathematica 28 (2001), 1–17. The discovery of hyperbolic logarithms has been variously attributed to Gregory of St. Vincent (1584–1667) and to de Sarasa (1618–1667). In fact de Sarasa’s hyperbolas were not defined analytically, and he did not insist on a particular base for his logarithms, nor choose log 1 to have the value 0, so he did not focus on what Euler was to call natural logarithms. The assumption, or rational reconstruction, that he did owes as much to the needs of 20th-century students as to what happened in the 17th century. (JGF) #28.3.28 Burnett, Charles. Why We Read Arabic Numerals Backwards, in #28.3.193, pp. 197–202. Considers how the representations of decimal numbers in the Latin Middle Ages came to be in order from digits of greatest value to smallest, rather than the opposite, as in Arabic script. (GVB) #28.3.29 Burton, David M.; and Van Osdol, Donovan H. Toward the Definition of an Abstract Ring, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathemat- ical Association of America, 1995, pp. 241–251. Gives a brief sketch of the early evolution of the concepts of rings and ideals, from the conviction that the history of a subject is essential for a true appreciation of it. (GVB) #28.3.30 Caquero Mart´ınez,JoséM. See #28.3.37. HMAT 28 ABSTRACTS 259

Carvalho e Silva, Jaime. See #28.3.55 and #28.3.83. Caveing, Maurice. La Constitution du Type Mathematique´ de l’Idealite´ dans la Pensee´ Grecque [The Constitu- tion of the Mathematical Type of Idealness in Greek Thought], vol. 2, Villeneuve d’Ascq: Presses Universitaires du Septentrion, 1997, 428 pp., 240 F. A new edition of the second of three volumes of the author’s doctoral dissertation, in which the author identified two stages in the development of the theoretical structure of mathematical knowledge in ancient Greece. This volume analyzes the first stage, when Greek mathematics begin to differ from its Mesopotamian and Egyptian counterparts. (GVB) #28.3.31 Cazaran, Jilyana. See #28.3.128. Cegielski, Patrick. Un Fondement des Mathématiques[A Foundation for Mathematics], in Michel Serfati, ed., La Recherche de la Verit´ e´, Paris: ACL—Les Editions´ du Kangourou, 1999, pp. 175–209. Beginning with ancient Egyptian and Babylonian mathematics, this paper attempts “to show how and why we have arrived at Zermelo– Fraenkel set theory as a foundation of mathematics.” See the review by E. Mendelson in Mathematical Reviews 2001c:03003. (JA) #28.3.32 Chaboud, Marcel. Desargues Lyonnais, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 433–452. Chabout provides new elements concerning Desargues’s presence and activity in the district of Lyon, results of one and a half years of research into the “Archives municipales de Lyon” and the “Archives départementalesdu Rhône.” The information is organized by wide themes and Taton’s book of 1951 is the introduction to this contribution. (AF) #28.3.33 Cicenia, Salvatore. The Mathematical Writings of Giuseppe Torelli [in Italian], Physis 35 (1998), 85–124. This is a survey of the mathematical work of Giuseppi Torelli (1721–1781); among other achievements, Torelli translated the collected works of Archimedes into Latin. See the review by Umberto Bottazzini in Mathematical Reviews 2001c:01015. (JA) #28.3.34 Clucas, Stephen. “No Small Force”: Natural Philosophy and Mathematics in Thomas Gresham’s London, in #28.3.5, pp. 146–173. Gresham’s public endowment marked an investment in a new epistemological advance in mathematics. Mathematical practitioners in London in the late 16th century shifted the epistemic foundation of mathematics from mathematical idealism toward a more immediate relationship between the mathematical and the physical, seen especially by comparing the approaches of John Dee and Thomas Harriot. (JGF) #28.3.35 Clucas, Stephen. Thomas Harriot and the Field of Knowledge in the English Renaissance, in #28.3.70, pp. 93–136. To understand Harriot we need to listen to his procedures, rather than impose them on a later conceptu- alization of the field of knowledge and praxis. Thus seen, Harriot is remarkably diverse in his mathematical and experimental practices, transcending modern classifications. (JGF) #28.3.36 Cobos Bueno, José;and Caquero Mart´ınez,JoséM. Matemáticasy Exilio: La Primera Etapa Americana de Francisco Vera [Mathematics and Exile: Francisco Vera’s First American Period], LLULL 23 (2000), 569–588. From the author’s abstract: “Francisco Vera is considered to be one of the most important historians of science in Spain. He was, like many others of the time, forced to exile in America because of his political ideas after Spanish Civil War (1936–1938). In this paper, the first years of exile (in the Dominican Republic and Colombia) are narrated and commented.” (VA) #28.3.37 Cohen, I. Bernard. Newton’s Scholarship in Historical Perspective, in #28.3.44, pp. 11–26. An account of the progress of Newtonian scholarship over the past century and a half, from Brewster’s 1855 biography and Edleston’s 1850 edition of the Newton–Cotes correspondence to the later 20th-century editions of Rupert and Marie Boas Hall and Tom Whiteside. (JGF) #28.3.38 Conrad, Keith. The Origin of Representation Theory, L’Enseignement Mathematique´ (2) 44 (3–4) (1998), 361–392. The article considers some of the pre-1900 work of G. Frobenius in representation theory. See the review by Godofredo Iommi Amunategui in Mathematical Reviews 2001b:01013. (TBC) #28.3.39 Cooke, Roger L. See #28.3.74, #28.3.87, and #28.3.204. Coray, Daniel. See #28.3.83. 260 ABSTRACTS HMAT 28

Correia de Sá,Carlos. See #28.3.188 and #28.3.206. Corry, Leo. The Origins of the Definition of Abstract Rings, Gazette des Mathematiciens 83 (2000), 29–47. The origins of Fraenkel’s axiomization of rings (1914) are traced back to work of E. H. Moore and Ernst Steinitz. See the review by Jonathan Golan in Mathematical Reviews 2001c:01004. (JA) #28.3.40 Cottin, Fran¸cois-Régis. L’Architecte et l’Architecture àLyon au Temps de Desargues, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 425–432. Cottin shows the difference in origin and disposition of those who carried out the traditional functions of an architect between the 16th and 17th century. The oval stairs of the Hotelˆ de Ville de Lyon and the “trompe de la Maison Saint Oyen” are as- cribed to Desargues. In the documents Desargues was cited not as an “architect,” but as intelligent in the matter. According to the author this is remarkable, because it testifies that the subsidiary sciences are going to become absolutely necessary to architecture, not only stone-cutting with Desargues, but afterwards also statics, resistance of materials, descriptive geometry, and others. (AF) #28.3.41 Cousquer, Eliane.´ See #28.3.60 and #28.3.175. Cuer, Georges. Le Notariat Lyonnais au XVIIe Siècle,in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 453–459. Cuer gives some general information as regards the profession of a notary in Lyon in Desargues’s epoch. The significance of this theme is that Desargues was closely connected with the milieu of the legal professions, particularly as his father was a royal notary in Lyon. (AF) #28.3.42 Cushing, James. Philosophical Concepts in Physics. The Historical Relation Between Philosophy and Scien- tific Theories, Cambridge: Cambridge Univ. Press, 1998, xx+424 pp. This “well-written and accessible book” is a “fascinating overview of developments in physics ... from Aristotle to quantum theory, that includes all of the relevant and necessary mathematics.” See the review by Paul Ernest in Mathematical Reviews 2001c:01005. (JA) #28.3.43 Dalitz, Richard H.; and Nauenberg, Michael, eds. Foundationsof Newtonian Scholarship, River Edge, NJ/London: World Scientific, 2000, 260 pp., $65/£44. A collection of papers, most of which emerge from a symposium held at the Royal Society in London in March 1997. Many of the papers are abstracted separately. (GVB) #28.3.44 Damish, Hubert. Desargues et la “Metaphysique” de la Perspective, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 11–22. An exposition by Damish that considers the character of Desargues as a point of connection between art and science and studies the relationships that Desargues established with the artists of his epoch, painters, carvers, architects, stonecutters, with the aim of establishing mutual influences. The suggestions to develop the speech in parallel on the artistic and the geometric levels are remarkable. (AF) #28.3.45 Daniel, Coralie. See #28.3.55, #28.3.83, and #28.3.123. Dauben, Joseph W. See #28.3.211. De Guzmán,Miguel. See #28.3.83. Deakin, Michael A. B. See #28.3.170. Debarnot, Marie-Thérèse. Trigonometry, in Roshdi Rashed and RégisMorelon, eds., Encyclopedia of the History of Arabic Science, London: Routledge, 1996, vol. 2, pp. 495–538. The author traces the development of formulas in spherical and plane trigonometry in the Arabic zijes from the 11th through the 14th centuries A.D., a rich though compressed paper. See the review by J. S. Joel in Mathematical Reviews 2001b:01003. (TBC) #28.3.46 Diacu, Florian. A Century-Long Loop, Mathematical Intelligencer 22 (2) (2000), 19–25. The author presents his idea of how mathematical theories generally arise and illustrates it with the development of algebraic topology by tracing the history of Henri Poincaré’s three-body problem from 1892 to 1994. (FA) #28.3.47 Diacu, Florian. See also #28.3.95. Djebbar, Ahmed. Les ActivitésMathématiquesdans les Villes du Maghreb Central (XIe–XIXes) [Mathemati- cal Activities in the Cities of the Central Maghreb (XI–XIX centuries)], in Histoire des Mathematiques´ Arabes, HMAT 28 ABSTRACTS 261

Algiers: Association Algérienned’Histoire des Mathématiques,1998, vol. 2, pp. 73–115. Based on manuscripts (8th–15th centuries A.D.) and other indigenous sources, this paper gives “a meaningful global picture” of the development of mathematics and of its place in the culture of what has become present-day Algeria. See the review by Jens Høyrup in Mathematical Reviews 2001c:01010. (JA) #28.3.48 Djebbar, Ahmed. Les Livres Arithmétiquesdes El´ ements´ d’Euclide dans le Traitéd’al-Mu’taman du XIe Siècle, LLULL 23 (2000), 589–653. From the author’s abstract: “This paper studies the first chapter of Kitab¯ al-Istikmal¯ , a work of the 11th century A.D. by al-Mu’taman Ibn H¯ud,a mathematician from al-Andalus who was the king of Saragossa between 1081 and 1085. Different chapters of this remarkable work in the Arabic mathematical tradition have already been studied in the last decade, while other works are still in progress.” (VA) #28.3.49 Djebbar, Ahmed. See also #28.3.163. Dobson, Geoffrey J. On Lemmas 1 and 2 to Proposition 39 of Book 3 of Newton’s Principia, Archive for History of Exact Sciences 55 (2001), 345–363. The details of Newton’s arguments in these lemmas, concerned with the turning moment exerted on the Earth by tidal forces due to the gravitational attraction of the Sun, has not been well understood. Both conclusions are in fact correct, albeit based on Newton’s intuitive, highly original, idiosyncratic, and (for us) nonrigorous reasoning here. (JGF) #28.3.50 Docci, Mario; Migliari, Riccardo; and Bianchini, Carlo. Les “Vies Parallèles”de Girard Desargues et de Guarino Guarini, Fondateurs de la Science Moderne de la Représentation,in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son temps, Paris: Blanchard, 1994, pp. 395–412. Docci, Migliari, and Bianchini single out in the unity of theory and praxis the common denominator between Desargues and the Italian architect Guarino Guarini of Modena. The authors also underline Guarini’s contribution to the science of body’s geometrical representation as another aspect which places Guarini in the same historical perspective as Desargues. (AF) #28.3.51 Dorier, Jean-Luc. See #28.3.154. Echeverria, Javier. Leibniz, Interprètede Desargues, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son temps, Paris: Blanchard, 1994, pp. 283–293. Echeverr´ıaexamines the relationships between Leibniz and Desargues based on Leibniz’s available writings. According to the author, rather than Desargues’s direct influence on Leibniz, one has to deal with the interpretation by Leibniz of Desargues’s ideas and methods. Leibniz paid particular attention to Desargues’s “grille perspective” with the aim of introducing a new analysis in geometry, different from Viete’s and Descartes’. Desargues’s identification between parallel and converging straight lines could have played a heuristic role in Leibniz’s discovery of infinitesimal calculus, but for this subject the author refers to another article by himself. (AF) #28.3.52 Eckert, Michael. Mathematics, Experiments, and Theoretical Physics: The Early Days of the Sommerfeld School, Physics in Perspective 1 (3) (1999), 238–252. Covers the haphazard beginnings of the Sommerfeld school, which was later to produce such stars as Debye, Ewald, Pauli, Heisenberg, and Bethe. (GVB) #28.3.53 El Idrissi, Abdellah. See #28.3.90 and #28.3.175. Elschner, Johannes. The Work of Vladimir Maz’ya on Integral and Pseudodifferential Operators, in Jürgen Rossman, Peter Takác,and GüntherWildenhain, eds., The Maz’ya Anniversary Collection, Basel: Birkhäuser, 1999, vol. 1, pp. 35–52. Integral and pseudodifferential operators were one of the main themes of Maz’ya’s vast mathematical work. (GVB) #28.3.54 Ernest, Paul. See #28.3.43. Fasanelli, Florence; Arcavi, Abraham; Bekken, Otto; Carvalho e Silva, Jaime; Daniel, Coralie; Furinghetti, Fulvia; Grugnetti, Lucia; Hodgson, Bernard; Jones, Lesley; Kahane, Jean-Pierre; Kronfellner, Manfred; Lakoma, Ewa; van Maanen, Jan; Michel-Pajus, Anne; Millman, Richard; Nagaoka, Ryosuke; Niss, Mogens, Pitombeira de Car- valho, João;Silva da Silva, Mary Circe; Smid, Harm Jan; Thomaidis, Yannis; Tzanikis, Constantinos; Visokolskis, Sandra; and Zhang, Dian Zhou. The Political Context, in #28.3.59, pp. 1–38. Decisions on what mathematics is to be taught in schools, how, and with what historical resources or input, are ultimately political, influenced by a number of factors including the experience of teachers, expectations of parents and employers, and the social context of debates about the curriculum. (JGF) #28.3.55 262 ABSTRACTS HMAT 28

Fauvel, John G. Revisiting the History of Logarithms, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson and Victor Katz, eds., Learn from the Masters, Washington: Mathematical Association of America, 1995, pp. 39–48. Exploring the separate historical strands of logarithms (comparing arithmetic and geometric progressions, multiplying through addition, using the geometry of motion, and the power of exponential notation) can illuminate the subject for students and prepare them for studying logarithms later. (JGF) #28.3.56 Fauvel, John G. Newton’s Mathematical Language, in #28.3.44, pp. 145–159. From his earliest studies, Newton was deeply interested in questions of language and appropriate symbolism. These issues play an important yet ambiguous role in his discoveries and the communication of his ideas. (JGF) #28.3.57 Fauvel, John G. The Role of History of Mathematics Within a University Mathematics Curriculum for the 21st Century, Teaching and Learning Undergraduate Mathematics 12 (2000), 7–11. It is increasingly common for mathematics courses to incorporate a history of mathematics module, for a number of good reasons including adding motivation, breadth of experience and understanding, and consolidating a range of desirable skills. (JGF) #28.3.58 Fauvel, John G.; and van Maanen, Jan, eds. History in Mathematics Education: The ICMI Study, Dordrecht: Kluwer, 2000, xviii+437 pp., hardbound, $185. An international study of the uses of history in mathematics education arising from a 1998 ICMI conference in Luminy, France. The book has been edited to provide a coherence not found in typical conference proceedings. Individual chapters are abstracted separately. (GVB) #28.3.59 Fauvel, John G.; Cousquer, Eliane;´ Furinghetti, Fulvia; Heiede, Torkil; Lit, Chi Kai; Smid, Harm Jan; Thomaidis, Yannis; and Tzanikis, Constantinos. Bibliography for Further Work in the Area, in #28.3.59, pp. 371–418. A considerable amount of work has been done in recent decades on the relations between history and mathematics education, which is here summarized, in the form of an annotated bibliography, for works appear- ing in eight languages of publication (Chinese, Danish, Dutch, English, French, German, Greek, and Italian). (JGF) #28.3.60 Feingold, Mordechai. Gresham College and London Practitioners: The Nature of the English Mathematical Community, in #28.3.5, pp. 174–188. Part of the reason for poor attendance at early Gresham College lectures was that the traditional lecture format was becoming obsolete under the developing availability of books, and more private tutorial situations. Although the Gresham professoriate served both its instructional and research missions, other factors such as the rise of the Royal Society and the growth of coffee houses fostered its decline. (JGF) #28.3.61 Fenster, Della. The Development of the Concept of an Algebra: Leonard Eugene Dickson’s Role, Rendiconti del Circolo Matematico di Palermo, Serie II. Supplemento 61 (1999), 59–122. This paper describes how the “Chicago school of algebra” drew upon the study of axioms in the development of non-Euclidean geometry and on ideas from quaternions. See the review by Jaroslav Zemanek in Mathematical Reviews 2000c:01022. (JA) #28.3.62 Ferreirós,José. Mathematics and Platonism(s) [in Spanish], Gaceta de la Real Sociedad Matematica´ Espanola˜ 2 (3) (1999), 446–473. The author provides a brief historical survey of Platonism in mathematics in order to present an outline of his naturalistic project. See the review by Jaime Nubiola in Mathematical Reviews 2001b:00004. (TBC) #28.3.63 Fiorani, Francesca. The Theory of Shadows and Aerial Perspective: Leonardo, Desargues and Bosse, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son temps, Paris: Blanchard, 1994, pp. 267–282. Fiorani studies both shadow projection and aerial perspective in Desargues’s and Bosse’s work. With the aim of establishing the relationships among Leonardo, Desargues, and Bosse, he analyzes two issues: the origin and meaning of a drawing on shadow projection sent by Poussin to Paris and the understanding of what Desargues and Bosse called la regle` du fort et faible. Bosse’s writings provide precious insights on these topics, because they complement Desargues’s succinct rules with observation related more strictly to painting; moreover Bosse shows an accurate knowledge of the treatises influenced by Leonardesque ideas. (AF) #28.3.64 FitzSimons, Gail. See #28.3.123 and #28.3.188. Flacon, Albert. Voir et Représenter:Abraham Bosse, l’Intransigeant, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son temps, Paris: Blanchard, 1994, pp. 263–266. Flacon discusses the work of Abraham Bosse, HMAT 28 ABSTRACTS 263 friend of Desargues, professor of perspective at the Parisian Academie´ royale de peinture et sculpture and the strongest supporter of Desargues’s ideas about perspective. The author explains the terms of the controversy between Bosse and the artists which was originated by Bosse’s idea that the artist has to draw according to perspective rules. He also points out that Bosse gave deep thought to the problems of aerial perspective, and that the eternal conflict between the tangible world and the rational comprehension of it was present in Bosse’s mind. (AF) #28.3.65 Floyd, Juliet. On Saying What You Really Want to Say: Wittgenstein, Gödel,and the Trisection of the Angle, in Jaakko Hintikka, ed., From Dedekind to Godel¨ , Boston/Dordrecht: Kluwer, 1995, pp. 373–425. This paper attempts to show how Wittgenstein understood Gödel’s first incompleteness theorem “as a piece of mathematics.” Reportedly, Wittgenstein quite often compared Gödel’s theorem with the proof of the impossibility of trisect- ing an angle with straightedge and compass only. See the review by Hourya Sinaceur in Mathematical Reviews 2001c:03005. (JA) #28.3.66 Font, Josep Maria. On the Contributions of Helena Rasiowa to Mathematical Logic, Multi-Valued Logic 4 (1999), 159–179. This paper discusses algebraic logic, as conceived by Rasiowa (“infinistic methods”) in the years following World War II, especially in contrast to the Dutch school during the same period (“constructivity in mathematics”). See the review by Marcel Guillaume in Mathematical Reviews 2001c:03006. (JA) #28.3.67 Ford, Kenneth. See #28.3.212. Forinash, Kyle; Rumsey, William; and Lang, Chris. Galileo’s Language of Nature, Science and Education 9 (2000), 449–456. Undergraduate students do not always make a clear distinction between physics and mathematics. The case study of Galileo’s treatment of motion under uniform acceleration illustrates the differences and relationships between the two, and is accessible to students not specializing in mathematics. (JGF) #28.3.68 Fowler, David. Eudoxus: Parapegmata and Proportionality, in #28.3.193, pp. 33–48. A critical examination of the traditional claims that Eudoxus was mainly responsible for the ideas of proportionality in the fifth book of Euclid’s Elements. (GVB) #28.3.69 Fox, Robert, ed. Thomas Harriot: An Elizabethan Man of Science, Aldershot: Ashgate, 2000, hardbound, 330 pp., $84.95. A collection of essays on Thomas Harriot based on a series of lectures held at Oriel College, Oxford since 1990. Many of the articles are abstracted separately. (GVB) #28.3.70 Frege, Gottlob. Zwei Schriften zur Arithmetik [Two Papers on Arithmetic], Hildesheim: Georg Olms Verlag, 1999, 97 pp. This book contains reproductions of Frege’s two “mini-monographs,” Function und Begriff (1891) and Uber¨ die Zahlen des Herrn H. Schubert (1899), a “Nachwort” by Wolfgang Kienzler, and a brief commentary by Uwe Dathe. See the review by Kai F. Wehmeier in Mathematical Reviews 2001c:01044. (JA) #28.3.71 Fung, Chun-Ip. See #28.3.175 and #28.3.188. Furinghetti, Fulvia. See #28.3.55, #28.3.60, and #28.3.90. Galuzzi, Massimo. See #28.3.144. Gardiner, Anthony D. In Hilbert’s Shadow: Notes Toward a Redefinition of Introductory Group Theory, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical Association of America, 1995, pp. 253–265. Considers several approaches to motivating the abstractions of group theory in the classroom, rejecting an abstract internalist approach, yet not wholly espousing the alternatives. (GVB) #28.3.72 Gario, Paola. Guido Castelnuovo: Documents for a Biography, Historia Mathematica 28 (2001), 48–53. The archive of Castelnuovo (1865–1952), one of the most important mathematicians of the Italian school of algebraic geometry, contains a large scientific correspondence and 49 notebooks of his lectures for the last two years of the Italian mathematics degree. In due course it will be available at the Accademia dei Lincei in Rome. (JGF) #28.3.73 Gispert, Hélène. See #28.3.83, #28.3.175, and #28.3.188. Glas, Eduard. Model-Based Reasoning and Mathematical Discovery: The Case of Felix Klein, Studies in His- tory and Philosophy of Science 31A (1) (2000), 71–86. The author uses Felix Klein as an example of a creative 264 ABSTRACTS HMAT 28 mathematician who opposed the foundational view of the development of mathematics and favored a model-based approach. He surveys Klein’s work to support this hypothesis. See the review by Roger L. Cooke in Mathematical Reviews 2001b:01015. (TBC) #28.3.74 Glas, Eduard. The “Popperian Programme” and Mathematics. 1. The Fallibilist Logic of Mathematical Discov- ery, Studies in the History and Philosophy of Science 32 (2001), 119–137. In Proofs and Refutations (1976), Imre Lakatos not only applied Popper’s philosophy of science to a domain which Popper himself had not envisaged, but brought a much larger part of the Popperian corpus to bear on mathematics. As a test case for Popperian methodology, however, Lakatos’s work showed that some of Popper’s ideas needed to be revised and further refined. (JGF) #28.3.75 Glas, Eduard. See also #28.3.3, #28.3.150, and #28.3.174. Gluchoff, Alan; and Hartmann, Frederick. On a “Much Underestimated” Paper of Alexander, Archive for His- tory of Exact Sciences 55 (2000), 1–41. J. W. Alexander (1888–1971) is mainly remembered as a pioneering topologist who with Veblen and Lefshetz made Princeton a world leader in the new subject of algebraic topology. But his 1915 doctoral dissertation on univalent functions, whose informal and highly intuitive arguments may have led to its being underestimated, opened up new areas of investigation for researchers in geometric function theory. (JGF) #28.3.76 Golan, Jonathan. See #28.3.40. Golland, Louise; and Sigmund, Karl. Exact Thought in a Demented Time: Karl Menger and His Viennese Math- ematical Colloquium, Mathematical Intelligencer 22 (1) (2000), 34–45. A history of the famous Mathematisches Kolloquium at the University of Vienna in the period 1928–1936 whose participants included, in addition to Menger, Hans Hahn, Kurt Gödel,Alfred Tarski, Abraham Wald, John von Neumann, Franz Alt, Olga Taussky-Todd, and Oskar Morgenstern. (FA) #28.3.77 Gómez, Francisco Teixidó. See #28.3.78 and #28.3.172. Gottwald, Siegfried. See #28.3.116. Gould, Stephen Jay. Ciencia Versus Religion.´ Un Falso Conflicto [in Spanish], Barcelona: Cr´ıtica,2000, 232 pp. A Spanish translation of Gould’s Science vs. Religion. See the review by Francisco TeixidóGómez in LLULL 23 (2000), 504–507. (VA) #28.3.78 Goulding, Robert. Testimonia Humanitatis: The Early Lectures of Henry Savile, in #28.3.5, pp. 125–145. The Bodleian library has some four and a half years’ worth of Henry Savile’s astronomy lectures, delivered from 1570 onwards, attesting to an enormous amount of reading and study on Savile’s part. His notebooks of 1566–1569 indicate that for the history of the subject (though not ideologically) he was a close student of Peter Ramus. Savile introduced the mathematical sciences as historical disciplines and argued strongly, as a Platonist, against too utilitarian a conception of mathematics. (JGF) #28.3.79 Grattan-Guinness, Ivor. Daniel Bernoulli and the Varieties of Mechanics in the 18th Century, Nieuw Archief voor Wiskunde (5)1 (2000), 242–249. Daniel Bernoulli (1700–1782) has been rather underrated since his death. But he lived through major developments in mechanics and made major contributions to several principles and topics. His choice of problems and approach suggests a lateral thinker, taking up questions and making connections avoided or not noticed by others. (JGF) #28.3.80 Grattan-Guinness, Ivor. Response to Moore’s Letter, Notices of the American Mathematical Society 48 (2) (2001), 167. A response to Moore’s letter to the editor on the same page, including new information about a 24th problem of Hilbert. (KVM) #28.3.81 Greenstadt, John. Reminiscences on the Development of the Variational Approach to Davidon’s Variable-Metric Method, Mathematical Programming 87 (2) (2000), 265–280. Describes the mathematical context and motivation of attempts to improve upon Davidon’s method, since the mid-1960s. (GVB) #28.3.82 Grugnetti, Lucia; Rogers, Leo; Carvalho e Silva, Jaime; Daniel, Coralie; Coray, Daniel; de Guzmán,Miguel; Gispert, Hélène;Ismael, Abdulcarimo; Jones, Lesley; Menghini, Marta; Phillippou, George; Radford, Luis; HMAT 28 ABSTRACTS 265

Rottoli, Ernesto; Taimina, Daina; Troy, Wendy; and Vasco, Carlos. Philosophical, Multicultural and Interdisci- plinary Issues, in #28.3.59, pp. 39–62. Philosophically, mathematics is both within individual cultures and also outside any particular one. Students find their understanding of both mathematics and their other subjects enriched through the history of mathematics. Mathematical evolution comes from a sum of many contributions growing from different cultures. (JGF) #28.3.83 Grugnetti, Lucia. See also #28.3.9 and #28.3.55. Guillaume, Marcel. See #28.3.67. Gundlach, K.-B. See #28.3.161. Guo, Shi Rong. See #28.3.109. GutiérrezDávila,Antonio. Some Methods Used by Euler for Power Series Expansions [in Spanish], Epsilon 15 (3) (1999), 311–338. Attempts to recover some of the methods employed by Euler in his Introductio in analysin infinitorum to study some power series expansions, and compares with Cauchy’s work in his Cours d’Analyse. (GVB) #28.3.84 Harkleroad, Leon. See #28.3.8 and #28.3.132. Hartmann, Frederick. See #28.3.76. Heath-Brown, D. R. See #28.3.134. Hedberg, Lars Inge. On Maz’ya’s Work in Potential Theory and the Theory of Function Spaces, in Jürgen Rossman, Peter Takác,and GüntherWildenhain, eds., The Maz’ya Anniversary Collection, Basel: Birkhäuser, 1999, vol. 1, pp. 7–16. Presents the highlights of Maz’ya’s work in potential theory, function spaces, and partial differential operators. (GVB) #28.3.85 Heiede, Torkil. See #28.3.60, #28.3.175, and #28.3.188. Helfgott, Michel. Improved Teaching of the Calculus through the Use of Historical Materials, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical Association of America, 1995, pp. 135–144. Describes a historically oriented calculus course in- spired by Otto Toeplitz’s Calculus: A Genetic Approach, at the Universidad Nacional Mayor de San Marcos, Lima, Peru. (GVB) #28.3.86 Hodgson, Bernard. See #28.3.55. Horng, Wann-Sheng. See #28.3.188. Houzel, Christian. Bourbaki et AprèsBourbaki, in Travaux Mathematiques´ Fasc. XI, Luxembourg: Centre Universitaire de Luxembourg, 1999, pp. 23–32. The author evaluates the influence of the Bourbaki works, their mathematical innovations and their influence on education, society in general, and the style of French mathematical writing. See the review by Roger L. Cooke in Mathematical Reviews 2001b:01029. (TBC) #28.3.87 Høyrup, Jens. See #28.3.48. Husserl, E. Introduction a` la Logique et alaTh` eorie´ de la Connaisance: Cours (1906–1907) [Introduction to Logic and the Theory of Knowledge: Course (1906–1907)], trans. Laurent Jourmier, with preface by Jacques English, Paris: Librairie Philosophique J. Vrin, 1998, 440 pp., 300 F. A French translation of Husserl’s lectures of 1906–1907. See the review by Michael Otte in Mathematical Reviews 2001b:01030. (TBC) #28.3.88 Ismael, Abdulcarimo. See #28.3.83 and #28.3.175. Isoda, Masami. See #28.3.133 and #28.3.206. Jackson, Allyn. Interview with Raoul Bott, Notices of the American Mathematical Society 48 (4) (2001), 374–382. The interview explores some of Bott’s thought about mathematics and briefly, some of the colleagues he has had contact with. (KVM) #28.3.89 266 ABSTRACTS HMAT 28

Jahnke, Hans Niels; Arcavi, Abraham; Barbin, Evelyne; Bekken, Otto; Furinghetti, Fulvia; El Idrissi, Abdellah; Silva da Silva, Mary Circe; and Weeks, Chris. The Use of Original Sources in the Mathematics Classroom, in #28.3.59, pp. 291–328. The study of original sources is the most ambitious way in which history might be integrated into the teaching of mathematics, but also one of the most rewarding for students both at school and at teacher training institutions. (JGF) #28.3.90 Jahnke, Hans Niels. See also #28.3.175. Janiak, Andrew. Space, Atoms and Mathematical Divisibility in Newton, Studies in the History and Philosophy of Science 31 (2000), 203–230. Newton’s conception of space and his views on the atom are intimately linked, through a distinction between the mathematical division of an object, in thought, from the physical division of that object through some force. (JGF) #28.3.91 Jaworski, Piotr. See #28.3.159. Joel, J. S. See #28.3.46 and #28.3.164. Johnson, F. E. A. See #28.3.101. Johnson, George. Strange Beauty. Murray Gell-Mann and the Revolution in Twentieth-Century Physics,New York: Alfred A. Knopf, 1999, x+436 pp. This is a “sympathetic and insightful” discussion of Gell-Mann’s life that includes his conflicts with other scientists and gives as clear a description of the theoretical physics as is possible while avoiding the mathematics. See the review by Lawrence Sklar in Mathematical Reviews 2001c:01029. (JA) #28.3.92 Jones, Alexander. Pappus’ Notes to Euclid’s Optics, in #28.3.193, pp. 49–58. Addresses whether writers in ancient optics studied problems of perspective, concentrating on Euclid and (especially) Pappus. (GVB) #28.3.93 Jones, Lesley. See #28.3.55 and #28.3.83. Jones, Phillip S. The Role in the History of Mathematics of Algorithms and Analogies, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson and Victor Katz, eds., Learn from the Masters, Washington: Mathematical Association of America, 1995, pp. 13–23. History of mathematics helps students to reach the important understanding that mathematics proceeds in a number of nondeductive ways involving conjectures, analogies, algorithms, and other aspects of a human creative art. (JGF) #28.3.94 Kahane, Jean-Pierre. Hadamard et la Stabilitédu SystèmeSolaire [Hadamard and the Stability of the Solar Sys- tem], in Travaux Mathematiques´ Fasc. XI, Luxembourg: Centre Universitaire de Luxembourg, 1999, pp. 33–48. Aware of Poincaré’s work on celestial mechanics, Hadamard anticipated symbolic dynamics in 1898. This is a “mathematical essay” that “employs a reduced discrete model” to describe some of the development of symbolic dynamics and chaos. See the review by Florian N. Diacu in Mathematical Reviews 2001c:70001. (JA) #28.3.95 Kahane, Jean-Pierre. See also #28.3.55. Katz, Victor J. Historical Ideas in Teaching Linear Algebra, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical Association of Amer- ica, 1995, pp. 189–206. Covers “ancestral” forms of basic concepts in linear algebra such as row reduction, back substitution, matrix notation, inclusion of algebraic rules, and abstract vector spaces. (MP) #28.3.96 Katz, Victor J. Napier’s Logarithms Adapted for Today’s Classroom, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington: Mathematical Association of America, 1995, pp. 49–55. An adaptation of Napier’s own way of introducing logarithms can be used in today’s classrooms to lead bright precalculus students toward understanding logarithms. (JGF) #28.3.97 Katz, Victor J. See also #28.3.154 and #28.3.188. Kennedy, Edward S.; Kunitzsch, Paul; and Lorch, Richard P. The Melon-Shaped Astrolabe in Arabic Astronomy, Stuttgart: Franz Steiner Verlag,1999, viii+235 pp. Included are both the original Arabic and the English translation of all nine of the available texts describing projections “in which distances between points along the longitude circles of the sphere are preserved on the flat surface upon which the sphere is mapped.” For the modern reader, this HMAT 28 ABSTRACTS 267 is augmented by an extensive discussion and analysis. See the review by George Saliba in Mathematical Reviews 2001c:01011. (JA) #28.3.98

Kilic, Berna Eden. John Venn’s Evolutionary Logic of Chance, Studies in History and Philosophy of Science 30A (1999), 559–585. By rejecting “the distinction between individual and type” and inﬂuenced by Darwin’s On the Origin of Species (1859), “the author shows that John Venn’s The Logic of Chance (1866) was a reaction not only to the idea of statistical law but also to that of probability based on such laws.” See the review by Philip A. Beeley in Mathematical Reviews 2001c:01020. (JA) #28.3.99

Klein, Erwin. See #28.3.138.

Kleiner, Israel. The Teaching of Abstract Algebra: An Historical Perspective, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical Association of America, 1995, pp. 225–239. Describes a number of means by which the historical development of linear algebra can be used to motivate an otherwise challenging subject. (GVB) #28.3.100 Knobloch, Eberhard. See #28.3.180. Koroński,Jan. See #28.3.4. Koumaris, Panagiotis. See #28.3.177. Kronfellner, Manfred. See #28.3.9, #28.3.55, and #28.3.188. Krysinska, Marysa. See #28.3.188. Kuhnel, Wolfgang. See #28.3.171. Kuiper, N. H. A Short History of Triangulation and Related Matters, in I. M. James, ed., History of Topology, Amsterdam: North-Holland, 1999, pp. 491–502. This is an “incomplete” account of the development of triangulation beginning with the work of Poincaréand Brouwer; it was written in 1977 and has never been revised. See the review by F. E. A. Johnson in Mathematical Reviews 2001c:57001. (JA) #28.3.101 Kunitzsch, Paul. See #28.3.98 Kuznetsov, N. G. Maz’ya’s Works in the Linear Theory of Water Waves, in Jürgen Rossman, Peter Takác, and GüntherWildenhain, eds., The Maz’ya Anniversary Collection, Basel: Birkhäuser, 1999, vol. 1, pp. 17–34. This survey describes Maz’ya’s achievements concerning the unique solvability of two steady-state problems, and “ends with a description of asymptotic expansions of unsteady waves arising from brief and high-frequency disturbances.” (GVB) #28.3.102 Lakoma, Ewa. See #28.3.9, #28.3.55, and #28.3.188. Lang, Chris. See #28.3.68. Laurent, Roger. La Perspective et la Rupture d’une Tradition, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 231–243. Laurent investigates Desargues’s sources in perspective. As the Exemple de l’une des manieres` universelles touchant la pratique de la perspective (1636) was addressed to the artisan, it was devoid of demonstrations, even if, according to Desargues, only two propositions were necessary to prove his universal method. The author makes suggestions about these two propositions and also points out Desargues’s contributions by using color to improve perspective depth. The last paragraph is devoted to the 10 pages Aux theoriciens´ published by Bosse in 1647. (AF) #28.3.103 Le Goff, Jean-Pierre. Aux Sources de la Perspective Arguésienne,in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 244–248. Le Goffe adds some personal suggestions about Desargues’s sources in perspective; according to him, Desargues was the heir of the Flemish tradition in this particular field. (AF) #28.3.104 Le Moël,Michel. Jacques Curabelle et le Monde des Architects Parisiens, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 389–392. Le Moël’s contribution is devoted to Curabelle, the architect mainly known for his polemics against Desargues. New elements concerning his life and activity are 268 ABSTRACTS HMAT 28 the result of research in the Archives Nationales undertaken by the author, who also examines the evolution of the trade of an architect between the reign of Louis XIII and that of Louis XIV. (AF) #28.3.105

Lehmann, Joel P. Converging Concepts of Series: Learning from History, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical As- sociation of America, 1995, pp. 161–180. Proposes a model, involving successive levels of abstraction, for the development of mathematical concepts, illustrated by various historical examples of ﬁnite and inﬁnite series. (GVB) #28.3.106

Lehto, Markku. See #28.3.141.

Leiser, Eckart. ?C´omosaber? El Positivismo y sus Cr´ıticosen la Filosoﬁa de la Ciencia [How to Know? Posi- tivism and its Critics in Philosophy of Science], LLULL 23 (2000), 357–397. From author’s abstract: “The paper brings into focus positivism as a multifaceted phenomenon and at the same time persistent and recurrent throughout the history of science... The endeavor to come to a valuation of positivism turns out to be even more complicated when we take into account its role in mathematics.” (VA) #28.3.107

Leiser, Eckart. Hegemon´ıay Estad´ısticaen la Psicolog´ıaAlemana: Estudio Hist´oricode una Guerra Despiadada Contra la Heterodoxia [Hegemony and Statistics in German Psychology: Historical Study of a Merciless War Against Heterodoxy], LLULL 23 (2000), 675–686. From the author’s abstract: “The basic thesis of this paper is that the hegemony of contemporary mainstream psychology does not rest on any paradigm relative to a theory, but on a speciﬁc concept concerning the method, which materializes in a kind of worship revolving around statistics and its teaching.” (VA) #28.3.108

Liang, Zhao Jun. From the Elimination Method in the Jiu Zhang Suanshu (Arithmetic in Nine Sections)to Automated Theorem Proving [in Chinese], Journal of Central China Normal University. Natural Sciences 33 (2) (1999), 179–185. The author discusses the elimination method in the Jiu Zhang Suanshu (Arithmetic in Nine Sections) and points out the effect it had on automated theorem proving. See the review by Shi Rong Guo in Mathematical Reviews 2001b:01001. (TBC) #28.3.109 Lingard, David. See #28.3.175 and #28.3.188. Lit, Chi Kai. See #28.3.60 and #28.3.206. Lloyd, Howell A. “Famous in the Field of Number and Measure”: Robert Recorde, Renaissance Mathematician, The Welsh History Review 20 (2000), 254–282. Recorde suffered or benefited from the Tudor policy of anglicizing those Welsh people who could otherwise have contributed to Wales’s own development. He kept some Welsh ties and knew other scholars of Welsh heritage such as John Dee. Despite Recorde’s espousal of humanist educational principles, his own books were flawed by mistakes and inadequacies. (JGF) #28.3.110 Lorch, Richard P. See #28.3.98. Macbeath, A. Murray. Hurwitz Groups and Surfaces, in Silvio Levy, ed., The Eightfold Way, Cambridge: Cam- bridge Univ. Press, 1999, pp. 103–113. This paper discusses the motivations, through the work of Klein, Hurwitz, and Poincaré,for Hurwitz’s theorem, namely that a curve of genus g 2 can have no more than 84(g 1) birational self-transformations. See the review by Doru S¸tef˘anescuin Mathematical Reviews 2001c:14002. (JA) #28.3.111 Maffini, Achille. The Origins of Nonstandard Analysis: Four Stages in the World of Actual Infinity and In- finitesimals [in Italian], Quaderni di Ricerca in Didattica 8 (1999), 27–45. This account begins just prior to Leibniz, dealing with the dispute between Leibniz and Newton, Berkeley’s criticism and 19th-century responses, and subsequent developments, concluding with a short survey of 20th-century responses. (GVB) #28.3.112 Malcolm, Noel. The Publications of John Pell, F.R.S. (1611–1685): Some New Light and Some Old Confu- sions, Notes and Records of the Royal Society 54 (2000), 275–292. A complete annotated listing of the fourteen items by John Pell published in the 17th century, as well as a discussion of his nine non-existent publications. (JGF) #28.3.113 Maltese, Corrado. Ellissi ed Ellissografi. “Querelles” Semi-Scientifiche e Applicazioni Pratiche Negli Anni di Desargues, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, HMAT 28 ABSTRACTS 269 pp. 101–109. Maltese discusses the recovery of knowledge about conic sections in western countries starting from the first Latin translations of the perspective works of the Arabian tradition, in their turn based on the Greek tradition, to the beginning of the 17th century. (AF) #28.3.114 Mancini Proia, Lina; and Menghini, Marta. Conic Sections in the Sky and on the Earth, Educational Studies in Mathematics 15 (1984), 191–210. An experiment carried out with high school students on the historical development of conic sections and the interactions in the baroque period with art, astronomy and mathematics. (JGF) #28.3.115 Marion, Mathieu. Wittgenstein and Ramsey on Identity, in Jaakko Hintikka, ed., From Dedekind to Godel¨ , Dor- drecht: Kluwer, 1995, pp. 343–371. The author considers a debate between Ludwig Wittgenstein and F. P. Ramsey. His premise is that in order to understand the differences in their positions, it is important to have in mind the possibilities offered by a nonstandard reading of higher order quantifications. See the review by Siegfried Gottwald in Mathematical Reviews 2001b:03003. (TBC) #28.3.116 Mart´ınezGarc´ıa,Mar´ıa Angeles.´ Las Matematicas´ en los Planes de Estudio de los Ingenieros Civiles en Espana˜ en el Siglo XIX [Mathematics in Civil Engineering Curricula in 19th Century Spain], University of Saragossa, 2000. A doctoral dissertation written at the University of Saragossa. (VA) #28.3.117 Martzloff, Jean-Claude. Le Qizheng Tuibu de Bei Lin (vers 1477) [The Qizheng Tuibu of Bei Lin (ca. 1477)], in Histoire des Mathematiques´ Arabes, Algiers: Association Algérienned’Histoire des Mathématiques,1998, vol. 2, pp. 227–237. The Qizheng Tuibu (Astronomical Calculations of Seven Governors, i.e., the sun, the moon, and five planets) was compiled ca. A.D. 1477. The author reports that this is the most complete of the extant treatises on Islamic astronomy written in Chinese and asks questions about its origins. See the review by Alexei K. Volkov in Mathematical Reviews 2001b:01002. (TBC) #28.3.118 Masuda, Mikiya. See #28.3.142. Mazotti, Massimo. For Science and for the Pope–King: Writing the History of the Exact Sciences in Nineteenth- Century Rome, British Journal for the History of Science 33 (2000), 257–282. Boncompagni’s Bullettino (1868– 1887) was the first journal entirely devoted to the history of mathematics. Far from being merely the outcome of the eccentric personality of its editor, it reflected at the level of historiography of science the struggle of the official Roman Catholic culture against the growing secularization of knowledge and society. (JGF) #28.3.119 Mejlbo, Lars. Historical Thoughts on Infinite Numbers, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Jo- hansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical Association of America, 1995, pp. 181–187. Discusses a portion of the author’s course on the concept of infinity in mathematics, especially episodes involving Euler, Bolzano, and Cantor. (GVB) #28.3.120 Mendell, Henry. The Trouble with Eudoxus, in #28.3.193, pp. 59–138. An extensive study of the role played by Eudoxus’s theory of homocentric spheres in Greek astronomy. (GVB) #28.3.121 Mendell, Henry. See also #28.3.193. Mendelson, E. See #28.3.22 and #28.3.32. Menghini, Marta. See #28.3.9, #28.3.83, and #28.3.115. Mesnard, Jean. Desargues et Pascal, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 87–99. Mesnard shows that the relationship between Desargues and Pascal was deeper than it appears: the same concrete mind, a strong creative imagination, and the idea of the universal value of the mathematical experience were at the basis of this relation. Also the mature Pascal, the philosopher of the human spirit, felt the influence of the master. (AF) #28.3.122 Meyer, Burnett. See #28.3.148 and #28.3.182. Michalowicz, Karen Dee; Daniel, Coralie; FitzSimons, Gail; Ponza, Mar´ıaVictoria; and Troy, Wendy. History in Support of Diverse Educational Requirements: Opportunities for Change, in #28.3.59, pp. 171–200. Using historical resources, teachers are better able to support the mathematical learning of students in diverse situations: returning to education, in under-resourced schools and communities, with educational challenges, and mathematically gifted. (JGF) #28.3.123 270 ABSTRACTS HMAT 28

Michalowicz, Karen Dee. See also #28.3.133. Michel-Pajus, Anne. See #28.3.55. Migliari, Riccardo. See #28.3.51. Miller, Richard K. VolterraIntegral Equations at Wisconsin, in G. Corduneanu and I. W. Sandberg, eds., Volterra Equations and Applications, Amsterdam: Gordon & Breach, 2000, pp. 15–26. Contains personal recollections of work at the Wisconsin school in the late 1950s and the 1960s; “the initial motivation was to understand certain nuclear reactor models but the ultimate goal was to develop a general qualitative theory of Volterra integral equations.” (GVB) #28.3.124 Millman, Richard. See #28.3.55. Milnor, John, Classification of n 1-Connected 2n-Dimensional Manifolds and the Discovery of Exotic Spheres, in Sylvain Cappell, Andrew Ranicki, and Jonathan Rosenberg, eds., Surveys on Surgery Theory, Princeton, NJ: Princeton Univ. Press, 2000, vol. I, pp. 25–30. “A short history of one of the most amazing discoveries of modern topology, namely the discovery of exotic spheres.” This paper also describes how the author was led to devise, in the 1950s, for the first time, a 7-dimensional exotic sphere. See the review by Wieslaw J. Oledzki in Mathematical Reviews 2001c:57002. (JA) #28.3.125 Moore, Gregory H. Correction to the History of Hilbert’s Problems, Notices of the American Mathematical Society 48 (2) (2001), 167. A brief letter to the editor correcting an impression given the reader regarding Peano and Padoa in Ivor Grattan-Guinness’s article “A Sideways Look at Hilbert’s Twenty-Three Problems of 1900.” (KVM) #28.3.126 Moravcsik, Julius M. Plato on Numbers and Mathematics, in #28.3.193, pp. 177–196. Examines the relation between Plato’s concept of number and the Theory of Forms, showing that Plato’s distinctions do not easily translate to modern foundational questions. (GVB) #28.3.127 Moravcsik, Julius M. See also #28.3.193. Moree, Pieter; and Cazaran, Jilyana. On a Claim of Ramanujan in His First Letter to Hardy, Expositiones Math- ematicae 17 (1999), 289–311. In Part I, this paper is “a broad and comprehensive historical survey” of results relating Ramanujan’s claim concerning the number of either squares or sums of squares in a given interval. In Part II, the authors provide improvements of some of these results and several connections to other parts of number theory. See the review by S. L. Segal in Mathematical Reviews 2001c:11103. (JA) #28.3.128 Movchan, A. B. Contributions of V. G. Maz’ya to Analysis of Singularly Perturbed Boundary Value Prob- lems, in Jürgen Rossman, Peter Takác,and GüntherWildenhain, eds., The Maz’ya Anniversary Collection, Basel: Birkhäuser, 1999, vol. 1, pp. 201–212. Reviews the contributions made by Maz’ya and his colleagues to the development of the method of compound asymptotic expansions. (GVB) #28.3.129 Mueller, Ian. Plato’s Geometrical Chemistry and Its Exegesis in Antiquity, in #28.3.193, pp. 159–176. What Mueller calls “geometrical chemistry” in Plato’s Timaeus has been thought of as a predecessor to mathematical physics. Mueller proposes that we view it instead “as part of a metaphysical conception of the physical world as dependent on a transcendental world through the intermediary of mathematics.” (GVB) #28.3.130 Mueller, William. Reform Now, before It’s Too Late! American Mathematical Monthly 108 (2001), 126–143. Today’s clamor for reform of mathematical teaching in the U.S. may usefully be seen against the very similar debates in the 1890s, about teaching and about the nature of mathematics itself, recorded in Cajori’s Teaching and History of Mathematics in the United States (1890) and elsewhere. (JGF) #28.3.131 Murawski, Roman. The Contribution of Polish Logicians to Recursion Theory, in Katarzyna Kijania-Placek and Jan Woleński, The Lvov–Warsaw School and Contemporary Philosophy, Dordrecht: Kluwer, 1998, pp. 265–282. “This paper provides an overview of mid-20th-century research in recursion theory done by Polish mathematicians.” See the review by Leon Harkleroad in Mathematical Reviews 2001c:03007. (JA) #28.3.132 Nagaoka, Ryosuke; Barrow-Green, June; Bartolini Bussi, Maria G.; Isoda, Masami; van Maanen, Jan; Michalow- icz, Karen Dee; Ponza, Mar´ıaVictoria; and Van Brummelen, Glen R. Non-standard Media and Other Resources, HMAT 28 ABSTRACTS 271 in #28.3.59, pp. 329–370. The integration of history is not confined to traditional teaching delivery methods, but can often be better achieved through a variety of media which add to the resources available for learner and teacher. (JGF) #28.3.133 Nagaoka, Ryosuke. See also #28.3.55. Narkiewicz, Wladyslaw. The Development of Prime Number Theory. From Euclid to Hardy and Littlewood, Berlin: Springer-Verlag, 2000, xii+448 pp. This is a textbook on the development of the theory of prime numbers up to the first decade of the 20th century. “Issues of computational interest are largely excluded.” It has over 3000 entries in the bibliography! See the review by D. R. Heath-Brown in Mathematical Reviews 2001c:11098. (JA) #28.3.134

Nauenberg, Michael. See #28.3.44.

Navarro de Zuvillaga, Javier. L’Influence des Traitésde Desargues dans les TraitésEspagnols, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 313–328. Navarro de Zuvillaga studies the influence of Desargues’s work on the Spanish authors in perspective, stereotomy, and gnomonics. He establishes that, as regards perspective and stereotomy, there exists a thread which leads to Desargues, even if it is a feeble and indirect thread; this influence is present in Thomas Vincente Tosca’s work (1713) through Deschales and in Benito Bails’s work (1779) through Frézierand La Hire. As regards gnomonics, the Spanish had a strong tradition of such studies, starting from the epoch of King Alphonsus X, and no reference to Desargues was found. (AF) #28.3.135

Neal, Katherine. The Rhetoric of Utility: Avoiding Occult Associations for Mathematics through Proﬁtability and Pleasure, History of Science 37 (1999), 151–178. The rhetorical strategies pursued by English mathematical practitioners and textbook writers in the period 1550–1650 attempted to dissociate mathematics from its danger- ous or magical associations through discussions of its usefulness, expressed in self-consciously plain English. (JGF) #28.3.136 Netz, Reviel. Why Did Greek Mathematicians Publish Their Analyses? In #28.3.193, pp. 139–157. Argues that analyses were a tool for the presentation of results, rather than (as commonly understood) a heuristic tool for discovery. (GVB) #28.3.137 Nicola, PierCarlo. Mainstream Mathematical Economics in the 20th Century, Berlin: Springer-Verlag, 2000, xx+521 pp. This book combines mathematical rigor with a chronological history of economics using “general equilibrium theory as the unifying element.” See the review by Erwin Klein in Mathematical Reviews 2001c:91002. (JA) #28.3.138 Niss, Mogens. See #28.3.55 and #28.3.206. Nivison, David S. The Chronology of the Three Dynasties, in #28.3.193, pp. 203–227. Uses data from Chinese astronomy to shed light on the chronology of the three dynasties in ancient China. (GVB) #28.3.139 Nobre, Sergio. See #28.3.175. Norton, John D. “Nature is the Realisation of the Simplest Conceivable Mathematical Ideas”; Einstein and the Canon of Mathematical Simplicity, Studies in the History and Philosophy of Modern Physics 31 (2000), 135–170. Einstein did not develop his later Platonism, believing that true laws of nature were discovered by seeking those with the simplest mathematical formulation, from a priori reasoning or aesthetic considerations; he learned the canon of mathematical simplicity from his own experiences in discovering general relativity. (JGF) #28.3.140 Novikov, I. D. Cosmology Then and Now, Acta Physica Polonica B 30 (10) (1999), 2989–3001. A discussion of Infeld’s cosmology 50 years ago and the development of cosmology since. See the review by Markku Lehto in Mathematical Reviews 2001b:83113. (TBC) #28.3.141 Novikov, S. P. Surgery in the 1960s, in Sylvain Cappell, Andrew Ranicki, and Jonathan Rosenberg, eds., Surveys on Surgery Theory, Princeton, NJ: Princeton Univ. Press, 2000, vol. I, pp. 31–39. “Reminiscences of the author” describing his early motivations in studying surgery theory, including “the so-called higher signature (or Novikov) 272 ABSTRACTS HMAT 28 conjecture and Hermitian K -theory.” See the review by Mikiya Masuda in Mathematical Reviews 2001c:57003. (JA) #28.3.142

Nubiola, Jaime. See #28.3.63.

Oledski, Wieslaw J. See #28.3.125.

Otte, Michael. See #28.3.88.

Oudet, Jean-Fran¸cois. Le Style de Desargues: L’Observation AssociéeàlaThéorie pour Placer le Style d’une Cadran Solaire, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 331–339. Oudet analyses Desargues’s method of setting the sundial’s style which consists in determining the axis of a cone of revolution, noting three of its generatrices. The author also discusses Curabelle’s criticism as regards the accuracy and the exactness of Desargues’s method. (AF) #28.3.143

Palladino, Franco. Useful Quantities for Reasoning and Research. Differentials and Summation in a Debate among Nieuwentijt, Leibniz and Hermann [in Italian], in Marco Panza and Clara Silvia Roero, eds., Geometry, Fluxions and Differentials [in Italian], Naples: La Citt`adel Sole, 1995, pp. 397–441. The author gives a careful analysis of Jacob Hermann’s Responsio to Nieuwentijt’s Considerationes secundae circa calculi differentialis principia (1696). The author argues that Hermann’s work is a collective work of the Leibnizians. See the review by Massimo Galuzzi in Mathematical Reviews 2001b:01007. (TBC) #28.3.144

Papp, F. J. See #28.3.205.

Peckhaus, Volker. Hugh MacColl and the German Algebra of Logic, Nordic Journal of Philosophical Logic 3 (1–2) (1998), 17–34. The German algebraist of logic, Ernst Schroder, considered Hugh MacColl to be one of his most important precursors; MacColl’s inﬂuence on some of Schroder’s work is considered. (GVB) #28.3.145

Peckhaus, Volker. See also #28.3.208. Phillippou, George. See #28.3.83 and #28.3.175. Picolet, Guy. Documents InéditsConcernant Desargues, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 125–153. Picolet publishes 10 of the 26 documents concerning Desargues and his family which were recently found in the Parisian Archives. These documents show the financial circum- stances of the family. The author makes the suggestion that Desargues might have been presented at court and that his career could have suffered the consequence of the financial judicial events in which he was involved. (AF) #28.3.146 Picon, Antoine. Girard Desargues Ingénieur, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 413–422. Picon provides evidence of Desargues as an engineer, whose main contribution is the water raising machine, where he combined geometrical science and mechanical ingenuity to solve the problem of friction; Philippe de La Hire’s research on the epicycloid originated with the same problem and, according to the author, Desargues can be considered his main inspiration. (AF) #28.3.147 Pier, Jean-Paul. L’Analyse Mathématique:Un ConceptaG´ ` eométrieVariable et àCaractèresynthétique[Math- ematical Analysis: A Concept with Variable Geometry and Synthetic Character], in Travaux Mathematiques´ Fasc. XI, Luxembourg: Centre Universitaire de Luxembourg, 1999, pp. 139–148. “The author examines the changing meanings of ‘analysis’ and ‘algebra’ in various periods of history.” See the review by Burnett Meyer in Mathematical Reviews 2001c:01007. (JA) #28.3.148 Pinault, Madeleine. L’Etude´ de la Perspective dans l’Histoire de Saint Etienne de Laurent de la Hyre, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 249–262. Pinault studies the pictorial cycle which Laurent de la Hyre carried out for the Parisian church of Saint Etienne-du-Mont; he shows how, from this work of art, the perspective study of the artist appears with emphasis. The unison of this pictorial cycle follows from the architecture and the executive technique, but also from the perspective concept under the drawings. (AF) #28.3.149 Pitombeira de Carvalho, João. See #28.3.55, #28.3.175, #28.3.188, and #28.3.206. HMAT 28 ABSTRACTS 273

Poincaré,Henri. Een Nacht Vol Opwinding: Een Keuze uit de Filosofische Essays [A Night Full of Tension: A Selection from the Philosophical Essays] [in Dutch], trans. from the French by Dieuwke Eringa and with an introduction by Ferdinand Verhulst, Utrecht: Epsilon Uitgaven, 1998, ii+152 pp., BF 550. A biographical sketch of Poincaré’s life and translations into Dutch of nine of Poincaré’s philosophical and popular essays. See the review by Eduard Glas in Mathematical Reviews 2001c:01033. (JA) #28.3.150 Ponza, Mar´ıaVictoria. See #28.3.123 and #28.3.133. Potjekhinn, A. F. On the Evolution of the Relativity Principle from Copernicus to Einstein, Hadronic Journal Supplement 14 (3) (1999), 297–313. The author asserts that, using no mathematical symbols, it becomes necessary to revise the physical contents of the basic principles of Einstein’s special and general relativity theories. See the review by Abraham A. Ungar in Mathematical Reviews 2001b:83006. (TBC) #28.3.151 Pourciau, Bruce. Intuitionism as a (Failed) Kuhnian Revolution in Mathematics, Studies in the History and Philosophy of Science 31 (2000), 297–329. Kuhnian revolutions in mathematics are logically possible, actually possible, and historically possible. Intuitionism is an example, in the sense that a shift from a classical conception of mathematics to an intuitionist one would be incommensurable (that is, some classical statements would become unintelligible). (JGF) #28.3.152 Pourciau, Bruce. Newton and the Notion of Limit, Historia Mathematica 28 (2001), 18–30. From certain proofs in the Principia it is apparent that Newton, not Cauchy, was first to present an epsilon argument, and that his understanding of limits was clearer than is commonly thought. (JGF) #28.3.153 Radford, Luis; Bartolini Bussi, Maria G.; Bekken, Otto; Boero, Paolo; Dorier, Jean-Luc; Katz, Victor; Rogers, Leo; Sierpinska, Anna; and Vasco, Carlos. Historical Formation and Student Understanding of Mathematics, in #28.3.59, pp. 143–170. The use of history of mathematics in the teaching and learning of mathematics requires didactical reflection. A crucial area to explore and analyze is the relation between how students achieve understanding in mathematics and the historical construction of mathematical thinking. (JGF) #28.3.154 Radford, Luis. See also #28.3.83. Rahman, Shahid. Ways of Understanding Hugh MacColl’s Concept of Symbolic Existence, Nordic Journal of Philosophical Logic 3 (1–2) (1998), 35–58. Offers an interpretation of MacColl’s proposals on the role of ontology in logics: “in an argumentation, it sometimes makes sense to restrict the use and introduction of singular terms in the context of quantification to a formal use of those terms. That is, the Proponent is allowed to use a constant iff this constant has been explicitly conceded by the Opponent.” (GVB) #28.3.155 Rashed, Roshdi. Oeuvres Philosophiques et Scientifiques d’al-Kindi. Vol I: L’Optique et la Catoptrique, Leiden: E. J. Brill, 1997, xiv+776 pp. This volume contains an introduction to all extant optical works by al-Kindi (ca. A.D. 801–866). See the very detailed review by Julio Samsó-Moya in Mathematical Reviews 2001b:01004. (TBC) #28.3.156 Read, Stephen. Hugh MacColl and the Algebra of Strict Implication, Nordic Journal of Philosophical Logic 3 (1–2) (1998), 59–83. This analysis of MacColl’s methods shows that “MacColl’s model logic is in fact the logic T introduced by Feys and von Wright many decades later, the smallest normal epistemic modal logic.” (GVB) #28.3.157 Reich, Karen. Who Needs Vectors? in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical Association of America, 1995, pp. 215–224. Gives a brief history of vectors with a concentration on the different symbols and processes used by various figures throughout the development of vector algebra. (MG) #28.3.158 Reitberger, Heinrich. The Turbulent Fifties in Resolution of Singularities, in H. Hauser, J. Lipman, F. Oort, and A. Quirós,eds., Resolution of Singularities, Basel: Birkhäuser, 2000, pp. 533–537. A description of attempts in the late 1940s and 1950s to “construct” the resolution of singular varieties. See the review by Piotr Jaworski in Mathematical Reviews 2001c:14003. (JA) #28.3.159 Rickey, V. Frederick. My Favorite Ways of Using History in Teaching Calculus, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical 274 ABSTRACTS HMAT 28

Association of America, 1995, pp. 123–134. Argues that history should interact closely with the mathematical topics in the classroom, and provides three examples, entitled “Perrault and the Tractrix,” “Suspension Bridges,” and “Cauchy’s Famous Wrong Theorem.” (GVB) #28.3.160 Robson, Eleanor. Mesopotamian Mathematics, 2100–1600 B.C. New York: Oxford Univ. Press, 1999, xvi+334 pp. This book begins with a thorough study of the 12 Old Babylonian coefficient lists and it also presents copies and transliterations of other texts, many of which have only been partly investigated in past studies. These examples lead to “a discussion of the role of mathematics in administration and education in Old Babylonian times.” See the review by K.-B. Gundlach in Mathematical Reviews 2001c:01008. (JA) #28.3.161 Rodriguez, Michel. See #28.3.188 and #28.3.206. Roero, Clara Silvia. The Legacy of the Geometric Tradition in Leibniz’s Infinitesimal Calculus [in Italian], in Marco Panza and Clara Silvia Roero, eds., Geometry, Fluxions and Differentials [in Italian], Naples: La Cittàdel Sole, 1995, pp. 353–395. The author studies the geometrical aspect of the differential calculus in the works of Leibniz and other geometers of his time. See the review by Bernard Rouxel in Mathematical Reviews 2001b:01008. (TBC) #28.3.162 Rogers, Leo. See #28.3.83 and #28.3.154. Rommevaux, S.; Djebbar, Ahmed; and Vitrac, B. Remarques sur l’Histoire du Texte des El´ ements´ d’Euclide, Archive for History of Exact Sciences 55 (2001), 221–295. Euclid’s Elements has the richest textual tradition of all ancient Greek mathematics, not least because of the range of ancient and mediaeval versions and languages: Greek, Latin, Arabic, Syriac, Persian, Armenian, Hebrew...Heiberg’s critical edition of the Greek text (1883–1888), challenged at the time by Klamroth, needs far more careful location in the light of work on the rich Arabic textual tradition. (JGF) #28.3.163 Rosenfeld, Boris A.; and Youschkevitch, Adolf P. Geometry, in Roshdi Rashed and RégisMorelon, eds., En- cyclopedia of the History of Arabic Science, London: Routledge, 1996, vol. 2, pp. 447–494. A nice survey that indicates the breadth of medieval Arabic contributions to geometry and how those contributions fit between the geometrical investigations of Greek antiquity and those of the European Middle Ages and Renaissance. However, there is no bibliography. See the review by J. S. Joel in Mathematical Reviews 2001b:01005. (TBC) #28.3.164 Rottoli, Ernesto. See #28.3.83. Rouxel, Bernard. See #28.3.162. Rowe, David E. Episodes in the Berlin–GöttingenRivalry, 1870–1930, Mathematical Intelligencer 22 (1) (2000), 60–69. A detailed description of the mathematical scenes at the Universities of Berlin and Göttingenleading up to the supremacy of Göttingenover Berlin after 1892. Felix Klein’s pivotal role is emphasized. (FA) #28.3.165 Ruffner, J. A. Newton’s Propositions on Comets: Steps in Transition, 1681–84, Archive for History of Exact Sciences 54 (2000), 259–277. A collection of untitled propositions concerning comets drastically revise the po- sition Newton had held versus Flamsteed in 1681,“and may signal his adoption of a single comet solution for the appearances of 1680–81.” (GVB) #28.3.166 Ruiz, Angel;´ and Barrantes, Hugo. La Reforma Liberal y las Matemáticasen la Costa Rica del Siglo XIX [The Liberal Reform and Mathematics in 19th-Century Costa Rica], LLULL 23 (2000), 145–171. The 1880s educational reform in Costa Rica had consequences for the teaching of mathematics, which are studied in this paper. (VA) #28.3.167 Rumsey, William. See #28.3.68. Saint Aubin, Jean-Paul. Les Enjeux Architecturaux de la Didactique Stéréotomiquede Desargues, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 363–370. Saint Aubin emphasizes the great number of treatises devoted to stereotomy and the large number of architectural buildings with stairs on freestone vaults during the 17th century. According to him this phenomenon looks like a reaction by a guild which fears losing its prerogative and wishes to prove its practical ability. He also compares other contemporaneous authors’ ideas, M. Jousse’s, F. Derand’s, and A. Bosse’s, the latter being Desargues’s scholar par excellence. (AF) #28.3.168 HMAT 28 ABSTRACTS 275

Sakarovitch, Joël. Le Fascicule de Stéréotomie:Entre Savoir et Métiers,la Fonction de l’Architecte, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 347–362. Sakarovitch’s contribution concerns Desargues’s short tract on stonecutting (1640) where only one architectural object is studied, the “descente biaise dans un mur en talus,” where the term “descente” means a kind of vault whose geometrical definition is a cylinder with a nonhorizontal axis. Sakarovitch explains the character of this tract, its methods, and why it makes difficult reading. The last paragraph is devoted to the polemics between Curabelle and Desargues regarding not just the technical subject of the tract, but also how to verify the legitimacy of a prescribed method. (AF) #28.3.169

Saladino Garcia, Alberto. Mathematics in Latin American Newspapers during the Enlightenment [in Spanish], Quipu 10 (1993), 223–242. “The author details the mathematical contents of twenty Latin American periodicals published in the latter half of the eighteenth century.” See the review by Michael A. B. Deakin in Mathematical Reviews 2001c:01016. (JA) #28.3.170

Saliba, George. See #28.3.98.

Samelson, Hans. Kronecker and Topology, Rendiconti del Circolo Mathematico di Palermo. Serie II Supple- mento 61 (1999), 49–57. “The almost forgotten contributions of L. Kronecker and W. Dyck are illustrated by various speciﬁc results on the Kronecker characteristic, the degree of vector ﬁelds, indices of singularities and related topics.” See the review by Wolfgang Kuhnel in Mathematical Reviews 2001c:57004. (JA) #28.3.171

Sams´o-Moya, Julio. See #28.3.156 and #28.3.210.

Sánchez Ron, JoséManuel. Cincel, Martillo y Piedra. Historia de la Ciencia en España(Siglos XIX y XX) [Chisel, Hammer, and Stone. The History of Science in Spain (19th and 20th Centuries)], Madrid: Taurus, 1999, 468 pp. This recent history of Spanish science is reviewed by Francisco TeixidóGómez in LLULL 23 (2000), 217–220. (VA) #28.3.172

Santos del Cerro, Jésus. Una Teor´ıaSobre la Creacióndel Concepto Moderno de Probabilidad: Aportaciones Españolas[A Theory on the Establishment of the Modern Concept of Probability: Spanish Contributions], LLULL 23 (2000), 431–450. The author contends that probabilistic thinking stems from Aristotle, passing through philosophical and theological considerations, based mostly on games of chance, of Carneades, Cicero, Augustine, Thomas Aquinas, and Spanish theologians (Concina, Medina, Vásquez),whose moral probabilism was absorbed into the theory, up to Pascal and Fermat. (VA) #28.3.173 Schneider, Maggy. See #28.3.188. Schreiber, Peter. Uber¨ Beziehungen zwischen Heinrich Scholz und Polnischen Logikern [On Relations Between Heinrich Scholz and Polish Logicians], History and Philosophy of Logic 20 (1999), 97–109. Based on recently discovered letters and other documents, relations between Heinrich Scholz (1884–1956) and Jan Lukasiewicz (1878–1956), especially during 1938 to 1950, are discussed. See the review by Eduard Glas in Mathematical Reviews 2001c:03008. (JA) #28.3.174 Schubring, Gert; Cousquer, Eliane;´ Fung, Chun-Ip; El Idrissi, Abdellah; Gispert, Hélène;Heiede, Torkil; Ismael, Abdulcarimo; Jahnke, Hans Niels; Lingard, David; Nobre, Sergio; Phillippou, George; Pitombeira de Carvalho, João;and Weeks, Chris. History of Mathematics for Trainee Teachers, in #28.3.59, pp. 91–142. The move- ment to integrate mathematics history into the training of future teachers, and into the in-service training of current teachers, has been a theme of international concern over much of the past century. Examples of current practice from many countries, for training teachers at all levels, enable us to begin to learn lessons and press ahead both with adopting good practices and also putting continued research effort into assessing the effects. (JGF) #28.3.175 Segal, S. L. See #28.3.128. Seltman, Muriel. Harriot’s Algebra: Reputation and Reality, in #28.3.70, pp. 153–185. Comparing Harriot’s algebra, from his unpublished papers, with the form in which it appears in the posthumously printed Ars analyticae praxis of 1631, shows that the latter was a very inadequate and distorted account of Harriot’s achievements in developing the theory of equations. (JGF) #28.3.176 276 ABSTRACTS HMAT 28

Seroglou, Fanny; and Koumaris, Panagiotis. The Contribution of the History of Physics in Physics Education: A Review, Science and Education 10 (2001), 153–172. A classiﬁcation and comparative study of some 60 proposals about the contribution of the history of physics to physics education that have been designed and/or carried out as part of either research or curriculum development during the 20th century. A chart summarizes and locates the proposals on a timeline from 1893 to the present day. (JGF) #28.3.177

Shea, William R. See #28.3.25.

Shenitzer, Abe. A Topics Course in Mathematics, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical Association of America, 1995, pp. 283–295. Describes and gives bibliographies for eight historical topics within the author’s course, which is intended to convey the meaningfulness and profundity of mathematics, as well as convincing the participants that “the evolution of some of its ideas is an exciting chapter of intellectual history.” (GVB) #28.3.178 Sherman, William H. Putting the British Seas on the Map: John Dee’s Imperial Cartography, Cartographica 35 (3–4) (1998), 1–10. Although now obscured by the legacy of later 16th-century explorers such as Drake and Raleigh, Dee’s cartographic output brought together advanced science and sophisticated rhetoric and played an important role in the genesis of the British Empire. (JGF) #28.3.179 Shiryaev, A. N. On the History of the Founding of the Russian Academy of Sciences and on the First Publications on Probability Theory in Russian Editions [in Russian], Teoriya VeroyatnosteYi ee Primeneniya 44 (2) (1999), 241–248; English translation in Theory of Probability and its Applications 44 (2) (2000), 225–230. The author sketches the foundation and early history of the Imperial St. Petersburg Academy of Sciences, its structure, its first members, and its journals. See the review by Eberhard Knobloch in Mathematical Reviews 2001b:01011. (TBC) #28.3.180 Sibbett, Trevor. Early Insurance in and around the Royal Exchange, in #28.3.5, pp. 62–76. Insurance and the money it generates made an important contribution to the early years of Gresham College (and still does, since Gresham College is funded from rents on the Royal Exchange building). John Graunt, the first student of mortality tables, lived in a lane near Lombard Street, and William Petty, the developer of political arithmetic, was third Gresham professor of music. (JGF) #28.3.181 Sierksma, Gerard; and Sierksma, Wybe. The Great Leap to the Infinitely Small. Johann Bernoulli: Mathemati- cian and Philosopher, Annals of Science 56 (1999), 433–449. While he was in Groningen (1695–1715), Johann Bernoulli expounded his ideas about the infinitely large and the infinitely small in mathematics; included is a discussion of his correspondence with Leibniz about infinitesimals in the latter’s calculus. See the review by Burnett Meyer in Mathematical Reviews 2001c:01017. (JA) #28.3.182 Sierksma, Wybe. See #28.3.182. Sierpinska, Anna. See #28.3.154. Sigmund, Karl. See #28.3.77. Silva da Silva, Mary Circe. See #28.3.55 and #28.3.90. Silva, ClóvisPereira da. Manoel Amoroso Costa: O Continuador da Obra Matematica de Otto de Alencar Silva [Manoel Amoroso Costa: The Continuer of Otto Alencar Silva’s Mathematical Work], LLULL 23 (2000), 91–101. The author analyzes the scientific contribution of Manoel Amoroso Costa (1885–1928) to the development of university mathematics teaching in Brazil. (VA) #28.3.183 Sinaceur, Hourya. See #28.3.66. Sinisgalli, R.; and Vastola,S. Desargues e la Gnomonica, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 341–346. Sinisgalli and Vastola work out an historical research on gnomonics methods before Desargues’s epoch. They conclude that Desargues was influenced by Clavio, even if his methods show peculiar features. By means of models of sundials and by following Desargues’s instructions, the authors prove the agreement with the theory and so the validity of Desargues’s gnomonics. (AF) #28.3.184 HMAT 28 ABSTRACTS 277

Siu, Man-Keung. Concept of Function—Its History and Teaching, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington: Mathematical Association of Amer- ica, 1995, pp. 105–121. Felix Klein in the late 19th century advocated using the function conception in teaching as a unifying idea. The historical development of the concept can be incorporated into teaching at various levels from secondary school to university. (JGF) #28.3.185 Siu, Man-Keung. Euler and Heuristic Reasoning, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical Association of America, 1995, pp. 145–160. Uses examples from Euler’s writings to bring out the intuitions behind a number of his discoveries, with obvious pedagogical benefits. (GVB) #28.3.186 Siu, Man-Keung. Mathematical Thinking and the History of Mathematics, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington, DC: Mathematical As- sociation of America, 1995, pp. 279–282. Describes the goals and various aspects of the author’s course on the “Development of Mathematical Ideas” at the University of Hong Kong, which uses various excerpts from primary source material. (GVB) #28.3.187 Siu, Man-Keung; Bagni, Giorgio T.; Correia de Sá,Carlos; FitzSimons, Gail; Fung, Chun-Ip; Gispert, Hélène; Heiede, Torkil; Horng, Wann-Sheng; Katz, Victor; Kronfellner, Manfred; Krysinska, Marysa; Lakoma, Ewa; Lingard, David; Pitombeira de Carvalho, João;Rodriguez, Michel; Schneider, Maggy; Tzanikis, Constantinos; and Zhang, Dian Zhou. Historical Support for Particular Subjects, in #28.3.59, pp. 241–290. Specific examples of using historical mathematics in the classroom indicate ways in which the teaching of particular subjects may be supported by the integration of historical resources. (JGF) #28.3.188 Siu, Man-Keung. See also #28.3.206. Sklar, Lawrence. See #28.3.92. Smid, Harm Jan. See #28.3.55 and #28.3.60. Smith, George E. Fluid Resistance: Why Did Newton Change His Mind?, in #28.3.44, pp. 105–142. Section 7 of Book II of the Principia concerns Newton’s attempts to combine mathematical solutions for motion in resisting media with experimental results in order to reach conclusions about the resistance forces. Between the first and second editions of the Principia Newton changed his mind about the magnitude and make-up of fluid resistance forces. (JGF) #28.3.189 Smithies, Frank. A Forgotten Paper on the Fundamental Theorem of Algebra, Notes and Records of the Royal Society 54 (2000), 333–341. A paper by James Wood (1760–1839) in the Royal Society’s Philosophical Trans- actions for 1798 predates Gauss’s 1799 proof of the fundamental theorem of algebra. Although Wood’s proof is incomplete, it contains an original idea used later (without knowledge of Wood’s work) by von Staudt, Gordan, and others. (JGF) #28.3.190 Speiser, Maryvonne. ProblèmesLinéairesdans le Compendy de la Praticque des Nombres de Barthélemyde Romans et Mattieu Préhoude(1471): Une Approche Nouvelle Baséesur des Sources Proches du Liber abbaci de Léonard de Pise, Historia Mathematica 27 (2000), 362–383. The 1471 Compendy, one of a number of commercial arithmetics produced in southern France during this period, deals with general problem-solving methods for only a few types of problem. It drew on sources close to Leonardo of Pisa’s 1202 Liber abbaci and thus sheds new light on the transmission of arithmetical thought into Europe. (JGF) #28.3.191 Stedall, Jacqueline. Catching Proteus: The Collaborations of Wallis and Brouncker, Notes and Records of the Royal Society 54 (2000), 293–344. During the 1650s, William Brouncker (1620–1685) worked closely with John Wallis (1616–1703) on some original and unusual mathematics. Although Brouncker is almost forgotten in this context (he was also first President of the Royal Society), he was a skilled mathematician, perhaps more original, intuitive, and surefooted than the persevering and systematic Wallis. (JGF) #28.3.192 S¸tef˘anescu,Doru. See #28.3.111. Suppes, Patrick; Moravcsik, Julius M.; and Mendell, Henry, eds. Ancient and Medieval Traditions in the Exact Sciences: Essays in Memory of Wilbur Knorr, Stanford, CA: CSLI Publications, 2000, xi + 227 pp. A collection 278 ABSTRACTS HMAT 28 of papers emerging from a 1998 conference at Stanford to honor the memory of Wilbur Knorr. The individual papers are abstracted separately. (GVB) #28.3.193

Swetz, Frank J. An Historical Example of Mathematical Modeling: The Trajectory of a Cannonball, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington: Mathematical Association of America, 1995, pp. 93–101. The history of modelling trajectories provides a valuable classroom example of the need to balance pragmatic concerns with theoretical considerations, as well as providing interest. (JGF) #28.3.194

Swetz, Frank J. Trigonometry Comes out of the Shadows, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson and Victor Katz, eds., Learn from the Masters, Washington: Mathematical Association of America, 1995, pp. 57–71. The teaching of trigonometry is enriched and illuminated by acknowledging its origins in the study of shadow ratios and reckoning. (JGF) #28.3.195

Swetz, Frank J. Using Problems from the History of Mathematics in Classroom Instruction, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington: Math- ematical Association of America, 1995, pp. 25–38. A direct approach to enriching mathematics learning through history is to have students solve problems that interested earlier mathematicians. Example are given from Chinese, Babylonian, and Greek mathematics. (JGF) #28.3.196

Szalajko, Kazimierz. What Was Written Fifty Years Ago about Lw´owMathematicians and Not Only about Lw´owMathematicians [in Polish], Zeszty Naukowe Uniwerstetu Opole Matematyka 30 (1997), 169–180. A description of the beginnings of the Wroclaw branch of the Polish Mathematical Society from October 1945 until the congress in Krakow in May 1947. See the review by Jaroslav Zemanek in Mathematical Reviews 2001c:01041. (JA) #28.3.197

Taimina, Daina. See #28.3.83. Tanaka, Setsuko. Boltzmann on Mathematics, Synthese 119 (1–2) (1999), 203–232. Boltzmann’s lectures on natural philosophy contained mathematical content. Behind his mathematics stood his support of Darwinian evolution; he supported non-Euclidean geometry; and attempted to “refute Kant’s static a priori categories and his identification of space with ‘non-sensuous intuition’.” (GVB) #28.3.198 Taton, René. A` la Redécouverte des Oeuvres de Girard Desargues, in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 463–475. An essay by Taton devoted to the discovery and to the editions of Desargues’s scientific, technical and polemical works, concludes the volume. The importance and the value of Poudra’s edition (1864), but also the following considerable progresses in the knowledge of Desargues’s original works, show up. (AF) #28.3.199 Taton, René. Desargues et le Monde Scientifique de son Epoque,´ in Jean Dhombres and JoëlSakarovitch, eds., Desargues et son Temps, Paris: Blanchard, 1994, pp. 23–53. Taton sketches out a picture of the Parisian scientific and cultural environment in Desargues’s era with the aim of pointing out the relationships established by Desar- gues. Taton shows the contradiction of this character, whose intellectual qualities were recognized by the most important mathematicians of his epoch, but who was also strongly opposed when he tried to establish graphic techniques on theoretical bases. (AF) #28.3.200 Thiele, Rüdiger. Felix Klein in Leipzig: 1880–1886, Mitteilungen der Deutschen Mathematiker-Vereinigung 102 (2000), 69–93. The creation of a chair assigned to geometry in Leipzig and the decision to call Klein was of great importance not only for the University of Leipzig but also for the development of mathematics in Germany. The years Klein stayed in Leipzig (1880–1886) are the most important in his mathematical work. Arguably the mathematical work that Klein did after his collapse in 1882/1883 is underestimated, and in general his organizing efforts are overstressed. (JGF) #28.3.201 Thomaidis, Yannis. See #28.3.55 and #28.3.60. Thomas, Robert S. D. See #28.3.215. Tietz, Horst. Menschen—Mein Studium, mein Lehrer [People—My Studies, My Teachers], Mitteilungen der Deutschen Mathematiker-Vereinigung, 4 (1999), 43–52. Tietz gives a detailed account of his life as a non-Aryan HMAT 28 ABSTRACTS 279 student of mathematics at the University of Hamburg during World War II and as a docent at the University of Mar- burg after the war. Photographs. See the review by Michael von Renteln in Mathematical Reviews 2001c:01037. (JA) #28.3.202 Tikhomirov, V. M. Letters “Poste Restante” [in Russian], Vestnik Rossi˘ıskaya Akademiya Nauk 69 (3) (1999), 243–245. A commentary on Kolmogorov accompanying the publication of two letters written by Kolmogorov to Aleksandrov in 1942; see #28.3.10. (GVB) #28.3.203 Trakhtenbrot, B. A. In Memory of S. A. Yanovskaya (1896–1966) on the Centenary of Her Birth, Modern Logic 7 (2) (1997), 160–187. The author relates some of his experiences as a mathematical logician interested in the work of Church and others during the Stalin period and his interactions with Yanovskaya. See the review by Roger L. Cooke in Mathematical Reviews 2001b:01027. (TBC) #28.3.204 Treder, H. See #28.3.212. Troy, Wendy. See #28.3.83 and #28.3.123. Tweddle, Ian. Simson on Porisms. An Annotated Translation of Robert Simson’s Posthumous Treatise on Porisms and Other Items on This Subject, London: Springer-Verlag, 2000, x+274 pp. This book is an annotated translation into English of Robert Simson’s (1687–1768) posthumously published (1776) treatise on Euclid’s porisms and the work of Pappus, Fermat, and others on these theorems. See the review by F. J. Papp in Mathematical Reviews 2001c:01018. (JA) #28.3.205 Tzanakis, Constantinos; Arcavi, Abraham; Correia de Sá,Carlos; Isoda, Masami; Lit, Chi-Kai; Niss, Mogens; Pitombeira de Carvalho, João;Rodriguez, Michel; and Siu, Man-Keung. Integrating History of Mathematics in the Classroom: An Analytic Survey, in #28.3.59, pp. 201–240. An analytical survey of how history of mathematics has been and can be integrated into the mathematics classroom provides a range of models for teachers and mathematics educators to use or adapt. (JGF) #28.3.206 Tzanikis, Constantinos. See also #28.3.55, #28.3.60, and #28.3.188. Ungar, Abraham A. See #28.3.151. Váldes Castro, Concepción. La Primera PublicaciónPeriódicaCubana de Ciencias F´ısico-Matemáticas(1942– 1959): Noticias y Consideraciones [The First Cuban Periodical on Physics and Mathematics (1942–1959), LLULL 23 (2000), 411–468. From the author’s abstract: “In this paper we study the main characteristics and the evolution of the Revista de la Sociedad Cubana de Ciencias F´ısicas y Matematicas´ over the 18 years of its life. Moreover, we describe the content of the sections which make up the publication.” (VA) #28.3.207 Van Brummelen, Glen R. See #28.3.19, #28.3.20, and #28.3.133. Van Dalen, Dirk. The Role of Language and Logic in Brouwer’s Work, in Ewa Orlowska, ed., Logic at Work, Heidelberg: Physica, 1999, pp. 3–14. L. E. J. Brouwer’s interest in language is “deduced from his activities in the Dutch Signific Circle.” See the review by Volker Peckhaus in Mathematical Reviews 2001c:03004. (JA) #28.3.208 Van Maanen, Jan. Alluvial Deposits, Conic Sections, and Improper Glasses, or History of Mathematics Applied in the Classroom, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds., Learn from the Masters, Washington: Mathematical Association of America, 1995, pp. 73–91. Historical research can yield direct possibilities for classroom activities to provide a stimulus for learning, here illustrated in three specific instances. Using history in the classroom requires much energy, but the profits are high: ordinary lessons require less energy and yield lesser profit. (JGF) #28.3.209 Van Maanen, Jan. See also #28.3.55, #28.3.59, and #28.3.133. Van Osdol, Donovan H. See #28.3.30. Vasco, Carlos. See #28.3.83 and #28.3.154. Vastola, S. See #28.3.184. Vilain, Christiane. Mouvement Droit, Mouvement Courbe. II. Les Méchaniques (13ème—14ème siècles) [Straight Motion, Curved Motion. II. Mechanics (13th–14th centuries)], Archives Internationales d’Histoire des 280 ABSTRACTS HMAT 28

Sciences 48 (1998), 255–268. This is a continuation of the author’s Part I [Archives Internationales d’Histoire des Sciences 47 (1997), 271–294]. Rectilinear and circular motions of falling weights are studied in medieval works on mechanics, especially works on the lever and the balance. See the review by Julio Samsó-Moya in Mathematical Reviews 2001c:01012. (JA) #28.3.210 Visokolskis, Sandra. See #28.3.55. Vitrac, B. See #28.3.163. Volkov, Alexei K. See #28.3.118. Von Renteln, Michael. See #28.3.202. Wang, Yuan. Hua Loo-Keng: A Biography, trans. Peter Shiu, Singapore: Springer-Verlag Singapore, 1999, xiv+ 423 pp. A biography of the Chinese number theorist Hua Loo-Keng written by an admiring student. In addition to his mathematics the biographer includes Hua’s difficult childhood, his political experiences, and his success in popularizing mathematics with the public. “An inspiration to anyone who has ever thought about becoming a mathematician.” See the review by Joseph W. Dauben in Mathematical Reviews 2001b:01028. (TBC) #28.3.211 Weeks, Chris. See #28.3.90 and #28.3.175. Wehmeier, Kai F. See #28.3.71. Wheeler, John Archibald; and Ford, Kenneth. Geons, Black Holes, and Quantum Foam. A Life in Physics,New York: W. W. Norton, 1998, 380 pp. “This autobiography ... describes important events in the history of 20th century physics [especially nuclear fission, quantum field theory, and gravitation as the geometry of the universe], to which Wheeler has made significant contributions.” See the review by H. Treder in Mathematical Reviews 2001c:01025. (JA) #28.3.212 Whiteside, Derek T. How Does One Come to Edit Newton’s Mathematics?, in #28.3.44, pp. 209–220. Reminis- cences of how Whiteside came to work on editing Newton’s mathematical papers and some of those who helped, notably the “thoroughly honest and utterly fascinating” Sir Harold Hartley. (JGF) #28.3.213 Wilson, Curtis. From Kepler to Newton: Telling the Tale, in #28.3.44, pp. 223–242. How Newton, having set out to solve some problems for the astronomers, had by 1685 begun to uncover the staggeringly systematic and mathematical character of the System of the World. (JGF) #28.3.214 Woleński,Jan. The Reception of the Lvov–Warsaw School, in Katarzyna Kijania-Placek and Jan Woleński, The Lvov–Warsaw School and Contemporary Philosophy, Dordrecht: Kluwer, 1998, pp. 3–19. A discussion of the Lvov School, the Lvov–Warsaw School, and the Warsaw School of Logic. See the review by Robert S. D. Thomas in Mathematical Reviews 2001c:01042. (JA) #28.3.215 Xu, Zelin. Takebe Katahiro and Romberg Algorithm, Historia Scientiarum 9 (1999), 155–164. “A method for the acceleration of convergence described by Katahiro in 1722 is described” and applied to the evaluation of to 40 decimal places. See the review by A. D. Booth in Mathematical Reviews 2001c:01009. (JA) #28.3.216 Ycart, B. Le Procèsdes Etoiles´ entre de Moivre et Laplace, Cubo 3 (1) (2001), 1–11. On the 18th-century history of the Central Limit Theorem, especially the question why “it took so long to be understood and applied.” Sections are devoted to the general intellectual climate of the age and to the meridian-measuring expedition to South America in 1735. (HG) #28.3.217 Youschkevitch, Adolf P. See #28.3.164. Zemanek, Jaroslav. See #28.3.4, #28.3.62, and #28.3.197. Zhang, Dian Zhou. See #28.3.55 and #28.3.188.