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Historia Mathematica28 (2001), 255–280doi:10.1006/hmat.2001.2322, available online at http://www.idealibrary.com on

ABSTRACTS

Edited byGlen Van Brummelen

DEDICATED TO THE MEMORY OF JOHN FAUVEL

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The initials in parentheses at the end of an entry indicate the abstractor. In this issue there are abstractsby Francine Abeles (Kean, NJ), Victor Albis (Bogota, Colombia), Joe Albree (Montgomery, AL), TimCarroll (Ypsilanti, MI), John G. Fauvel (Milton Keynes, UK), Alessandra Fiocca (Ferrara, Italy), HardyGrant (Ottawa, Canada), Ivor Grattan-Guinness (Middlesex, UK), Martha Grover (Bennington, VT),Stefan Popovici (Bennington, VT), Mili Pradhan (Bennington, VT), Kevin VanderMeulen (Hamilton,Canada), and Glen Van Brummelen.

Acerbi, F. Plato:Parmenides149a7-c3: A Proof by Complete Induction?,Archive for History of Exact Sciences55 (2000), 57–76. InParmenides, Plato gives a full-fledged example of proof by complete induction, indeed theonly such example in the ancient mathematical corpus. Other alleged examples are untenable, suggesting thatthe 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 AppliedMathematics, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds.,Learn from theMasters, 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 Wiskunde1 (2000), 59–67. “Thisis the first of a series of four articles on the relations between mathematics and reality.” It includes a discussionof how modern Dutch modeling began in the 1930s with Tinbergen’s economic policy models. See the review byEduard Glas inMathematical Reviews2001c:01003. (JA) #28.3.3

Alexiewicz, Andrzej; Baranski, Feliks; and Koronski, Jan. The Mathematics–Physics Students Circle at theJan Kazimierz University in Lwow [in Polish],Zeszty Naukowe Uniwerstetu Opole Matematyka30 (1997),9–42. The activities of the Mathematics-Physics Students Circle at the Polish university in Lvov for the 40 years

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256 ABSTRACTS HMAT 28

from 1899 to 1939 are described. See the review by Jaroslav Zemanek inMathematical Reviews2001c: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 GreshamCollege. 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 MathematicalScientist25 (2000), 63–71. The intriguing relationship between beautiful mathematics and physical applicationsmay be illustrated through the Dirac equation for relativistic electrons, whose antecedents lie in 18th-centurydifferential equations and 19th-century Clifford algebras, emerging into physics through the need to combinespecial 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, JohnFauvel, Otto Bekken, Bengt Johansson and Victor Katz, eds.,Learn from the Masters, Washington: MathematicalAssociation of America, 1995, pp. 3–12. Educating teachers in the history of mathematics can help in at leastfour areas: giving insight into learning difficulties; improving modes of instruction; incorporating problem solvingin 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 forPhilosophy and History of Science10(1998), 5–31. This paper is a discussion of the early days of set theory; how-ever, it contains historical inaccuracies. See the review by Leon Harkleroad inMathematical Reviews2001b:01016.(TBC) #28.3.8

Bagni, Giorgio T. See#28.3.9 and #28.3.188.

Baranski, 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 ofintegrating historical resources into mathematics teaching may not be susceptible to the research techniquesof the quantitative experimental scientist. Research paradigms to explore and analyze include those developed byanthropologists. (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 AkademiyaNauk 69 (3) (1999), 245–255. Two letters written in 1942 from Kolmogorov to Aleksandrov show that theirwartime separation did not prevent the interchange of scientific ideas and philosophical reflections. The article isaccompanied 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 recentstudies 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 Mathematiques6 (2000), 95–126. The beginning ofthe 19th century saw the emergence of several new approaches to negative numbers. In the early 19th-centuryNetherlands, Dutch mathematicians opted for an approach different from that of their contemporaries in Germanyand France. The 1821 Dutch translation of Lacroix’sElemens 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 inComparison to its Various Counterparts in Europe,Historia Mathematica28(2001), 31–47. As in other countries,the Netherlands fostered several amateur mathematical societies during the 18th and early 19th centuries. One ofthese, the Amsterdam Mathematical Society, developed into the national professional society of today, WiskundigGenootschap. (JGF) #28.3.13

Beckers, Danny J. Definitely Infinitesimal: Foundations of the Calculus in the Netherlands, 1840–1870,Annalsof Science58 (2001), 1–15. The foundations of analysis offered by Cauchy and Riemann were not immediatelywelcomed by the mathematical community. Before 1870 the foundations of mathematics were considered more orless a national affair. Mid-19th century Dutch mathematicians were aware of developments abroad but preferredthe 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, andVictor 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 itto today’s geometric representation of complex numbers. Also contains three exercises that greatly enhance thematerial. (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 disappointinglyprivate, reluctant to share his insights. But our viewpoint may be wrong. Seeing Harriot as a professional mathe-matical 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 onthe status and role of mathematics and the history of astronomy, foreshadowing the theoretically informed practicalmathematical direction that his work was later to take. (JGF) #28.3.17

Berger, Marcel. La Geometrie de Riemann: Apercu Historique et Resultats Recents,Cubo3 (1) (2001), 13–36.Sections on the pioneering work of Gauss and of Riemann respectively are followed by a substantial accountof 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 andSynthesis in Ancient Greece and Medieval Islam, in #28.3.193, pp. 1–31. A discussion and comparison ofthe 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 u Sahl al-K uh ı on “Two Geometrical Questions,”Zeitschrift fur Geschichte der Arabisch-Islamischen Wissenschaften13 (2000), 165-187. A translation, with com-mentary, of a treatise by al-K uh ı (10th century A.D.) on two geometrical problems: the construction of a circle asa locus (a special case of a problem reportedly discussed in Apollonius), and a second unrelated problem, perhapsa fragment of another work. (JGF) #28.3.20

Bessot, Dider. Les AspectsEpistemologiques de la Pensee Didactique de Desargues: L’Usage des ExemplesGenerique, in Jean Dhombres and Joel Sakarovitch, eds.,Desargues et son Temps,Paris: Blanchard, 1994, pp.295–312. Bessot’s contribution concerns Desargues’s epistemological and didactic remarks which confirm, as theauthor has shown, the synthetic character of his thought. According to Bessot they also reveal that Desarguesrecognized the superiority of theory with respect to practice as the correctness of the artisan’s technique comesfrom 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.


Biryukova, L. G.; and Biryukov, B. V. On the Axiomatic Sources of Fundamental Algebraic Structures: TheAchievements of Hermann Grassmann and Robert Grassmann [in Russian],Modern Logic7 (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 inMathematical Reviews2001b:01012. (TBC) #28.3.22

Bkouche, Rudolf. Desargues au XIXe Siecle: L’Influence d’un Livre non Lu, in Jean Dhombres and JoelSakarovitch, eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 207–217. Bkouche analyzes the workby M. Chasles,Apercu historique sur l’origine et le developpement des methodes en geometrie (1837), in whichthe French geometer restored Desargues’ thought, having only an indirect knowledge of his major work, theBrouillon 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, theprojective 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 whichmight be called a curvature method, where an element of the continuous orbit is represented by a vanishingly smallarc of the circle of curvature. Newton developed this measure of the rate of bending of curves before he began hisanalysis of orbital motion. (JGF) #28.3.24

Brigaglia, Aldo. The Rediscovery of Analysis and the Apollonian Problems [in Italian], in Marco Panza and ClaraSilvia Roero, eds.,Geometry, Fluxions and Differentials[in Italian], Naples: La Citta del Sole, 1995, pp. 221–269.This paper discusses certain problems of Apollonius that were analyzed in Pappus’sCollection, Book VII, andthen were reformulated in algebraic language between 1659 (Descartes’sGeometry)and the 1680s (Newton’streatise on geometry). See the review by William R. Shea inMathematical Reviews2001c:01013. (JA) #28.3.25

Bueno, Otavio. Empiricism, Scientific Change and Mathematical Change,Studies in the History and Philosophyof Science31(2000), 269–296. A unified account of scientific and mathematical change in a thoroughly empiricistsetting may be illustrated through examining the early history of formulating set theory (in particular, the worksof Cantor, Zermelo, and Skolem). (JGF) #28.3.26

Burn, Bob. Gregory of St. Vincent and the Rectangular Hyperbola,Mathematical Gazette84 (2000), 480–485.One of the proofs by Gregory of St. Vincent (1584–1667) of the area under a rectangular hyperbola, which de Sarasanoticed has a logarithm-like property, has a remarkable similarity to Archimedes’s quadrature of the parabola. Theproof is here given an analytical exposition. (JGF) #28.3.27

Burn, R. P. Alphonse Antonio de Sarasa and Logarithms,Historia Mathematica28 (2001), 1–17. The discoveryof 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 particularbase for his logarithms, nor choose log 1 to have the value 0, so he did not focus on what Euler was to call naturallogarithms. The assumption, or rational reconstruction, that he did owes as much to the needs of 20th-centurystudents 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 therepresentations of decimal numbers in the Latin Middle Ages came to be in order from digits of greatest value tosmallest, 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, JohnFauvel, 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 ringsand ideals, from the conviction that the history of a subject is essential for a true appreciation of it. (GVB) #28.3.30

Caquero Martınez, Jos´e M. See#28.3.37.


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 Universitairesdu Septentrion, 1997, 428 pp., 240 F. A new edition of the second of three volumes of the author’s doctoral dis-sertation, in which the author identified two stages in the development of the theoretical structure of mathematicalknowledge in ancient Greece. This volume analyzes the first stage, when Greek mathematics begin to differ fromits Mesopotamian and Egyptian counterparts. (GVB) #28.3.31

Cazaran, Jilyana. See#28.3.128.

Cegielski, Patrick. Un Fondement des Mathematiques [A Foundation for Mathematics], in Michel Serfati, ed.,La Recherche de la Verite, Paris: ACL—LesEditions du Kangourou, 1999, pp. 175–209. Beginning with ancientEgyptian 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 inMathematical Reviews2001c:03003. (JA) #28.3.32

Chaboud, Marcel. Desargues Lyonnais, in Jean Dhombres and Joel Sakarovitch, eds.,Desargues et son Temps,Paris: Blanchard, 1994, pp. 433–452. Chabout provides new elements concerning Desargues’s presence and ac-tivity in the district of Lyon, results of one and a half years of research into the “Archives municipales de Lyon”and the “Archives departementales du Rhone.” The information is organized by wide themes and Taton’s book of1951 is the introduction to this contribution. (AF) #28.3.33

Cicenia, Salvatore. The Mathematical Writings of Giuseppe Torelli [in Italian],Physis35(1998), 85–124. This isa survey of the mathematical work of Giuseppi Torelli (1721–1781); among other achievements, Torelli translatedthe collected works of Archimedes into Latin. See the review by Umberto Bottazzini inMathematical Reviews2001c: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 advancein mathematics. Mathematical practitioners in London in the late 16th century shifted the epistemic founda-tion of mathematics from mathematical idealism toward a more immediate relationship between the math-ematical 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 andexperimental practices, transcending modern classifications. (JGF) #28.3.36

Cobos Bueno, Jose; and Caquero Martınez, Jose M. Matematicas y Exilio: La Primera Etapa Americana deFrancisco 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 sciencein Spain. He was, like many others of the time, forced to exile in America because of his political ideas afterSpanish 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 theprogress of Newtonian scholarship over the past century and a half, from Brewster’s 1855 biography and Edleston’s1850 edition of the Newton–Cotes correspondence to the later 20th-century editions of Rupert and Marie BoasHall 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 thereview by Godofredo Iommi Amunategui inMathematical Reviews2001b: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.


Correia de Sa, Carlos.See#28.3.188 and #28.3.206.

Corry, Leo. The Origins of the Definition of Abstract Rings,Gazette des Mathematiciens83 (2000), 29–47. Theorigins of Fraenkel’s axiomization of rings (1914) are traced back to work of E. H. Moore and Ernst Steinitz. Seethe review by Jonathan Golan inMathematical Reviews2001c:01004. (JA) #28.3.40

Cottin, Francois-Regis. L’Architecte et l’Architecture a Lyon au Temps de Desargues, in Jean Dhombres andJoel Sakarovitch, eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 425–432. Cottin shows the differencein origin and disposition of those who carried out the traditional functions of an architect between the 16th and17th century. The oval stairs of theHotel de Ville de Lyonand 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 becomeabsolutely necessary to architecture, not only stone-cutting with Desargues, but afterwards also statics, resistanceof 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 Siecle, in Jean Dhombres and Joel Sakarovitch, eds.,Desargueset son Temps, Paris: Blanchard, 1994, pp. 453–459. Cuer gives some general information as regards the professionof a notary in Lyon in Desargues’s epoch. The significance of this theme is that Desargues was closely connectedwith 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 ofthe relevant and necessary mathematics.” See the review by Paul Ernest inMathematical Reviews2001c:01005.(JA) #28.3.43

Dalitz, Richard H.; and Nauenberg, Michael, eds.Foundations of Newtonian Scholarship, River Edge, NJ/London:World Scientific, 2000, 260 pp., $65/£44. A collection of papers, most of which emerge from a symposium heldat 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 Joel Sakarovitch,eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 11–22. An exposition by Damish that considers thecharacter of Desargues as a point of connection between art and science and studies the relationships that Desarguesestablished with the artists of his epoch, painters, carvers, architects, stonecutters, with the aim of establishingmutual influences. The suggestions to develop the speech in parallel on the artistic and the geometric levels areremarkable. (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 Guzman, Miguel. See#28.3.83.

Deakin, Michael A. B. See#28.3.170.

Debarnot, Marie-Therese. Trigonometry, in Roshdi Rashed and Regis Morelon, eds.,Encyclopedia of the Historyof Arabic Science, London: Routledge, 1996, vol. 2, pp. 495–538. The author traces the development of formulasin spherical and plane trigonometry in the Arabiczijesfrom the 11th through the 14th centuries A.D., a rich thoughcompressed paper. See the review by J. S. Joel inMathematical Reviews2001b:01003. (TBC) #28.3.46

Diacu, Florian. A Century-Long Loop,Mathematical Intelligencer22 (2) (2000), 19–25. The author presentshis idea of how mathematical theories generally arise and illustrates it with the development of algebraic topologyby tracing the history of Henri Poincare’s three-body problem from 1892 to 1994. (FA) #28.3.47

Diacu, Florian. See also#28.3.95.

Djebbar, Ahmed. Les Activites Mathematiques dans les Villes du Maghreb Central (XIe–XIXes) [Mathemati-cal Activities in the Cities of the Central Maghreb (XI–XIX centuries)], inHistoire des Mathematiques Arabes,


Algiers: Association Algerienne d’Histoire des Mathematiques, 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 thedevelopment of mathematics and of its place in the culture of what has become present-day Algeria. See thereview by Jens Høyrup inMathematical Reviews2001c:01010. (JA) #28.3.48

Djebbar, Ahmed. Les Livres Arithmetiques desElementsd’Euclide dans le Traite d’al-Mu’taman du XIe Siecle,LLULL 23 (2000), 589–653. From the author’s abstract: “This paper studies the first chapter ofKitab 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 kingof Saragossa between 1081 and 1085. Different chapters of this remarkable work in the Arabic mathematicaltradition 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’sPrincipia,Archive for Historyof Exact Sciences55 (2001), 345–363. The details of Newton’s arguments in these lemmas, concerned with theturning moment exerted on the Earth by tidal forces due to the gravitational attraction of the Sun, has not been wellunderstood. 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 Paralleles” de Girard Desargues et de GuarinoGuarini, Fondateurs de la Science Moderne de la Representation, in Jean Dhombres and Joel Sakarovitch, eds.,Desargues et son temps, Paris: Blanchard, 1994, pp. 395–412. Docci, Migliari, and Bianchini single out in theunity of theory and praxis the common denominator between Desargues and the Italian architect Guarino Guariniof Modena. The authors also underline Guarini’s contribution to the science of body’s geometrical representationas 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, Interprete de Desargues, in Jean Dhombres and Joel Sakarovitch, eds.,Desargueset son temps, Paris: Blanchard, 1994, pp. 283–293. Echeverrıa examines the relationships between Leibniz andDesargues based on Leibniz’s available writings. According to the author, rather than Desargues’s direct influenceon Leibniz, one has to deal with the interpretation by Leibniz of Desargues’s ideas and methods. Leibniz paidparticular 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 linescould have played a heuristic role in Leibniz’s discovery of infinitesimal calculus, but for this subject the authorrefers 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 Perspective1 (3) (1999), 238–252. Covers the haphazard beginnings of the Sommerfeld school, whichwas 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 JurgenRossman, Peter Takac, and Gunther Wildenhain, eds.,The Maz’ya Anniversary Collection, Basel: Birkhauser,1999, vol. 1, pp. 35–52. Integral and pseudodifferential operators were one of the main themes of Maz’ya’s vastmathematical 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, Joao; 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 mathematicsis to be taught in schools, how, and with what historical resources or input, are ultimately political, influenced bya number of factors including the experience of teachers, expectations of parents and employers, and the socialcontext of debates about the curriculum. (JGF) #28.3.55


Fauvel, John G. Revisiting the History of Logarithms, in Frank Swetz, John Fauvel, Otto Bekken, BengtJohansson 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 geometricprogressions, 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, Newtonwas deeply interested in questions of language and appropriate symbolism. These issues play an important yetambiguous 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 the21st Century,Teaching and Learning Undergraduate Mathematics12 (2000), 7–11. It is increasingly commonfor mathematics courses to incorporate a history of mathematics module, for a number of good reasons includ-ing 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 mathemat-ics education arising from a 1998 ICMI conference in Luminy, France. The book has been edited to pro-vide 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 math-ematics 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 MathematicalCommunity, in #28.3.5, pp. 174–188. Part of the reason for poor attendance at early Gresham College lectureswas that the traditional lecture format was becoming obsolete under the developing availability of books, andmore private tutorial situations. Although the Gresham professoriate served both its instructional and researchmissions, other factors such as the rise of the Royal Society and the growth of coffee houses fostered itsdecline. (JGF) #28.3.61

Fenster, Della. The Development of the Concept of an Algebra: Leonard Eugene Dickson’s Role,Rendiconti delCircolo Matematico di Palermo, Serie II. Supplemento61(1999), 59–122. This paper describes how the “Chicagoschool of algebra” drew upon the study of axioms in the development of non-Euclidean geometry and on ideasfrom quaternions. See the review by Jaroslav Zemanek inMathematical Reviews2000c:01022. (JA) #28.3.62

Ferreiros, Jose. Mathematics and Platonism(s) [in Spanish],Gaceta de la Real Sociedad Matematica Espanola2(3) (1999), 446–473. The author provides a brief historical survey of Platonism in mathematics in order to presentan outline of his naturalistic project. See the review by Jaime Nubiola inMathematical Reviews2001b:00004.(TBC) #28.3.63

Fiorani, Francesca. The Theory of Shadows and Aerial Perspective: Leonardo, Desargues and Bosse, in JeanDhombres and Joel Sakarovitch, eds.,Desargues et son temps, Paris: Blanchard, 1994, pp. 267–282. Fiorani stud-ies both shadow projection and aerial perspective in Desargues’s and Bosse’s work. With the aim of establishingthe relationships among Leonardo, Desargues, and Bosse, he analyzes two issues: the origin and meaning of adrawing on shadow projection sent by Poussin to Paris and the understanding of what Desargues and Bosse calledla regle du fort et faible. Bosse’s writings provide precious insights on these topics, because they complementDesargues’s succinct rules with observation related more strictly to painting; moreover Bosse shows an accurateknowledge 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 Representer: Abraham Bosse, l’Intransigeant, in Jean Dhombres and Joel Sakarovitch,eds.,Desargues et son temps, Paris: Blanchard, 1994, pp. 263–266. Flacon discusses the work of Abraham Bosse,


friend of Desargues, professor of perspective at the ParisianAcademie royale de peinture et sculptureand thestrongest supporter of Desargues’s ideas about perspective. The author explains the terms of the controversybetween Bosse and the artists which was originated by Bosse’s idea that the artist has to draw according to per-spective rules. He also points out that Bosse gave deep thought to the problems of aerial perspective, and thatthe 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, Godel, and the Trisection of the Angle,in Jaakko Hintikka, ed.,From Dedekind to Godel, Boston/Dordrecht: Kluwer, 1995, pp. 373–425. This paperattempts to show how Wittgenstein understood Godel’s first incompleteness theorem “as a piece of mathematics.”Reportedly, Wittgenstein quite often compared Godel’s theorem with the proof of the impossibility of trisect-ing an angle with straightedge and compass only. See the review by Hourya Sinaceur inMathematical Reviews2001c:03005. (JA) #28.3.66

Font, Josep Maria. On the Contributions of Helena Rasiowa to Mathematical Logic,Multi-Valued Logic4(1999), 159–179. This paper discusses algebraic logic, as conceived by Rasiowa (“infinistic methods”) in theyears following World War II, especially in contrast to the Dutch school during the same period (“constructivityin mathematics”). See the review by Marcel Guillaume inMathematical Reviews2001c: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 Education9(2000), 449–456. Undergraduate students do not always make a clear distinction between physics and mathemat-ics. The case study of Galileo’s treatment of motion under uniform acceleration illustrates the differences andrelationships between the two, and is accessible to students not specializing in mathematics. (JGF) #28.3.68

Fowler, David. Eudoxus:Parapegmataand Proportionality, in #28.3.193, pp. 33–48. A critical examination ofthe traditional claims that Eudoxus was mainly responsible for the ideas of proportionality in the fifth book ofEuclid’sElements. (GVB) #28.3.69

Fox, Robert, ed. Thomas Harriot: An Elizabethan Man of Science, Aldershot: Ashgate, 2000, hardbound, 330pp., $84.95. A collection of essays on Thomas Harriot based on a series of lectures held at Oriel College, Oxfordsince 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)andUber die Zahlen des Herrn H. Schubert(1899), a “Nachwort” by Wolfgang Kienzler, and a brief commentaryby Uwe Dathe. See the review by Kai F. Wehmeier inMathematical Reviews2001c: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 FrankSwetz, 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 theabstractions of group theory in the classroom, rejecting an abstract internalist approach, yet not wholly espousingthe alternatives. (GVB) #28.3.72

Gario, Paola. Guido Castelnuovo: Documents for a Biography,Historia Mathematica28 (2001), 48–53. Thearchive of Castelnuovo (1865–1952), one of the most important mathematicians of the Italian school of alge-braic geometry, contains a large scientific correspondence and 49 notebooks of his lectures for the last two yearsof the Italian mathematics degree. In due course it will be available at the Accademia dei Lincei in Rome.(JGF) #28.3.73

Gispert, Helene. 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 Science31A (1) (2000), 71–86. The author uses Felix Klein as an example of a creative


mathematician who opposed the foundational view of the development of mathematics and favored a model-basedapproach. He surveys Klein’s work to support this hypothesis. See the review by Roger L. Cooke inMathematicalReviews2001b: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 Science32 (2001), 119–137. InProofs and Refutations(1976), ImreLakatos 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 Popperianmethodology, however, Lakatos’s work showed that some of Popper’s ideas needed to be revised and furtherrefined. (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 Sciences55 (2000), 1–41. J. W. Alexander (1888–1971) is mainly remembered as a pioneeringtopologist 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 mayhave led to its being underestimated, opened up new areas of investigation for researchers in geometric functiontheory. (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 Intelligencer22 (1) (2000), 34–45. A history of the famous MathematischesKolloquium at the University of Vienna in the period 1928–1936 whose participants included, in addition to Menger,Hans Hahn, Kurt Godel, Alfred Tarski, Abraham Wald, John von Neumann, Franz Alt, Olga Taussky-Todd, andOskar Morgenstern. (FA) #28.3.77

Gomez, Francisco Teixido.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: Crıtica, 2000, 232 pp.A Spanish translation of Gould’sScience vs. Religion. See the review by Francisco Teixid´o Gomez inLLULL 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. TheBodleian library has some four and a half years’ worth of Henry Savile’s astronomy lectures, delivered from 1570onwards, attesting to an enormous amount of reading and study on Savile’s part. His notebooks of 1566–1569indicate 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, againsttoo 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 voorWiskunde(5)1 (2000), 242–249. Daniel Bernoulli (1700–1782) has been rather underrated since his death. But helived through major developments in mechanics and made major contributions to several principles and topics. Hischoice of problems and approach suggests a lateral thinker, taking up questions and making connections avoidedor not noticed by others. (JGF) #28.3.80

Grattan-Guinness, Ivor. Response to Moore’s Letter,Notices of the American Mathematical Society48 (2)(2001), 167. A response to Moore’s letter to the editor on the same page, including new information about a 24thproblem of Hilbert. (KVM) #28.3.81

Greenstadt, John. Reminiscences on the Development of the Variational Approach to Davidon’s Variable-MetricMethod,Mathematical Programming87(2) (2000), 265–280. Describes the mathematical context and motivationof 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 Guzman, Miguel;Gispert, Helene; Ismael, Abdulcarimo; Jones, Lesley; Menghini, Marta; Phillippou, George; Radford, Luis;


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 alsooutside any particular one. Students find their understanding of both mathematics and their other subjects enrichedthrough the history of mathematics. Mathematical evolution comes from a sum of many contributions growingfrom 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.

Gutierrez Davila, Antonio. Some Methods Used by Euler for Power Series Expansions [in Spanish],Epsilon15(3) (1999), 311–338. Attempts to recover some of the methods employed by Euler in hisIntroductio in analysininfinitorum to study some power series expansions, and compares with Cauchy’s work in hisCours 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 JurgenRossman, Peter Takac, and Gunther Wildenhain, eds.,The Maz’ya Anniversary Collection, Basel: Birkhauser,1999, vol. 1, pp. 7–16. Presents the highlights of Maz’ya’s work in potential theory, function spaces, and partialdifferential 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’sCalculus: 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 Apres Bourbaki, inTravaux Mathematiques Fasc. XI, Luxembourg: CentreUniversitaire de Luxembourg, 1999, pp. 23–32. The author evaluates the influence of the Bourbaki works, theirmathematical innovations and their influence on education, society in general, and the style of French mathematicalwriting. See the review by Roger L. Cooke inMathematical Reviews2001b:01029. (TBC) #28.3.87

Høyrup, Jens. See#28.3.48.

Husserl, E. Introductiona la Logique eta la Theorie de la Connaisance: Cours(1906–1907) [Introduction toLogic and the Theory of Knowledge: Course (1906–1907)], trans. Laurent Jourmier, with preface by JacquesEnglish, Paris: Librairie Philosophique J. Vrin, 1998, 440 pp., 300 F. A French translation of Husserl’s lecturesof 1906–1907. See the review by Michael Otte inMathematical Reviews2001b: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 Society48 (4) (2001),374–382. The interview explores some of Bott’s thought about mathematics and briefly, some of the colleagueshe has had contact with. (KVM) #28.3.89


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 beintegrated into the teaching of mathematics, but also one of the most rewarding for students both at school and atteacher 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 Philosophyof Science31 (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 ofthat 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, NewYork: Alfred A. Knopf, 1999, x+436 pp. This is a “sympathetic and insightful” discussion of Gell-Mann’s lifethat includes his conflicts with other scientists and gives as clear a description of the theoretical physics as is pos-sible while avoiding the mathematics. See the review by Lawrence Sklar inMathematical Reviews2001c:01029.(JA) #28.3.92

Jones, Alexander. Pappus’ Notes to Euclid’sOptics, in #28.3.193, pp. 49–58. Addresses whether writersin 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, JohnFauvel, Otto Bekken, Bengt Johansson and Victor Katz, eds.,Learn from the Masters, Washington: MathematicalAssociation of America, 1995, pp. 13–23. History of mathematics helps students to reach the important understand-ing 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 Stabilite du Systeme Solaire [Hadamard and the Stability of the Solar Sys-tem], inTravaux Mathematiques Fasc. XI, Luxembourg: Centre Universitaire de Luxembourg, 1999, pp. 33–48.Aware of Poincare’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 symbolicdynamics and chaos. See the review by Florian N. Diacu inMathematical Reviews2001c: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, BengtJohansson, 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, backsubstitution, 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 ofAmerica, 1995, pp. 49–55. An adaptation of Napier’s own way of introducing logarithms can be used in today’sclassrooms 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 translationof all nine of the available texts describing projections “in which distances between points along the longitudecircles of the sphere are preserved on the flat surface upon which the sphere is mapped.” For the modern reader, this


is augmented by an extensive discussion and analysis. See the review by George Saliba inMathematical Reviews2001c:01011. (JA) #28.3.98

Kilic, Berna Eden. John Venn’s Evolutionary Logic of Chance,Studies in History and Philosophy of Science30A (1999), 559–585. By rejecting “the distinction between individual and type” and influenced by Darwin’sOnthe Origin of Species(1859), “the author shows that John Venn’sThe Logic of Chance(1866) was a reaction notonly to the idea of statistical law but also to that of probability based on such laws.” See the review by Philip A.Beeley inMathematical Reviews2001c: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: MathematicalAssociation of America, 1995, pp. 225–239. Describes a number of means by which the historical developmentof linear algebra can be used to motivate an otherwise challenging subject. (GVB) #28.3.100

Knobloch, Eberhard. See#28.3.180.

Koronski, 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 triangu-lation beginning with the work of Poincare and Brouwer; it was written in 1977 and has never been revised. Seethe review by F. E. A. Johnson inMathematical Reviews2001c: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 Jurgen Rossman, Peter Takac,and Gunther Wildenhain, eds.,The Maz’ya Anniversary Collection, Basel: Birkhauser, 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-frequencydisturbances.” (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 Joel Sakarovitch, eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 231–243. Laurent investigates Desargues’s sources in per-spective. As theExemple de l’une des manieres universelles touchant la pratique de la perspective(1636) wasaddressed to the artisan, it was devoid of demonstrations, even if, according to Desargues, only two propositionswere necessary to prove his universal method. The author makes suggestions about these two propositions and alsopoints out Desargues’s contributions by using color to improve perspective depth. The last paragraph is devotedto the 10 pagesAux theoricienspublished by Bosse in 1647. (AF) #28.3.103

Le Goff, Jean-Pierre. Aux Sources de la Perspective Arguesienne, in Jean Dhombres and Joel Sakarovitch, eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 244–248. Le Goffe adds some personal suggestions aboutDesargues’s sources in perspective; according to him, Desargues was the heir of the Flemish tradition in thisparticular field. (AF) #28.3.104

Le Moel, Michel. Jacques Curabelle et le Monde des Architects Parisiens, in Jean Dhombres and Joel Sakarovitch,eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 389–392. Le Moel’s contribution is devoted to Curabelle,the architect mainly known for his polemics against Desargues. New elements concerning his life and activity are


the result of research in the Archives Nationales undertaken by the author, who also examines the evolution of thetrade 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, OttoBekken, 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 thedevelopment 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. ?Como saber? El Positivismo y sus Crıticos en 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 paperbrings into focus positivism as a multifaceted phenomenon and at the same time persistent and recurrent throughoutthe history of science... The endeavor to come to a valuation of positivism turns out to be even more complicatedwhen we take into account its role in mathematics.” (VA) #28.3.107

Leiser, Eckart. Hegemonıa y Estadıstica en la Psicologıa Alemana: Estudio Historico de una Guerra DespiadadaContra la Heterodoxia [Hegemony and Statistics in German Psychology: Historical Study of a Merciless WarAgainst Heterodoxy],LLULL 23 (2000), 675–686. From the author’s abstract: “The basic thesis of this paper isthat the hegemony of contemporary mainstream psychology does not rest on any paradigm relative to a theory, buton a specific concept concerning the method, which materializes in a kind of worship revolving around statisticsand its teaching.” (VA) #28.3.108

Liang, Zhao Jun. From the Elimination Method in theJiu Zhang Suanshu(Arithmetic in Nine Sections) toAutomated Theorem Proving [in Chinese],Journal of Central China Normal University. Natural Sciences33(2) (1999), 179–185. The author discusses the elimination method in theJiu Zhang Suanshu(Arithmetic in NineSections) and points out the effect it had on automated theorem proving. See the review by Shi Rong Guo inMathematical Reviews2001b: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 Review20(2000), 254–282. Recorde suffered or benefited from the Tudor policy of anglicizingthose Welsh people who could otherwise have contributed to Wales’s own development. He kept some Welsh tiesand knew other scholars of Welsh heritage such as John Dee. Despite Recorde’s espousal of humanist educationalprinciples, 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 Poincare, for Hurwitz’s theorem, namely that a curve of genusg ≥ 2 can have no more than 84(g−1) birationalself-transformations. See the review by Doru Stefanescu inMathematical Reviews2001c: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 Didattica8 (1999), 27–45. This account begins just prior toLeibniz, 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 Society54 (2000), 275–292. A complete annotated listing of the fourteenitems 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 Annidi Desargues, in Jean Dhombres and Joel Sakarovitch, eds.,Desargues et son Temps, Paris: Blanchard, 1994,


pp. 101–109. Maltese discusses the recovery of knowledge about conic sections in western countries starting fromthe first Latin translations of the perspective works of the Arabian tradition, in their turn based on the Greektradition, 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 Studiesin Mathematics15 (1984), 191–210. An experiment carried out with high school students on the historical de-velopment 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 thepossibilities offered by a nonstandard reading of higher order quantifications. See the review by Siegfried Gottwaldin Mathematical Reviews2001b:03003. (TBC) #28.3.116

Martınez Garcıa, MarıaAngeles. Las Matematicas en los Planes de Estudio de los Ingenieros Civiles en Espanaen 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. LeQizheng Tuibude Bei Lin (vers 1477) [TheQizheng Tuibuof Bei Lin (ca. 1477)], inHistoire des Mathematiques Arabes, Algiers: Association Algerienne d’Histoire des Mathematiques, 1998, vol.2, pp. 227–237. TheQizheng Tuibu(Astronomical Calculations of Seven Governors, i.e., the sun, the moon, andfive planets) was compiled ca. A.D. 1477. The author reports that this is the most complete of the extant treatiseson Islamic astronomy written in Chinese and asks questions about its origins. See the review by Alexei K. Volkovin Mathematical Reviews2001b: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 Science33 (2000), 257–282. Boncompagni’sBullettino(1868–1887) was the first journal entirely devoted to the history of mathematics. Far from being merely the outcome ofthe eccentric personality of its editor, it reflected at the level of historiography of science the struggle of the officialRoman 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, especiallyepisodes 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 byEudoxus’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 Joel Sakarovitch, eds.,Desargues et son Temps,Paris: Blanchard, 1994, pp. 87–99. Mesnard shows that the relationship between Desargues and Pascal was deeperthan it appears: the same concrete mind, a strong creative imagination, and the idea of the universal value of themathematical experience were at the basis of this relation. Also the mature Pascal, the philosopher of the humanspirit, 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, Marıa Victoria; and Troy, Wendy. Historyin Support of Diverse Educational Requirements: Opportunities for Change, in #28.3.59, pp. 171–200. Usinghistorical resources, teachers are better able to support the mathematical learning of students in diverse situ-ations: returning to education, in under-resourced schools and communities, with educational challenges, andmathematically gifted. (JGF) #28.3.123


Michalowicz, Karen Dee. See also#28.3.133.

Michel-Pajus, Anne. See#28.3.55.

Migliari, Riccardo. See#28.3.51.

Miller, Richard K. Volterra Integral Equations at Wisconsin, in G. Corduneanu and I. W. Sandberg, eds.,VolterraEquations and Applications, Amsterdam: Gordon & Breach, 2000, pp. 15–26. Contains personal recollectionsof work at the Wisconsin school in the late 1950s and the 1960s; “the initial motivation was to understand cer-tain nuclear reactor models but the ultimate goal was to develop a general qualitative theory of Volterra integralequations.” (GVB) #28.3.124

Millman, Richard. See#28.3.55.

Milnor, John, Classification ofn− 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 moderntopology, namely the discovery of exotic spheres.” This paper also describes how the author was led to devise, inthe 1950s, for the first time, a 7-dimensional exotic sphere. See the review by Wieslaw J. Oledzki inMathematicalReviews2001c:57002. (JA) #28.3.125

Moore, Gregory H. Correction to the History of Hilbert’s Problems,Notices of the American MathematicalSociety48 (2) (2001), 167. A brief letter to the editor correcting an impression given the reader regarding Peanoand 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 relationbetween Plato’s concept of number and the Theory of Forms, showing that Plato’s distinctions do not easilytranslate 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-ematicae17 (1999), 289–311. In Part I, this paper is “a broad and comprehensive historical survey” of resultsrelating Ramanujan’s claim concerning the number of either squares or sums of squares in a given interval. In PartII, the authors provide improvements of some of these results and several connections to other parts of numbertheory. See the review by S. L. Segal inMathematical Reviews2001c:11103. (JA) #28.3.128

Movchan, A. B. Contributions of V. G. Maz’ya to Analysis of Singularly Perturbed Boundary Value Prob-lems, in Jurgen Rossman, Peter Takac, and Gunther Wildenhain, eds.,The Maz’ya Anniversary Collection, Basel:Birkhauser, 1999, vol. 1, pp. 201–212. Reviews the contributions made by Maz’ya and his colleagues to thedevelopment 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. WhatMueller calls “geometrical chemistry” in Plato’sTimaeushas been thought of as a predecessor to mathematicalphysics. Mueller proposes that we view it instead “as part of a metaphysical conception of the physical world asdependent on a transcendental world through the intermediary of mathematics.” (GVB) #28.3.130

Mueller, William. Reform Now, before It’s Too Late!American Mathematical Monthly108 (2001), 126–143.Today’s clamor for reform of mathematical teaching in the U.S. may usefully be seen against the very similardebates in the 1890s, about teaching and about the nature of mathematics itself, recorded in Cajori’sTeaching andHistory 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 andJan Wolenski,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 mathemati-cians.” See the review by Leon Harkleroad inMathematical Reviews2001c:03007. (JA) #28.3.132

Nagaoka, Ryosuke; Barrow-Green, June; Bartolini Bussi, Maria G.; Isoda, Masami; van Maanen, Jan; Michalow-icz, Karen Dee; Ponza, Marıa Victoria; and Van Brummelen, Glen R. Non-standard Media and Other Resources,


in #28.3.59, pp. 329–370. The integration of history is not confined to traditional teaching delivery methods, butcan 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 numbersup to the first decade of the 20th century. “Issues of computational interest are largely excluded.” It has over3000 entries in the bibliography! See the review by D. R. Heath-Brown inMathematical Reviews2001c:11098.(JA) #28.3.134

Nauenberg, Michael. See#28.3.44.

Navarro de Zuvillaga, Javier. L’Influence des Traites de Desargues dans les Traites Espagnols, in Jean Dhombresand Joel Sakarovitch, eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 313–328. Navarro de Zuvillagastudies the influence of Desargues’s work on the Spanish authors in perspective, stereotomy, and gnomonics. Heestablishes that, as regards perspective and stereotomy, there exists a thread which leads to Desargues, even if it isa feeble and indirect thread; this influence is present in Thomas Vincente Tosca’s work (1713) through Deschalesand in Benito Bails’s work (1779) through Frezier and La Hire. As regards gnomonics, the Spanish had a strongtradition 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 Profitabilityand Pleasure,History of Science37 (1999), 151–178. The rhetorical strategies pursued by English mathematicalpractitioners 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 MathematiciansPublishTheir Analyses? In #28.3.193, pp. 139–157. Argues thatanalyses were a tool for the presentation of results, rather than (as commonly understood) a heuristic tool fordiscovery. (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 “generalequilibrium theory as the unifying element.” See the review by Erwin Klein inMathematical Reviews2001c: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 Chineseastronomy 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 andthe Canon of Mathematical Simplicity,Studies in the History and Philosophy of Modern Physics31 (2000),135–170. Einstein did not develop his later Platonism, believing that true laws of nature were discovered byseeking 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 B30 (10) (1999), 2989–3001. A discussionof Infeld’s cosmology 50 years ago and the development of cosmology since. See the review by Markku Lehto inMathematical Reviews2001b:83113. (TBC) #28.3.141

Novikov, S. P. Surgery in the 1960s, in Sylvain Cappell, Andrew Ranicki, and Jonathan Rosenberg, eds.,Surveyson 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)


conjecture and HermitianK -theory.” See the review by Mikiya Masuda inMathematical Reviews2001c: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-Francois. Le Style de Desargues: L’Observation Associee `a la Theorie pour Placer le Style d’uneCadran Solaire, in Jean Dhombres and Joel Sakarovitch, 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 theaxis of a cone of revolution, noting three of its generatrices. The author also discusses Curabelle’s criticism asregards 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 Debateamong Nieuwentijt, Leibniz and Hermann [in Italian], in Marco Panza and Clara Silvia Roero, eds.,Geometry,Fluxions and Differentials[in Italian], Naples: La Citta del Sole, 1995, pp. 397–441. The author gives a carefulanalysis of Jacob Hermann’sResponsioto Nieuwentijt’sConsiderationes secundae circa calculi differentialisprincipia (1696). The author argues that Hermann’s work is a collective work of the Leibnizians. See the reviewby Massimo Galuzzi inMathematical Reviews2001b: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 Logic3(1–2) (1998), 17–34. The German algebraist of logic, Ernst Schroder, considered Hugh MacColl to be one of hismost 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 Inedits Concernant Desargues, in Jean Dhombres and Joel Sakarovitch, eds.,Desargueset son Temps, Paris: Blanchard, 1994, pp. 125–153. Picolet publishes 10 of the 26 documents concerning Desarguesand 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 andthat 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 Ingenieur, in Jean Dhombres and Joel Sakarovitch, eds.,Desargues et sonTemps, Paris: Blanchard, 1994, pp. 413–422. Picon provides evidence of Desargues as an engineer, whose maincontribution is the water raising machine, where he combined geometrical science and mechanical ingenuity tosolve the problem of friction; Philippe de La Hire’s research on the epicycloid originated with the same problemand, according to the author, Desargues can be considered his main inspiration. (AF) #28.3.147

Pier, Jean-Paul. L’Analyse Mathematique: Un Concept `a Geometrie Variable et a Caractere synthetique [Math-ematical Analysis: A Concept with Variable Geometry and Synthetic Character], inTravaux MathematiquesFasc. XI, Luxembourg: Centre Universitaire de Luxembourg, 1999, pp. 139–148. “The author examines thechanging meanings of ‘analysis’ and ‘algebra’ in various periods of history.” See the review by Burnett Meyer inMathematical Reviews2001c:01007. (JA) #28.3.148

Pinault, Madeleine. L’Etude de la Perspective dans l’Histoire de Saint Etienne de Laurent de la Hyre, in JeanDhombres and Joel Sakarovitch, eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 249–262. Pinaultstudies 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 thispictorial cycle follows from the architecture and the executive technique, but also from the perspective conceptunder the drawings. (AF) #28.3.149

Pitombeira de Carvalho, Joao.See#28.3.55, #28.3.175, #28.3.188, and #28.3.206.


Poincare, 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 anintroduction by Ferdinand Verhulst, Utrecht: Epsilon Uitgaven, 1998, ii+152 pp., BF 550. A biographical sketchof Poincare’s life and translations into Dutch of nine of Poincare’s philosophical and popular essays. See thereview by Eduard Glas inMathematical Reviews2001c:01033. (JA) #28.3.150

Ponza, Marıa Victoria. See#28.3.123 and #28.3.133.

Potjekhinn, A. F. On the Evolution of the Relativity Principle from Copernicus to Einstein,Hadronic JournalSupplement14(3) (1999), 297–313. The author asserts that, using no mathematical symbols, it becomes necessaryto revise the physical contents of the basic principles of Einstein’s special and general relativity theories. See thereview by Abraham A. Ungar inMathematical Reviews2001b:83006. (TBC) #28.3.151

Pourciau, Bruce. Intuitionism as a (Failed) Kuhnian Revolution in Mathematics,Studies in the History andPhilosophy of Science31 (2000), 297–329. Kuhnian revolutions in mathematics are logically possible, actuallypossible, and historically possible. Intuitionism is an example, in the sense that a shift from a classical conceptionof mathematics to an intuitionist one would be incommensurable (that is, some classical statements would becomeunintelligible). (JGF) #28.3.152

Pourciau, Bruce. Newton and the Notion of Limit,Historia Mathematica28(2001), 18–30. From certain proofsin the Principia it is apparent that Newton, not Cauchy, was first to present an epsilon argument, and that hisunderstanding 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 re-quires didactical reflection. A crucial area to explore and analyze is the relation between how students achieveunderstanding 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 ofPhilosophical Logic3 (1–2) (1998), 35–58. Offers an interpretation of MacColl’s proposals on the role of ontologyin logics: “in an argumentation, it sometimes makes sense to restrict the use and introduction of singular terms inthe context of quantification to a formal use of those terms. That is, the Proponent is allowed to use a constant iffthis 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 Samso-Moya inMathematical Reviews2001b:01004.(TBC) #28.3.156

Read, Stephen. Hugh MacColl and the Algebra of Strict Implication,Nordic Journal of Philosophical Logic3 (1–2) (1998), 59–83. This analysis of MacColl’s methods shows that “MacColl’s model logic is in fact thelogic 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 VictorKatz, 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 figuresthroughout 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, andA. Quiros, eds.,Resolution of Singularities, Basel: Birkhauser, 2000, pp. 533–537. A description of attempts inthe late 1940s and 1950s to “construct” the resolution of singular varieties. See the review by Piotr Jaworski inMathematical Reviews2001c: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


Association of America, 1995, pp. 123–134. Argues that history should interact closely with the mathematicaltopics 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+334pp. This book begins with a thorough study of the 12 Old Babylonian coefficient lists and it also presents copies andtransliterations of other texts, many of which have only been partly investigated in past studies. These exampleslead to “a discussion of the role of mathematics in administration and education in Old Babylonian times.” Seethe review by K.-B. Gundlach inMathematical Reviews2001c: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], inMarco Panza and Clara Silvia Roero, eds.,Geometry, Fluxions and Differentials[in Italian], Naples: La Citta delSole, 1995, pp. 353–395. The author studies the geometrical aspect of the differential calculus in the works ofLeibniz and other geometers of his time. See the review by Bernard Rouxel inMathematical Reviews2001b: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 desElementsd’Euclide,Archive for History of Exact Sciences55 (2001), 221–295. Euclid’sElementshas the richest textual traditionof all ancient Greek mathematics, not least because of the range of ancient and mediaeval versions and lan-guages: 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 richArabic textual tradition. (JGF) #28.3.163

Rosenfeld, Boris A.; and Youschkevitch, Adolf P. Geometry, in Roshdi Rashed and Regis Morelon, eds.,En-cyclopedia of the History of Arabic Science, London: Routledge, 1996, vol. 2, pp. 447–494. A nice survey thatindicates the breadth of medieval Arabic contributions to geometry and how those contributions fit between thegeometrical 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 inMathematical Reviews2001b:01005. (TBC) #28.3.164

Rottoli, Ernesto. See#28.3.83.

Rouxel, Bernard. See#28.3.162.

Rowe, David E. Episodes in the Berlin–Gottingen Rivalry, 1870–1930,Mathematical Intelligencer22(1) (2000),60–69. A detailed description of the mathematical scenes at the Universities of Berlin and Gottingen leading upto the supremacy of Gottingen over 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 ExactSciences54 (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 theappearances of 1680–81.” (GVB) #28.3.166

Ruiz, Angel; and Barrantes, Hugo. La Reforma Liberal y las Matematicas en la Costa Rica del Siglo XIX [TheLiberal Reform and Mathematics in 19th-Century Costa Rica],LLULL 23 (2000), 145–171. The 1880s educa-tional 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 Stereotomique de Desargues, in JeanDhombres and Joel Sakarovitch, eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 363–370. Saint Aubinemphasizes the great number of treatises devoted to stereotomy and the large number of architectural buildingswith stairs on freestone vaults during the 17th century. According to him this phenomenon looks like a reactionby a guild which fears losing its prerogative and wishes to prove its practical ability. He also compares othercontemporaneous authors’ ideas, M. Jousse’s, F. Derand’s, and A. Bosse’s, the latter being Desargues’s scholarpar excellence. (AF) #28.3.168


Sakarovitch, Joel. Le Fascicule de Stereotomie: Entre Savoir et Metiers, la Fonction de l’Architecte, in JeanDhombres and Joel Sakarovitch, eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 347–362. Sakarovitch’scontribution 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 geometricaldefinition is a cylinder with a nonhorizontal axis. Sakarovitch explains the character of this tract, its methods, andwhy it makes difficult reading. The last paragraph is devoted to the polemics between Curabelle and Desarguesregarding 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],Quipu10 (1993), 223–242. “The author details the mathematical contents of twenty Latin American periodicalspublished in the latter half of the eighteenth century.” See the review by Michael A. B. Deakin inMathematicalReviews2001c: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-mento61 (1999), 49–57. “The almost forgotten contributions of L. Kronecker and W. Dyck are illustrated byvarious specific results on the Kronecker characteristic, the degree of vector fields, indices of singularities andrelated topics.” See the review by Wolfgang Kuhnel inMathematical Reviews2001c:57004. (JA) #28.3.171

Samso-Moya, Julio. See#28.3.156 and #28.3.210.

Sanchez Ron, Jose Manuel. Cincel, Martillo y Piedra. Historia de la Ciencia en Espana (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 Teixid´o Gomez inLLULL 23 (2000),217–220. (VA) #28.3.172

Santos del Cerro, Jesus. Una Teorıa Sobre la Creacion del Concepto Moderno de Probabilidad: AportacionesEspanolas [A Theory on the Establishment of the Modern Concept of Probability: Spanish Contributions],LLULL23 (2000), 431–450. The author contends that probabilistic thinking stems from Aristotle, passing through philo-sophical and theological considerations, based mostly on games of chance, of Carneades, Cicero, Augustine,Thomas Aquinas, and Spanish theologians (Concina, Medina, Vasquez), whose moral probabilism was absorbedinto 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 BetweenHeinrich Scholz and Polish Logicians],History and Philosophy of Logic20 (1999), 97–109. Based on recentlydiscovered 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 inMathematicalReviews2001c:03008. (JA) #28.3.174

Schubring, Gert; Cousquer,Eliane; Fung, Chun-Ip; El Idrissi, Abdellah; Gispert, Helene; Heiede, Torkil; Ismael,Abdulcarimo; Jahnke, Hans Niels; Lingard, David; Nobre, Sergio; Phillippou, George; Pitombeira de Carvalho,Joao; 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 ofcurrent teachers, has been a theme of international concern over much of the past century. Examples of currentpractice from many countries, for training teachers at all levels, enable us to begin to learn lessons and pressahead 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 al-gebra, from his unpublished papers, with the form in which it appears in the posthumously printedArs analyticaepraxis of 1631, shows that the latter was a very inadequate and distorted account of Harriot’s achievements indeveloping the theory of equations. (JGF) #28.3.176


Seroglou, Fanny; and Koumaris, Panagiotis. The Contribution of the History of Physics in Physics Education: AReview,Science and Education10 (2001), 153–172. A classification and comparative study of some 60 proposalsabout the contribution of the history of physics to physics education that have been designed and/or carried outas part of either research or curriculum development during the 20th century. A chart summarizes and locates theproposals 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 isintended 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,Cartographica35 (3–4) (1998), 1–10. Although now obscured by the legacy of later 16th-century explorers such as Drake andRaleigh, Dee’s cartographic output brought together advanced science and sophisticated rhetoric and played animportant 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 Publicationson Probability Theory in Russian Editions [in Russian],Teoriya VeroyatnosteYi ee Primeneniya44 (2) (1999),241–248; English translation inTheory of Probability and its Applications44 (2) (2000), 225–230. The authorsketches the foundation and early history of the Imperial St. Petersburg Academy of Sciences, its structure, itsfirst members, and its journals. See the review by Eberhard Knobloch inMathematical Reviews2001b:01011.(TBC) #28.3.180

Sibbett, Trevor. Early Insurance in and around the Royal Exchange, in #28.3.5, pp. 62–76. Insurance and themoney it generates made an important contribution to the early years of Gresham College (and still does, sinceGresham College is funded from rents on the Royal Exchange building). John Graunt, the first student of mortalitytables, lived in a lane near Lombard Street, and William Petty, the developer of political arithmetic, was thirdGresham 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 Science56 (1999), 433–449. While he was in Groningen (1695–1715), JohannBernoulli expounded his ideas about the infinitely large and the infinitely small in mathematics; included is a dis-cussion of his correspondence with Leibniz about infinitesimals in the latter’s calculus. See the review by BurnettMeyer inMathematical Reviews2001c: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, Clovis Pereira da. Manoel Amoroso Costa: O Continuador da Obra Matematica de Otto de AlencarSilva [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 developmentof 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 Joel Sakarovitch, eds.,Desargueset son Temps, Paris: Blanchard, 1994, pp. 341–346. Sinisgalli and Vastola work out an historical researchon 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’sinstructions, the authors prove the agreement with the theory and so the validity of Desargues’s gnomonics.(AF) #28.3.184


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 teachingas a unifying idea. The historical development of the concept can be incorporated into teaching at various levelsfrom 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, OttoBekken, 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 primarysource material. (GVB) #28.3.187

Siu, Man-Keung; Bagni, Giorgio T.; Correia de Sa, Carlos; FitzSimons, Gail; Fung, Chun-Ip; Gispert, Helene;Heiede, Torkil; Horng, Wann-Sheng; Katz, Victor; Kronfellner, Manfred; Krysinska, Marysa; Lakoma, Ewa;Lingard, David; Pitombeira de Carvalho, Joao; Rodriguez, Michel; Schneider, Maggy; Tzanikis, Constantinos;and Zhang, Dian Zhou. Historical Support for Particular Subjects, in #28.3.59, pp. 241–290. Specific examplesof using historical mathematics in the classroom indicate ways in which the teaching of particular subjects maybe 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 7of Book II of thePrincipia concerns Newton’s attempts to combine mathematical solutions for motion in resistingmedia with experimental results in order to reach conclusions about the resistance forces. Between the first and sec-ond editions of thePrincipiaNewton 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 RoyalSociety54 (2000), 333–341. A paper by James Wood (1760–1839) in the Royal Society’sPhilosophical Trans-actionsfor 1798 predates Gauss’s 1799 proof of the fundamental theorem of algebra. Although Wood’s proof isincomplete, 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. Problemes Lineaires dans leCompendy de la Praticque des Nombresde Barthelemy deRomans et Mattieu Prehoude (1471): Une Approche Nouvelle Basee sur des Sources Proches duLiber abbacideLeonard de Pise,Historia Mathematica27(2000), 362–383. The 1471Compendy, one of a number of commercialarithmetics produced in southern France during this period, deals with general problem-solving methods for onlya few types of problem. It drew on sources close to Leonardo of Pisa’s 1202Liber abbaciand thus sheds new lighton 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 theRoyal Society54 (2000), 293–344. During the 1650s, William Brouncker (1620–1685) worked closely with JohnWallis (1616–1703) on some original and unusual mathematics. Although Brouncker is almost forgotten in thiscontext (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

Stefanescu, Doru. See#28.3.111.

Suppes, Patrick; Moravcsik, Julius M.; and Mendell, Henry, eds.Ancient and Medieval Traditions in the ExactSciences: Essays in Memory of Wilbur Knorr, Stanford, CA: CSLI Publications, 2000, xi+ 227 pp. A collection


of papers emerging from a 1998 conference at Stanford to honor the memory of Wilbur Knorr. The individualpapers are abstracted separately. (GVB) #28.3.193

Swetz, Frank J. An Historical Example of Mathematical Modeling: The Trajectory of a Cannonball, in FrankSwetz, 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 valuableclassroom example of the need to balance pragmatic concerns with theoretical considerations, as well as providinginterest. (JGF) #28.3.194

Swetz, Frank J. Trigonometry Comes out of the Shadows, in Frank Swetz, John Fauvel, Otto Bekken, BengtJohansson 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 thestudy 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 throughhistory is to have students solve problems that interested earlier mathematicians. Example are given from Chinese,Babylonian, and Greek mathematics. (JGF) #28.3.196

SzalÃajko, Kazimierz. What Was Written Fifty Years Ago about Lwow Mathematicians and Not Only aboutLwow Mathematicians [in Polish],Zeszty Naukowe Uniwerstetu Opole Matematyka30 (1997), 169–180. A de-scription of the beginnings of the Wroclaw branch of the Polish Mathematical Society from October 1945 until thecongress in Krakow in May 1947. See the review by Jaroslav Zemanek inMathematical Reviews2001c:01041.(JA) #28.3.197

Taimina, Daina. See#28.3.83.

Tanaka, Setsuko. Boltzmann on Mathematics,Synthese119 (1–2) (1999), 203–232. Boltzmann’s lectures onnatural philosophy contained mathematical content. Behind his mathematics stood his support of Darwinian evo-lution; he supported non-Euclidean geometry; and attempted to “refute Kant’s static a priori categories and hisidentification of space with ‘non-sensuous intuition’.” (GVB) #28.3.198

Taton, Rene. A la Redecouverte des Oeuvres de Girard Desargues, in Jean Dhombres and Joel Sakarovitch, eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 463–475. An essay by Taton devoted to the discovery andto the editions of Desargues’s scientific, technical and polemical works, concludes the volume. The importanceand the value of Poudra’s edition (1864), but also the following considerable progresses in the knowledge ofDesargues’s original works, show up. (AF) #28.3.199

Taton, Rene. Desargues et le Monde Scientifique de sonEpoque, in Jean Dhombres and Joel Sakarovitch, eds.,Desargues et son Temps, Paris: Blanchard, 1994, pp. 23–53. Taton sketches out a picture of the Parisian scientificand 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 mostimportant mathematicians of his epoch, but who was also strongly opposed when he tried to establish graphictechniques on theoretical bases. (AF) #28.3.200

Thiele, Rudiger. Felix Klein in Leipzig: 1880–1886,Mitteilungen der Deutschen Mathematiker-Vereinigung102(2000), 69–93. The creation of a chair assigned to geometry in Leipzig and the decision to call Klein was ofgreat 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 themathematical work that Klein did after his collapse in 1882/1883 is underestimated, and in general his organizingefforts 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 derDeutschen Mathematiker-Vereinigung,4 (1999), 43–52. Tietz gives a detailed account of his life as a non-Aryan


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 inMathematical Reviews2001c:01037.(JA) #28.3.202

Tikhomirov, V. M. Letters “Poste Restante” [in Russian],Vestnik Rossiıskaya Akademiya Nauk69 (3) (1999),243–245. A commentary on Kolmogorov accompanying the publication of two letters written by Kolmogorov toAleksandrov 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 Logic7 (2) (1997), 160–187. The author relates some of his experiences as a mathematical logician interested in thework of Church and others during the Stalin period and his interactions with Yanovskaya. See the review by RogerL. Cooke inMathematical Reviews2001b: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 Porismsand Other Items on This Subject, London: Springer-Verlag, 2000, x+274 pp. This book is an annotated translationinto English of Robert Simson’s (1687–1768) posthumously published (1776) treatise on Euclid’s porisms andthe work of Pappus, Fermat, and others on these theorems. See the review by F. J. Papp inMathematical Reviews2001c:01018. (JA) #28.3.205

Tzanakis, Constantinos; Arcavi, Abraham; Correia de Sa, Carlos; Isoda, Masami; Lit, Chi-Kai; Niss, Mogens;Pitombeira de Carvalho, Joao; Rodriguez, Michel; and Siu, Man-Keung. Integrating History of Mathematics inthe Classroom: An Analytic Survey, in #28.3.59, pp. 201–240. An analytical survey of how history of mathemat-ics has been and can be integrated into the mathematics classroom provides a range of models for teachers andmathematics 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.

Valdes Castro, Concepcion. La Primera Publicacion Periodica Cubana de Ciencias Fısico-Matematicas (1942–1959): Noticias y Consideraciones [The First Cuban Periodical on Physics and Mathematics (1942–1959),LLULL23 (2000), 411–468. From the author’s abstract: “In this paper we study the main characteristics and the evolutionof theRevista de la Sociedad Cubana de Ciencias Fısicas y Matematicasover 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 theDutch Signific Circle.” See the review by Volker Peckhaus inMathematical Reviews2001c:03004. (JA) #28.3.208

Van Maanen, Jan. Alluvial Deposits, Conic Sections, and Improper Glasses, or History of Mathematics Appliedin the Classroom, in Frank Swetz, John Fauvel, Otto Bekken, Bengt Johansson, and Victor Katz, eds.,Learn fromthe Masters, Washington: Mathematical Association of America, 1995, pp. 73–91. Historical research can yielddirect possibilities for classroom activities to provide a stimulus for learning, here illustrated in three specificinstances. Using history in the classroom requires much energy, but the profits are high: ordinary lessons requireless 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 Mechaniques (13eme—14eme siecles)[Straight Motion, Curved Motion. II. Mechanics (13th–14th centuries)],Archives Internationales d’Histoire des


Sciences48 (1998), 255–268. This is a continuation of the author’s Part I [Archives Internationales d’Histoire desSciences47(1997), 271–294]. Rectilinear and circular motions of falling weights are studied in medieval works onmechanics, especially works on the lever and the balance. See the review by Julio Samso-Moya inMathematicalReviews2001c: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 additionto his mathematics the biographer includes Hua’s difficult childhood, his political experiences, and his successin popularizing mathematics with the public. “An inspiration to anyone who has ever thought about becoming amathematician.” See the review by Joseph W. Dauben inMathematical Reviews2001b: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, NewYork: W. W. Norton, 1998, 380 pp. “This autobiography ... describes important events in the history of 20th centuryphysics [especially nuclear fission, quantum field theory, and gravitation as the geometry of the universe], to whichWheeler has made significant contributions.” See the review by H. Treder inMathematical Reviews2001c: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 setout to solve some problems for the astronomers, had by 1685 begun to uncover the staggeringly systematic andmathematical character of the System of the World. (JGF) #28.3.214

Wolenski, Jan. The Reception of the Lvov–Warsaw School, in Katarzyna Kijania-Placek and Jan Wolenski,TheLvov–Warsaw School and Contemporary Philosophy, Dordrecht: Kluwer, 1998, pp. 3–19. A discussion of theLvov School, the Lvov–Warsaw School, and the Warsaw School of Logic. See the review by Robert S. D. Thomasin Mathematical Reviews2001c:01042. (JA) #28.3.215

Xu, Zelin. Takebe Katahiro and Romberg Algorithm,Historia Scientiarum9 (1999), 155–164. “A method forthe acceleration of convergence described by Katahiro in 1722 is described” and applied to the evaluation ofπ to40 decimal places. See the review by A. D. Booth inMathematical Reviews2001c:01009. (JA) #28.3.216

Ycart, B. Le Proces desEtoiles entre de Moivre et Laplace,Cubo 3 (1) (2001), 1–11. On the 18th-centuryhistory 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 toSouth 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.