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The purpose of this department is to give sufficient information about the subject matter of each publication to enable users to decide whether to read it. It is our intention to cover all books, articles, and other materials in the field. Books for abstracting and eventual review should be sent to this department. Materi- als should be sent to Glen Van Brummelen, Bennington College, Bennington, VT 05201, U.S.A. (E-mail: [email protected]) Readers are invited to send reprints, autoabstracts, corrections, additions, and notices of publications that have been overlooked. Be sure to include complete bibliographic information, as well as transliteration and translation for non-European languages. We need volunteers willing to cover one or more journals for this department. In order to facilitate reference and indexing, entries are given abstract numbers which appear at the end following the symbol #. A triple numbering system is used: the first number indicates the volume, the second the issue number, and the third the sequential number within that issue. For example, the abstracts for Volume 20, Number 1, are numbered: 20.1.1, 20.1.2, 20.1.3, etc. For reviews and abstracts published in Volumes 1 through 13 there are an author index in Volume 13, Number 4, and a subject index in Volume 14, Number 1. The initials in parentheses at the end of an entry indicate the abstractor. In this issue there are abstracts by Francine Abeles (Kean, NJ), Victor Albis (Bogotá, Colombia), Timothy B. Carroll (Ypsilanti, MI), Patti Wilger Hunter (Westmont, CA), Calvin Jongsma (Sioux Center, IA), Albert C. Lewis (Indianapolis, IN), and Glen Van Brummelen.

Abraham, George. See #31.4.24.

Acerbi, F. Drowning by multiples. Remarks on the ﬁfth book of Euclid’s Elements, with special emphasis on prop. 8, Archive for History of Exact Sciences 57 (3) (2003), 175–242. Proposition 8 of the ﬁfth book is analyzed from the point of view of Greek and Arabic–Latin linguistics through its various translations. See the review by Richard L. Francis in Mathematical Reviews 2004d:01003. (ACL) #31.4.1

Adams, William J. See #31.4.171.

0315-0860/2004 Published by Elsevier Inc. doi:10.1016/j.hm.2004.08.002 Historia Mathematica 31 (2004) 502–530 503

Aghayani-chavoshi, Jafar. Omar Khayyam, theoretician of cubic equations [in Persian], Tarikh-e- Elm 1 (2003), 9–26. Omar Khayyam’s discussion of cubic equations, containing a geometric solution via conic sections, attempted to arrive at a consistent theory of cubics. (GVB) #31.4.2 Ahmedov, Ashraf; and Rosenfeld, Boris A. The mathematical treatise of Ulugh Beg, in Ekmeled- din Ihsano˙ glu˘ and Feza Günergun, eds., Science in Islamic Civilization, Istanbul:˙ Research Centre for Islamic History, Art & Culture, IRCICA, 2000, pp. 143–150. The authors analyze a treatise written in Arabic, entitled Risala¯ f¯ı istikhraj¯ jayb daraja wah¯ . ida (Treatise on the Determination of the Sine of One Degree), and attributed to Kadizade el-Rum¯ı. They argue that the author is actually Mirza Muh. ammad ibn Shahrukh ibn Timur Ulugh Beg Guragan (1394–1449), founder of the Samarkand astronomical ob- servatory. See the review by Emilia Calvo in Mathematical Reviews 2004d:01006. (ACL) #31.4.3 Alexander, Amir R. Exploration mathematics: The rhetoric of discovery and the rise of infinitesimal methods, Configurations 9 (1) (2001), 1–36. In the first part the ideas of Christopher Clavius and other scholars about the truth of mathematical propositions are presented. The author then presents works of Cavalieri, Galileo, Torricelli, Stevin, Guldin, Wallis, and other scientists on the theory of indivisibles and describes the role of indivisibles in the mathematics of exploration. See the review by DoruStef ¸ anescu˘ in Mathematical Reviews 2004d:01009. (ACL) #31.4.4 Ali-Ahyaie, Mashallah. A discussion about 2820-year cycle in the solar Hegira calendar [in Persian], Tarikh-e-Elm 1 (2003), 39–52. Discusses a proposed cycle for determining leap years in this calendar, and its “scientific and historical implications.” (GVB) #31.4.5 Alsina Catala, Claudi; and Gómez Serrano, Josep. Gaudí, geometrically [in Spanish], La Gaceta de la Real Sociedad Matemática Española 5 (3) (2002), 523–539. Antoni Gaudí Cornet’s (1852–1926) “vision of geometry is the result of boundless three-dimensional creativity based on systematic geometric experimentation.” (GVB) #31.4.6 Alvarez, Carlos. Two ways of reasoning and two ways of arguing in geometry. Some remarks concerning the application of figures in Euclidean geometry, Synthese 134 (1–2) (2003), 289–323. Deals with some of the “weak spots” in Euclid’s plane geometry and Hilbert’s attempts to repair some of them. See the review by Victor V. Pambuccian in Mathematical Reviews 2004b:01005. (GVB) #31.4.7 Amiras, Lucas. Lobatschefskis Anfangsgründe der Geometrie als Figurentheorie [Lobachevskii’s basic principles of geometry as a theory of spatial figures], Philosophia Naturalis 40 (1) (2003), 127– 153. Provides historical support for establishing the foundations of geometry in a way different from the usual axiomatic approach. This paper is influenced particularly by the constructivist school of Dingler– Lorenzen and its application to pedagogy. See the review by Albert C. Lewis in Mathematical Reviews 2004b:01020. (GVB) #31.4.8 Ansari, S.M. Razaullah. See #31.4.123. Antognazza, Maria Rosa. Leibniz and the post-Copernican universe. Koyré revisited, Studies in History and Philosophy of Science 34A (2) (2003), 309–327. The author proposes a revised presentation of Leibniz’s cosmological views. See the review by Eberhard Knobloch in Mathematical Reviews 2004e:01026. (TBC) #31.4.9 504 Historia Mathematica 31 (2004) 502–530

Archibald, Thomas. Priority claims and mathematical values: Disputes over quaternions at the end of the nineteenth century, Matematisk-fysiske Meddelelser. Det Kongelige Danske Videnskabernes Selskab 46 (2) (2001), 255–269. Examines the priority dispute between Tait and Klein over who discovered quaternions, Hamilton or Gauss. See the review by Capi Corrales-Rodriganez in Mathematical Reviews 2004f:01009. (CJ) #31.4.10

Asper, Markus. Mathematik, Milieu, Text. Die frühgriechische(n) Mathematik(en) und ihr Umfeld [Mathematics, milieu, text. Early Greek mathematics and its environment], Sudhoffs Archiv 87 (1) (2003), 1–31. Concentrates on the historical milieu of Greek mathematics, rather than those more well-known aspects that might be considered to be timeless, such as general theorems and axiomatic-deductive procedures. (GVB) #31.4.11

Bagheri, Mohammad. See #31.4.128.

Bain, Jonathan. See #31.4.54.

Bar-Am, Nimrod. A framework for a critical history of logic, Sudhoffs Archiv 87 (1) (2003), 80–89. A preliminary attempt to tell the history of logic as a critical process. (GVB) #31.4.12

Barbeau, E.J. See #31.4.164.

Barbieri-Viale, Luca. See #31.4.30.

Barney, Steven. See #31.4.157.

Bazhanov, V.A. I.E. Orlov—Logician, philosopher, and scientist. Peculiarities of scientiﬁc research [in Russian], in A.S. Karpenko, ed., Logical Investigations. No. 9 [in Russian] (Moscow: “Nauka,” 2002), pp. 32–54. Orlov (1886–1936), a pioneer of relevant logic, was inﬂuenced by the sociopolitical climate of the 1920s and 1930s. (GVB) #31.4.13

Behr, Christoph G. See #31.4.106.

Beligiannis, Apostolos D. See #31.4.87.

Bellhouse, David. See #31.4.193.

Bernard, Alain. Sophistic aspects of Pappus’s Collection, Archive for History of Exact Sciences 57 (2) (2003), 93–150. A translation of a puzzling passage in the third book of Pappus’s Collection is explained by a comparison with sophistic practice. See the review by Glen R. Van Brummelen in Mathematical Reviews 2004b:01007. (GVB) #31.4.14

Berndt, Bruce C. The problems solved by Ramanujan in the Journal of the Indian Mathematical Society, in A.K. Agarwal, Bruce C. Berndt, Christian F. Krattenthaler, Gary L. Mullen, K. Ramachandra, and Michel Waldschmidt, eds., Number Theory and Discrete Mathematics (Basel: Birkhäuser, 2002), pp. 189–200. These eight problems, presented here, apparently motivated some of the entries in Ra- manujan’s notebooks. (GVB) #31.4.15 Historia Mathematica 31 (2004) 502–530 505

Berndt, Bruce C.; and Reddi, C.A. Two exams taken by Ramanujan in India, American Mathematical Monthly 111 (4) (2004), 330–339. The exams reproduced here, taken by Ramanujan in 1903 and 1907, cover arithmetic, geometry, algebra, and trigonometry. (GVB) #31.4.16 Beukers, Frits; and Reinboud, Weia. Snellius Accelerated, Nieuw Archief voor Wiskunde (5) 3 (1) (2002), 60–63. Describes Snell’s 1621 demonstration that Archimedes’ method for determining the value of π could be improved, and offers two alternative algorithms. See the review by Ivor Grattan-Guinness in Mathematical Reviews 2004b:01032. (GVB) #31.4.17 Beyer, W.A.; and Zardecki, Andrew. The early history of the Ham Sandwich Theorem, American Mathematical Monthly 111 (1) (2004), 58–61. A note in an obscure pre-WWII journal clarifies the origins of this theorem from measure theory: Steinhaus posed the conjecture and Banach, not Ulam, gave the first proof. (GVB) #31.4.18 Bican, L. See #31.4.37. Bkouche, Rudolf. La géométrie dans les premières années de la revue L’Enseignement Mathéma- tique, in #31.4.35, pp. 95–112. (GVB) #31.4.19 Bombal, Fernando. Laurent Schwartz, the mathematician who wanted to change the world [in Span- ish], La Gaceta de la Real Sociedad Matemática Española 6 (1) (2003), 177–201. A tribute to Schwartz’s work. (GVB) #31.4.20 Booth, A.D. See #31.4.27. Bos, Erik-Jan; and Vermeulen, Corinna. An unknown autograph letter of Descartes to Joachim de Wicquefort, Studia Leibnitiana 34 (1) (2002), 100–109. This letter, dated October 2, 1640, contains information concerning the abandoned project of publishing objections to the Discourse and Essays together with Descartes’s replies. (GVB) #31.4.21 Bourguignon, Jean-Pierre. René Thom. “Mathématicien et apprenti philosophe,” Bulletin of the American Mathematical Society 41 (3) (2004), 273–274. This brief “personal perspective” on Thom’s life and work introduces an issue of the Bulletin devoted to Thom’s interests. (GVB) #31.4.22 Bouzoubaâ Fennane, Khalid. Réflexions sur la principe de continuité à partir du commentaire d’Ibn al-Haytham sur la Proposition I.7 des Éléments d’Euclide, Arabic Sciences and Philosophy 13 (1) (2003), 101–136. An analysis of Ibn al-Haytham’s discussion of the intersection of circles which attempts to determine the extent to which Ibn al-Haytham was aware of a principle of continuity operating in his thinking. (GVB) #31.4.23 Bowen, Alan C. Simplicius and the early history of Greek planetary theory, Perspectives on Science 10 (2) (2002), 155–167. The author argues against taking Aristotle’s report about the Eudoxan and Cal- lippan accounts of the celestial motions and Simplicius’s interpretation of this report as starting points for understanding early Greek planetary theory. See the review by George Abraham in Mathematical Reviews 2004d:01004. (ACL) #31.4.24 Brackenridge, J. Bruce. Newton’s easy quadratures “omitted for the sake of brevity,” Archive for History of Exact Sciences 57 (4) (2003), 313–336. Considers Newton’s treatment of the inverse problem 506 Historia Mathematica 31 (2004) 502–530 of finding the orbit associated with a given central force. Also poses a reason that Newton adopted a geometrical mode of presentation over an analytical one in the Principia. See the review by Massimo Galuzzi in Mathematical Reviews 2004f:01004. (CJ) #31.4.25 Bréard, Andrea. See #31.4.31. Breger, Herbert. See #31.4.113. Brillinger, David R. John W. Tukey: His life and professional contributions, Annals of Statistics 30 (6) (2002), 1535–1575. An introductory article for a special issue of the journal devoted to Tukey’s life and work. (GVB) #31.4.26 Burks, Alice Rowe. Who Invented the Computer? The Legal Battle that Changed Computing His- tory, foreword by Douglas Hofstadter, Amherst, NY: Prometheus Books, 2003, 463 pp. This book is the latest contribution to the battle to establish John V. Atanasoff as the “inventor of the computer.” The text reads like an exciting court drama in which Atanasoff emerges as a straightforward person while Mauchly gives the impression either that he has so bad a memory that one wonders how he could survive in the modern world, or that he is not telling the truth. See the review by A.D. Booth in Mathematical Reviews 2004e:01001. (TBC) #31.4.27 Bussotti, P. On the genesis of the Lagrange multipliers, Journal of Optimization Theory and Applica- tions 117 (3) (2003), 453–459. Lagrange introduced his multipliers in the context of statics, to determine the general equations of equilibrium for problems with constraints. (GVB) #31.4.28 Byrne, John G. See #31.4.123. Calderón, Catalina. Riemann’s zeta function [in Spanish], Revista de la Academia de Ciencias Ex- actas, Fisicas Químicas y Naturales de Zaragoza (2) 57 (2002), 67–87. This article gives a brief survey of the central classical results on Riemann’s zeta function. This article is intended as a short and com- prehensive account of the most central ideas of Riemann and his successors. See the review by Gunter Dufner in Mathematical Reviews 2004e:11095. (TBC) #31.4.29 Calvo, Emilia. See #31.4.3. Cerezo, María. See #31.4.36 and #31.4.77. Chatterji, Srishti D. See #31.4.51. Chen, Rong Si. See #31.4.144. Chern, S.S. See #31.4.30. Chow, Wei-Liang. The Collected Papers of Wei-Liang Chow, edited by S.S. Chern and V.V.Shokurov, River Edge, NJ: World Scientific Publishing, 2002, xiv + 507 pp. Contains papers, biography, and bibliography of a major 20th-century algebraic geometer. See the review by Luca Barbieri Viale in Mathematical Reviews 2004f:01043. (CJ) #31.4.30 Chu, Pingyi. Remembering our grand tradition: The historical memory of the scientific exchanges between China and Europe, 1600–1800, History of Science 41 (2) (2003), 193–215. A historiographic Historia Mathematica 31 (2004) 502–530 507 study of the role of the early 19th-century collection Chourenzhuan (Biographies of Astronomers and Mathematicians) as “a trace of the collective reminiscence of a glorious ancient Chinese past.” See the review by Andrea Bréard in Mathematical Reviews 2004d:01005. (ACL) #31.4.31 Ciesielski, Krzysztof. See #31.4.49. Clavelin, Maurice. Galilée astronome philosophe [in French], in José Montesinos and Carlos Solís, eds., Philosophy on a Wide Scale [in Italian] (La Orotava: Fundación Canaria Orotava de Historia de la Ciencia, 2001), pp. 19–39. This article considers a period in Galileo’s career in which he could be regarded as an “astronomer–philosopher,” i.e., one who not only is concerned with observational data but also undertakes to develop an explanatory theory, thereby encroaching on territory that scholastic doctrine had traditionally assigned to philosophy. See the review by Douglas M. Jesseph in Mathematical Reviews 2004d:01011. (ACL) #31.4.32 Cobos Bueno, José M. La Asociación Española de Historiadores de la Ciencia: Francisco Vera Fer- nández de Córdoba [The Spanish Association of Historians of Science: Francisco Vera Fernández de Córdoba] [in Spanish], LLULL 26 (55) (2003), 57–81. The history of this former Association is presented, remarking on the role of Francisco Vera in its creation and development, as well as in the founding of the journal Archeion. (VA) #31.4.33 Cohen, Paul. The discovery of forcing, Rocky Mountain Journal of Mathematics 32 (4) (2002), 1071–1100. This is a picture of the author’s invention of the method of forcing in axiomatic set theory. He describes some of the earlier work of Gödel and others. See the review by E. Mendelson in Mathematical Reviews 2004e:03002. (TBC) #31.4.34 Cook, Donald. See #31.4.170. Coray, Daniel; Furinghetti, Fulvia; Gispert, Hélène; Hodgson, Bernard R.; and Schubring, Gert, eds. One Hundred Years of L’Enseignement Mathématique, Geneva: L’Enseignement Mathéma- tique, 2003, 336 pp. A collection of papers on mathematics education in the 20th century, emerging from a symposium held in Geneva in October 2000. The papers are listed separately as #31.4.19, #31.4.40, #31.4.63, #31.4.68, #31.4.78, #31.4.92, #31.4.99, #31.4.101, #31.4.107, #31.4.133, #31.4.136, #31.4.165, #31.4.176, and #31.4.181. (GVB) #31.4.35 Corrales-Rodriganez, Capi. See #31.4.10, #31.4.145, and #31.4.166. Corry, Leo. David Hilbert and his empiricist philosophy of geometry [in Spanish], Boletín de la Asociación Matemática Venezolana 9 (1) (2002), 27–43. The author distinguishes between a “narrow” and a “wide” sense of formalism, and he offers historical evidence that David Hilbert is formalist only in the former sense. See the review by María Cerezo in Mathematical Reviews 2004e:01035. (TBC) #31.4.36 Corry, Leo. See also #31.4.80. Coutinho, S.C.; and McConnell, J.C. The quest for quotient rings (of noncommutative Noetherian rings), American Mathematical Monthly 110 (4) (2003), 298–313. This work is devoted to A.W. Goldie’s contribution to mathematics, especially to the connections between some properties of rings and their quotient rings. It includes a history of fractions and quotient rings, a biography of Goldie, and a descrip- 508 Historia Mathematica 31 (2004) 502–530 tion of his work and its context. See the review by L. Bican in Mathematical Reviews 2004d:16001. (ACL) #31.4.37 Craik, Alex D.D. The logarithmic tables of Edward Sang and his daughters, Historia Mathematica 30 (1) (2003), 47–84. Studies the history and methods of calculation behind this monumental late 19th- century table of logarithms. See the review by Paul C. Pasles in Mathematical Reviews 2004b:01021. (GVB) #31.4.38 Csörgö, Miklós. A glimpse of the impact of Pál Erdös on probability and statistics, Canadian Journal of Statistics 30 (4) (2002), 493–556. The author gives a survey of the contributions of Pál Erdös to probability and statistics and discusses many of the developments which were inspired by Erdös. There is a bibliography of about 200 items. Topics include the Erdös–Kac invariance principle of 1946, the Darling– Erdös theorems, Erdös–Feller–Kolmogorov–Petrovski integral tests, Erdös–Renyi laws, path properties of Brownian motion, the probabilistic method, probabilistic number theory, and random graphs. See the review by U. Krengel in Mathematical Reviews 2004d:60003. (ACL) #31.4.39 D’Ambrosio, Ubiratan. Stakes in mathematics education for the societies of today and tomorrow, in #31.4.35, pp. 301–316. (GVB) #31.4.40 Dallal, Gerard E. See #31.4.193. Dauben, Joseph W. See #31.4.82 and #31.4.126. Davis, A.E.L. The mathematics of the area law: Kepler’s successful proof in Epitome astronomiae Copernicanae (1621), Archive for History of Exact Sciences 57 (5) (2003), 355–393. A mathematical and historical analysis of the law that the area swept out by the line connecting a planet to the Sun is a measure of the time taken. (GVB) #31.4.41 Davitt, Richard. See #31.4.141. Dawson, John W. Jr. See #31.4.185. De Boer, Reint. Theory of Porous Media. Highlights in Historical Development and Current State, Berlin: Springer-Verlag, 2000, xvi + 618 pp. This predominantly historical work on the laws of continuum mechanics and of flows through porous media, intended for engineers, analyzes the origins (in Euler, Daniel Bernoulli, Coulomb, and Reinhard Woltmann) and the classical era (from Cauchy to von Mises), and describes the decisive steps toward the present views (especially Fillunger, von Terzaghi, Biot, Heinrich, and Frenkel). See the detailed favorable review by Antonio Fasano in Mathematical Re- views 2004d:76098. (ACL) #31.4.42 Del Centina, Andrea. Corrigendum to “The manuscript of Abel’s Parisian memoir found in its entirety” [Historia Mathematica 29 (1) (2002), 65–69], Historia Mathematica 30 (1) (2003), 94–95. The author has come across material almost identical to four of the pages in “The manuscript of Abel’s Parisian memoir found in its entirety” and which are surely in Abel’s hand. See the review by Willard Parker in Mathematical Reviews 2004e:01032. (TBC) #31.4.43 Delve, Janet. The College of Preceptors and the Educational Times: Changes for British mathematics education in the mid-19th century, Historia Mathematica 30 (2) (2003), 140–172. Discusses the role Historia Mathematica 31 (2004) 502–530 509 played in mathematics education by the College of Preceptors. Influential voices included Whewell, de Morgan, and Tate. One effect of these debates was the introduction of entrance examinations at Oxford and Cambridge. (GVB) #31.4.44 Dempster, A.P. John W. Tukey as “philosopher,” Annals of Statistics 30 (6) (2002), 1619–1628. Tukey clarified the relation between drawing conclusions and making decisions, and “less successfully” attempted to deal with R.A. Fisher’s “fiducial argument.” (GVB) #31.4.45 Derbyshire, John. Prime Obsession. Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, Washington, DC: Joseph Henry Press, 2003, xvi + 422 pp. In this book, intended for a non- specialist audience, the odd-numbered chapters explain the mathematics while the even-numbered chapters discuss the history of the Riemann hypothesis. The reviewer in Mathematical Reviews 2004d:11001, Don Redmond, judges the history reasonably successful but finds the mathematical exposition less so and is doubtful that the author has answered the question of why the Riemann hypothesis is important. (ACL) #31.4.46 Derriennic, Yves. Pascal et les problèmes du chevalier de Méré. De l’origine du calcul des prob- abilités aux mathématiques financières d’aujourd’hui, Gazette des Mathématiciens 97 (2003), 45–71. Pascal’s reasoning with respect to the notion of martingale was analogous to that of the calculation of stock option pricing, especially the Black–Scholes formula. (GVB) #31.4.47 Drago, Antonino. See #31.4.134. Dufner, Gunter. See #31.4.29. Dym, Harry; and Katsnelson, Victor. Contributions of Issai Schur to analysis, in Anthony Joseph, Anna Melnikov, and Rudolf Rentschler, eds., Studies in Memory of Issai Schur (Boston: Birkhäuser, 2003), pp. xci–clxxxviii. A lengthy discussion of nine thematic areas in which Schur made substantial contributions to analysis. (GVB) #31.4.48 Dyugak, P. The “case” of Luzin and French mathematicians [in Russian], translated from the French by N.S. Ermolaeva, Istoriko-Matematicheskie Issledovaniya (2) 5 (40) (2000), 119–142. Presents seven letters between Sierpinski,´ Denjoy, and Lebesgue discussing how to deal with the Luzin affair and support Luzin, who was attacked by the Soviet regime in the 1930s for his non-Marxist opinions. See the review by Krzysztof Ciesielski in Mathematical Reviews 2004b:01056. (GVB) #31.4.49 Efron, Bradley. Robbins, empirical Bayes and microarrays, Annals of Statistics 31 (2) (2003), 366– 378. Herbert Robbins’s idea of empirical Bayes methods is making a comeback after 50 years. One of three historical articles in this issue of Annals of Statistics devoted to the memory of Robbins; see also #31.4.109 and #31.4.173. (GVB) #31.4.50 Ellise, George F.Š. See #31.4.106. Emmer, Michele. See #31.4.161. Español González, Luis. See #31.4.83. Estabrook, Frank B. See #31.4.106. 510 Historia Mathematica 31 (2004) 502–530

Euler, Leonhard. Lettres à une Princesse d’Allemagne sur Divers Sujets de Physique & de Philoso- phie [Letters to a German Princess on Various Topics of Physics and Philosophy], edited by Srishti D. Chatterji, Lausanne: Presses Polytechniques et Universitaires Romandes, 2003, xxx + 512 pp. Reprint- ing of Euler’s letters to a princess as a separate publication, accompanied by a brief introduction. See the review by Albert C. Lewis in Mathematical Reviews 2004f:01024. (CJ) #31.4.51 Ewing, John H. See #31.4.113. Fasano, Antonio. See #31.4.42. Fenster, Della Dumbaugh. Funds for mathematics: Carnegie Institution of Washington support for mathematics from 1902 to 1921, Historia Mathematica 30 (2) (2003), 195–216. Covers the Carnegie Institution from its inception through the terms of its first two presidents. (GVB) #31.4.52 Ferraro, Giovanni; and Panza, Marco. Developing into series and returning from series: A note on the foundations of eighteenth-century analysis, Historia Mathematica 30 (1) (2003), 17–46. Developing a function into an infinite series was carried out in the 18th century as a general result concerning the formal nature of the function and not as an issue of the convergence of the series. Transforming a function into an infinite power series was particularly useful and considered a synthetic procedure, while the inverse was considered an analytic procedure. The authors classify the synthetic and analytic strategies accepted in the 18th century. See the review by Niccolò Guicciardini in Mathematical Reviews 2004d:01017. (ACL) #31.4.53 Finocchiaro, Maurice A. Physical–mathematical reasoning: Galileo on the extruding power of ter- restrial rotation, Synthese 134 (1–2) (2003), 217–244. Presents Galileo’s four arguments responding to the anti-Copernican case that a rotating Earth would cause objects to be thrown off of it; also argues that Galileo did not completely separate mathematical and physical truth. See the review by Jonathan Bain in Mathematical Reviews 2004b:01016. (GVB) #31.4.54 Franci, Raffaella. An exact solution of the problem of the division points of stakes in a manuscript from the first half of the fourteenth century [in Italian], Bollettino di Storia delle Scienze Matematiche 22 (2) (2002), 253–265. Contains the text and analysis of the earliest known solution to a division of stakes problem, equivalent to that later treated by Fermat. See the review by Warren Van Egmond in Mathematical Reviews 2004f:01003. (CJ) #31.4.55 Francis, Richard L. See #31.4.1. Fraser, Craig G. See #31.4.134. Fredette, Raymond. Galileo’s De motu antiquiora. Notes for a reappraisal, in José Montesinos and Carlos Solís, eds., Philosophy on a Wide Scale [in Italian] (La Orotava: Fundación Canaria Orotava de Historia de la Ciencia, 2001), pp. 165–181. A discussion of reactions to this unpublished work of Galileo, from Viviani (1674) to Giusti (1998). (GVB) #31.4.56 Freguglia, Paolo. Bellavitis’s equipollences calculus and his theory of complex numbers, Matema- tisk-fysiske Meddelelser. Det Kongelige Danske Videnskabernes Selskab 46 (2) (2001), 181–203. Bellavi- tis’s inspiration for his concept of complex numbers was an 1806 paper by A. Buée. His claim that all theorems from elementary geometry (including projective geometry) can be established using the method Historia Mathematica 31 (2004) 502–530 511 of equipollences is verified. See the review by Ivo Schneider in Mathematical Reviews 2004b:01022. (GVB) #31.4.57 Frei, Günther. Johann Jakob Burkhardt zum 100. Geburtstag am 13. Juli 2003, Elemente der Math- ematik 58 (4) (2003), 134–140. Burkhardt is known for his work toward a theory of motion groups and for his work in the history of mathematics. (GVB) #31.4.58 Frei, Günther. Zur Geschichte der Arithmetik der Algebren (1843–1932), Elemente der Mathematik 58 (4) (2003), 156–168. The publication of Leonard Eugene Dickson’s Algebren und ihre Zahlentheorie exerted a great influence on such mathematicians as Emil Artin, Helmut Hasse, and Emmy Noether. (GVB) #31.4.59 Frey, Louis. Genèse d’une théorie, Mathématiques et Sciences Humaines 156 (2001), 6–32. An arith- metical theory is used to explain various proportions found in Greek and Roman monuments. (GVB) #31.4.60 Fried, Michael N.; and Unguru, Sabetai. Apollonius of Perga’s Conica, Brill: Leiden, 2001, xii + 499 pp. This book addresses the historical roots of Greek mathematics in the works of Apollo- nius by recreating this book, Conica, without using the ahistorical geometrical algebra. See the review by John H. Ewing in Mathematical Reviews 2004e:01006. (TBC) #31.4.61 Friesen, John. Archibald Pitcairne, David Gregory and the Scottish origins of English Tory New- tonianism, 1688–1715. History of Science 41 (2) (2003), 163–191. Investigates support of Newton’s mathematical natural philosophy by various strains of Scottish and English churchmen in the early 18th century. See the review by James J. Tattersall in Mathematical Reviews 2004f:01007. (CJ) #31.4.62 Furinghetti, Fulvia. Mathematical instruction in an international perspective: The contribution of the journal L’Enseignement Mathématique, in #31.4.35, pp. 19–46. (GVB) #31.4.63 Furinghetti, Fulvia. See also #31.4.35. Galuzzi, Massimo. See #31.4.25. Ganeri, Jonardon. Jaina logic and the philosophical basis of pluralism, History and Philosophy of Logic 23 (4) (2002), 267–281. Offers an interpretation of a system that dealt with the situation where a number of propositions, each of which one has reason to believe, taken together produce an inconsistency. (GVB) #31.4.64 Gaukroger, Stephen; and Schuster, John. The hydrostatic paradox and the origins of Cartesian dynamics, Studies in History and Philosophy of Science 33A (3) (2002), 535–572. The paradox that the pressure exerted by a fluid on the bottom of a container does not depend on the shape of the container is traced particularly through the works of Simon Stevin and René Descartes. See the review by H. Scott Dumas in Mathematical Reviews 2004b:01017. (GVB) #31.4.65 Ghasemlu, Farid. A supplement to the book: A Survey of Islamic Astronomical Tables [in Persian], Tarikh-e-Elm 1 (2003), pp. 53–74. This supplement to E.S. Kennedy’s classic survey includes mostly Iranian manuscripts. (GVB) #31.4.66 512 Historia Mathematica 31 (2004) 502–530

Gingerich, Owen. Kepler then and now, Perspectives on Science 10 (2) (2002), 228–240. This literature review focuses on the most important of recent books dealing with Kepler’s astronomy, especially translations of Latin astronomical works. Besides the ongoing work of the Gesammelte Werke, coverage includes works by A.M. Duncan, William Donahue, Bruce Stephenson, E.J. Aiton, J.V. Field, Kitty Fer- guson, James Voelkel, Job Kozhamthadam, Rhonda Martens, and Charlotte Methuen. See the review by Douglas M. Jesseph in Mathematical Reviews 2004d:01013. (ACL) #31.4.67 Gingerich, Owen. See also #31.4.138. Gispert, Hélène. Applications: Les mathématiques comme discipline de service dans les années 1950–1960, in #31.4.35, pp. 251–270. (GVB) #31.4.68 Gispert, Hélène. See also #31.4.35. Glas, Eduard. See #31.4.72. Goldstein, Bernard R. An anonymous z¯ıj in Hebrew for 1400 A.D.: A preliminary report, Archive for History of Exact Sciences 57 (2) (2003), 151–171. This unattributed short z¯ıj contains some rare double-argument tables for planetary motions and has Andalusian inﬂuences. See the review by Glen R. Van Brummelen in Mathematical Reviews 2004b:01014. (GVB) #31.4.69 Gómez Serrano, Josep. See #31.4.6. González Redondo, Francisco A. From the Artem analyticem of Viète to the Mathesis universalis of Descartes: New perspectives on a singular period in the history of algebra [in Spanish], Boletin Sociedad “Puig Adam” 63 (2003), 51–67. These two works can be considered as the beginnings of modern algebra, but are also important in the origins of mathematical physics. (GVB) #31.4.70 Grattan-Guinness, Ivor. “In some parts rather rough”: A recently discovered manuscript version of William Stanley Jevons’s “General mathematical theory of political economy” (1862), History of Polit- ical Economy 34 (4) (2002), 685–726. Jevons submitted a paper to the Philosophical Magazine,which appears to have rejected it. The present paper provides an annotated transcription of the manuscript in- dicating the author’s alterations and provides guides to various topics, such as Jevons’s relation to his predecessors, the versions of the calculus available for Jevons’s mathematization, and the idea of function, continuous or otherwise. See the review by Salim Rashid in Mathematical Reviews 2004d:01018. (ACL) #31.4.71 Grattan-Guinness, Ivor. La psychologie dans les fondements de la logique et des mathématiques: Les cas de Boole, Cantor et Brouwer, in Michel Serfati, ed., De la Méthode (Besançon: Presses Universitaires Franc-Comtoises, 2002), pp. 215–244. This French translation of an article published originally in 1982 (History and Philosophy of Logic 3 (1) (1982), 33–53) examines the role given to mental processes in Boole’s logic, Cantor’s set theory, and Brouwer’s intuitionism. See the review by Eduard Glas in Mathematical Reviews 2004e:03006. (TBC) #31.4.72 Grattan-Guinness, Ivor. History or heritage? An important distinction in mathematics and for mathematics education, American Mathematical Monthly 111 (1) (2004), 1–12. The distinction is drawn between the mathematician’s desire to ﬁnd the heritage of a current notion in mathematics, and the Historia Mathematica 31 (2004) 502–530 513 historian’s desire to reconstruct a past way of thinking. The author does not prefer one or the other, but emphasizes the need to be clear on whether one is doing history or heritage. (GVB) #31.4.73 Grattan-Guinness, Ivor. See also #31.4.17, #31.4.84, and #31.4.186. Gray, Jeremy J. Obituary: John Grant Fauvel (1947–2001), Bulletin of the London Mathematical Society 35 (4) (2003), 565–569. This obituary contains a photograph and list of publications. (GVB) #31.4.74 Gronau, Detlef. On the early history of iteration theory and dynamics, in D. Bakic,´ P. Pandžic,´ and G. Peskir, eds., Functional Analysis, VII (Aarhus: Univ. of Aarhus, 2002), pp. 111–120. Deals with the works of Babbage, Schröder, Frege, and Fatou. (GVB) #31.4.75 Gruber, Peter. See #31.4.125. Guicciardini, Niccolò. See #31.4.53. Gundlach, K.-B. See #31.4.95.

Gupta, R.C. World’s longest lists of decuple terms, Gan. ita-Bharat¯ ¯ı 23 (1–4) (2001), 83–90. The ancient Indian mathematicians were exceptionally fond of large numbers and created long lists of names for powers of ten—the “decuple terms” of the author. See the review by David Singmaster in Mathematical Reviews 2004e:01016. (TBC) #31.4.76 Hacker, P.M.S. Wittgenstein, Carnap and the new American Wittgensteinians, Philosophical Quar- terly 53 (210) (2003), 1–23. This paper is a reply to the accusations made by the proponents of the “New American Wittgenstein,” in particular James Conant. See the review by María Cerezo in Mathematical Reviews 2004e:00003. (TBC) #31.4.77 Hanna, Gila. Journals of Mathematics Education, 1900–2000, in #31.4.35, pp. 67–84. (GVB) #31.4.78 Harkleroad, Leon. See #31.4.156. Hauser, Kai; and Lang, Reinhard. On the geometrical and physical meaning of Newton’s solution to Kepler’s problem, Mathematical Intelligencer 25 (4) (2003), 35–44. A detailed analysis of Newton’s solution to Proposition XVII in Book I of the Principia, a problem that ﬁrst appeared in De Motu,where it is called Problem B. The authors clarify the relation of the proof of this proposition to the physical concept of energy, proving a new theorem that makes Newton’s estimate of the energy quotient in Problem B precise. Newton’s original proof of Proposition XVII is reprinted. (FA) #31.4.79 Hayek, Nácere. A biography of Abel [in Spanish], Revista de la Academia Canaria de Ciencias 14 (1–2) (2002), 147–166, reprint of Revista Números 52 (2002), 3–26. See the review by Leo Corry in Mathematical Reviews 2004f:01027. (CJ) #31.4.80 Hazod, Wilfried. See #31.4.167. Heacox, Linda. See #31.4.84. 514 Historia Mathematica 31 (2004) 502–530

Hendry, David F. J. Denis Sargan and the origins of LSE econometric methodology, Econometric Theory 19 (3) (2003), 457–480. Sargan “radically altered the econometric approach of a generation, establishing a powerful approach to empirical modeling of economic time series.” (GVB) #31.4.81 Hernández, Jesús. Mathematics and its elements: From Euclid to Bourbaki [in Spanish], La Gaceta de la Real Sociedad Matemática Española 5 (3) (2002), 649–672. This paper offers a very broad comparison of the concept of “elements” in mathematics, especially as used in Euclid and Bourbaki. See the review by Joseph W. Dauben in Mathematical Reviews 2004d:00007. (ACL) #31.4.82 Hernández Hernández, Antonio. Monge. Libertad, Igualdad, Fraternidad y Geometría [Monge. Lib- erty, Equality, Fraternity, and Geometry] [in Spanish], Madrid: Nívola, 2002, 160 pp. See the review by Luis Español González in LLULL 26 (55) (2003), 327–329. (VA) #31.4.83 Hess, Heinz-Jürgen. See #31.4.113. Hickman, James C.; and Heacox, Linda. Actuaries in history: The wartime birth of operations research, North American Actuarial Journal 2 (4) (1998), 1–9. Five retired actuaries are interviewed about the role that they and their profession played in launching operations research during the Second World War. The reviewer in Mathematical Reviews 2004d:01021, Ivor Grattan-Guinness, calls attention to some limitations of the study. (ACL) #31.4.84 Hildebrandt, Stefan; and Lax, Peter D. Otto Toeplitz [in German], Bonn: Univ. Bonn, Mathema- tisches Institut, 1999, 211 pp. In this collection of papers honoring Toeplitz (1881–1940), Hildebrandt gives a sketch of Toeplitz’s life, in particular his fate in Bonn (1928–1939), and includes a bibliography of Toeplitz’s works, his curriculum vitae, and some documents regarding his interest in the history of mathematics. Lax analyzes his mathematical heritage. In addition to reprinting several of Toeplitz’s mathematical articles, five letters to him from Hurwitz (1911), Courant (1931), Born (1938), and two from Polya (both 1939) are reproduced. See the review by Karl-Heinz Schlote in Mathematical Reviews 2004d:01033. (ACL) #31.4.85 Hill, Paul. The development of the theory of p-groups, Rocky Mountain Journal of Mathematics 32 (4) (2002), 1135–1151. The author of this history of the theory of torsion Abelian groups has been the most important contributor to the subject. The paper begins with a description of early results and continues with the 1960s, which saw huge progress in the study of groups with elements of infinite height. The review in Mathematical Reviews 2004d:20063 by Patrick Keef gives an overview of the key results and consequences of the work. (ACL) #31.4.86 Hilton, Peter. The birth of homological algebra, Rocky Mountain Journal of Mathematics 32 (4) (2002), 1101–1117. This sequel to a 1987 paper by the author starts with the introduction of homotopy groups by Hurewicz and Cech,ˇ via work by Hopf. Contributions of Eckmann and the invention of group cohomology by Eilenberg and MacLane are included. The author also presents the fundamentals of homological algebra via derived functors. See the review by Apostolos D. Beligiannis in Mathematical Reviews 2004d:16019. (ACL) #31.4.87 Hinzen, Wolfram. Constructive versus ontological construals of Cantorian ordinals, History and Phi- losophy of Logic 24 (1) (2003), 45–63. Emphasizing Kantian themes in Cantor’s writing, the author offers a reconstruction of Cantor’s ordinal numbers that aims to improve on a similar project published recently Historia Mathematica 31 (2004) 502–530 515 by Kit Fine (see #29.3.53). See the review by Yehuda Rav in Mathematical Reviews 2004d:03012. (GVB) #31.4.88 Hlawka, Edmund. See #31.4.125. Hodgson, Bernard R. See #31.4.35. Hogendijk, Jan P. See #31.4.122. Hopkins, Brian; and Wilson, Robin J. The truth about Königsberg, The College Mathematics Jour- nal 35 (3) (2004), 198–207. The authors discuss the historical context of Euler’s views on the Königsberg bridges problem, present his method of solution, and examine the development of the present-day solution. (PWH) #31.4.89 Hormigón, Mariano. On the internationalization of mathematics journals [in Spanish], Revista Cien- cias Matemáticas (Havana) 19 (2) (2001), 103–119. Dealing particularly with the 17th and 18th centuries, this paper examines the growth from birth to internationalization of mathematics journals. (GVB) #31.4.90 Houzel, Christian. La Géométrie Algébrique: Recherches Historiques, Paris: Librairie Scientifique et Technique Albert Blanchard, 2002, vi + 365 pp. This collection of 15 papers includes 5 that have not previously appeared, covering topics from the 9th to the 19th centuries. The reviewer in Mathematical Reviews 2004b:14001, S.L. Kleiman, lauds the clarity and scholarship of the book, but regrets that several opportunities were missed to make a more polished volume. (GVB) #31.4.91 Howson, Albert Geoffrey. Geometry: 1950–70, in #31.4.35, pp. 113–131. (GVB) #31.4.92 Høyrup, Jens. See #31.4.110. Hungerbühler, Norbert; Kramer, Jürg; and Reichelt, Yngvar. The Abel Prize—The new coronation of mathematical careers, Elemente der Mathematik 58 (2) (2003), 45–48. A brief description of how the prize was established, and of the work of its first winner, Jean-Pierre Serre. (GVB) #31.4.93 Ihsano˙ glu,˘ Ekmeleddin;Se¸ ¸ sen, Ramazan; and Izgi,˙ Cevat. History of Mathematical Literature Dur- ing the Ottoman Period [in Turkish] (2 vols.), Istanbul: Research Centre for Islamic History, Art & Culture, IRCICA, 1999, vol. 1: cxii + 349 + iii pp., vol. 2: iv + 381 pp. Contains biographies and lists of works by 491 mathematicians of the time, most of which were written in Arabic or Turkish. (GVB) #31.4.94 Imhausen, Annette. Ägyptische Algorithmen. Eine Untersuchung zu den mittelägyptischen mathematischen Aufgabentexten [Egyptian Algorithms. An Investigation on Middle-Egyptian Mathematical Texts], Wiesbaden: Harrassowitz Verlag, 2003, xii + 387 pp. The author presents a new treatment and analysis of the preserved Old Egyptian mathematical problem texts (the Rhind Papyrus and the Moscow Papyrus). See the review by K.-B. Gundlach in Mathematical Reviews 2004e:01003. (TBC) #31.4.95 Information about the Institute’s Activities, Berlin: Max-Planck-Institut für Wissenschaftsgeschichte, 2002, softbound, 206 pp. A summary of the research activities conducted at the Institut in 2002. (GVB) #31.4.96 516 Historia Mathematica 31 (2004) 502–530

Izgi,˙ Cevat. See #31.4.94. Janssen, Michel. Reconsidering a scientific revolution: The case of Einstein versus Lorentz, Physics in Perspective 4 (4) (2002), 421–446. Einstein’s special theory of relativity was an improvement over Lorentz’s theory in that it provided a “common cause” explanation for the fact that the same rule of “corresponding states” that held for electromagnetic fields also held for the states of matter. See the review by Lawrence Sklar in Mathematical Reviews 2004b:83001. (GVB) #31.4.97 Jantzen, Robert. See #31.4.106. Jesseph, Douglas M. See #31.4.32, #31.4.67, and #31.4.135. Kahane, Jean-Pierre. Sets of uniqueness and sets of multiplicity, in Wiesław Zelazko,˙ ed., Fourier Analysis and Related Topics (Warsaw: Polish Academy of Sciences, 2002), pp. 55–68. Covers the time from Riemann and Cantor to the present, dealing especially with the works of Rajchman, Zygmund, and Marcinkiewicz. (GVB) #31.4.98 Kahane, Jean-Pierre. L’enseignement du calcul différentiel et intégral au début du vingtième siècle [The teaching of differential calculus at the beginning of the twentieth century], in #31.4.35, pp. 167–178. (GVB) #31.4.99 Kastanis, Andreas. The teaching of mathematics in the Greek military academy during the first years of its foundation (1828–1834), Historia Mathematica 30 (2) (2003), 123–139. Modeled after the École Polytechnique, the Academy treated mathematics seriously and used textbooks by Legendre, Bourdon, and Monge. (GVB) #31.4.100 Katsnelson, Victor. See #31.4.48. Keef, Patrick. See #31.4.86. Kilpatrick, Jeremy. Scientific solidarity today and tomorrow, in #31.4.35, pp. 317–330. (GVB) #31.4.101 Kleiman, S.L. See #31.4.91. Kleinert, Ernst. Über Assoziativität und Kommutativität, Mathematische Semesterberichte 50 (1) (2003), 29–43. Attempts to determine the origins of several manifestations of associativity and commu- tativity. (GVB) #31.4.102 Knobloch, Eberhard. See #31.4.9. Knuth, Donald E. Selected Papers on Computer Languages, Stanford: Center for the Study of Lan- guage and Information, 2003, xvi + 594 pp. A collection of 25 papers by Knuth on computer languages, many written in the 1960s. (GVB) #31.4.103 Knuth, Donald E. Selected Papers on Discrete Mathematics, Stanford: Center for the Study of Lan- guage and Information, 2003, xvi + 812 pp. A collection of 41 papers by Knuth on discrete mathematics. Several of the papers have historical content. (GVB) #31.4.104 Historia Mathematica 31 (2004) 502–530 517

Komjáth, Péter. Paul Erdös’s adventures in the realm of infinite graphs [in Hungarian], Matematikai Lapok (N.S.) 7 (3–4) (1997), 51–66. Surveys some of Erdös’s work in this field, especially the Ramsey phenomenon and the chromatic number. (GVB) #31.4.105 Kraner, Jürg. See #31.4.93. Krasinski,´ A.; Behr, Christoph G.; Schücking, Engelbert; Estabrook, Frank B; Wahlquist, Hugo D.; Ellis, George F.Š; Jantzen, Robert; and Kundt, Wolfgang. The Bianchi classification in the Schücking– Behr approach, General Relativity and Gravitation 35 (3) (2003), 475–489. The paper is a historical account of the development of the well-known Bianchi classification. See the review by Michael Tsam- parlis in Mathematical Reviews 2004e:83014. (TBC) #31.4.106 Krengel, U. See #31.4.39. Kundt, Wolfgang. See #31.4.106. Laborde, Colette. Géométrie—Période 2000 et après, in #31.4.35, pp. 133–154. (GVB) #31.4.107 Lacki, Jan. Styles of physical thinking versus mathematical ones, Synthese 134 (1–2) (2003), 273– 288. Contrasts Clausius’s introduction of entropy with Heisenberg’s discovery of the rules governing quantum mechanical representations of physical quantities. (GVB) #31.4.108 Lai, Tze Leung. Stochastic approximation, Annals of Statistics 31 (2) (2003), 391–406. A review of Herbert E. Robbins’s contributions to the founding of this subject. One of three historical articles in this issue of Annals of Statistics devoted to the memory of Robbins; see also #31.4.50 and #31.4.173. (GVB) #31.4.109 Laird, W.R. Renaissance mechanics and the new science of motion, in José Montesinos and Carlos Solís, eds., Philosophy on a Wide Scale [in Italian] (La Orotava: Fundación Canaria Orotava de Historia de la Ciencia, 2001), pp. 255–267. This article describes the roles of the various strands of mechanical thought that went into Galileo’s Discorsi and the importance of (virtual) velocity in a circular movement in his writings on mechanics and motion. Laird argues that in spite of Galileo’s allegiance to Archimedes one of his principal breakthroughs was based on a synthesis of the pseudo-Aristotelian “physical” and the Archimedean mathematical–statistical approach. See the review by Jens Høyrup in Mathematical Reviews 2004d:01014. (ACL) #31.4.110

Lal, R.S.; and Prasad, Ramashis. Contribution of Nar¯ ayan¯ . aPan.d.ita to the solution of the equations of the type NX2 ± 1 = Y 2, Gan. ita-Bharat¯ ¯ı 24 (1–4) (2002), 117–121. Brings to light some of the contributions of this 14th-century mathematician to solutions of the so-called varga-prakr.ti (“square-nature”) problem. (GVB) #31.4.111 Lang, Reinhard. See #31.4.79. Langevin, Rémi. Gaspard Monge, de la planche à dessin aux lignes de courbure [Gaspard Monge, from the drawing board to curvature lines], in Michel Serfati, ed., De la Méthode: Recherches en Histoire et Philosophie des Mathématiques (Besançon: Presses Universitaires Franc-Comtoises, 2002), pp. 127– 154. Gaspard Monge’s experience in drawing maps and his scientiﬁc curiosity led to his visual approach to mathematics and was related to his pedagogical interests. (GVB) #31.4.112 518 Historia Mathematica 31 (2004) 502–530

Lax, Peter D. See #31.4.85. Leibniz, Gottfried Wilhelm. Sämtliche Schriften und Briefe. Reihe III. Mathematischer, natur- wissenschaftlicher und technischer Briefwechsel. Fünfter Band. 1691–1693 [Collected Works and Let- ters. Series III. Mathematical, Scientific and Technical Correspondence. Vol. 5. 1691–1693], edited by Heinz-Jürgen Hess and James G. O’Hara, foreword by Herbert Breger, Berlin: Akademie Verlag, 2003, lxxx + 734 pp. This volume covers Leibniz’s letters on a broad range of topics over the years 1691–1693. Meticulously edited, but the breadth of topics guarantees that not everything will interest all readers. See the review by John H. Ewing in Mathematical Reviews 2004f:01045. (CJ) #31.4.113 Leonesi, Stefano; Toffalori, Carlo; and Tordini, Samanta. Mathematics, miracles and paradoxes [in Italian], Lettera Matematica Pristem 46 (2002), 31–42. Taking the Banach–Tarski paradox as a motivat- ing example the authors present a survey of the early history of set theory and its paradoxes to show how mathematics can “scientifically” prove the “miraculous” possibility of duplicating matter. They proceed through Cantor, Zermelo, Russell’s paradox, Hilbert, and the axiom of choice. See the review by Paloma Pérez-Ilzarbe in Mathematical Reviews 2004d:01022. (ACL) #31.4.114 Lewis, Albert C. See #31.4.8 and #31.4.51. Lewis, David W. “To the glory of God, honour of Ireland and fame of America”: A biographical sketch of Francis D. Murnaghan, Mathematical Proceedings of the Royal Irish Academy 103A (1) (2003), 101–112. Murnaghan was an Irish mathematician with influence in the United States in the first half of the 20th century. (GVB) #31.4.115 Lichtenberg, Heiner. Das anpassbar zyklische, solilunare Zeitzählungssystem des gregorianischen Kalendars [The adjustably cyclical, solilunar time-measuring system of the Gregorian calendar], Math- ematische Semesterberichte 50 (1) (2003), 45–76. A discussion of various mathematical aspects of the Gregorian calendar. (GVB) #31.4.116 Llombart Palet, José; and Vicente, Jorge Lorenzo. From Santiago de Cuba to Madrid: Academic and scientific biography of the Hispano–Cuban mathematician José Maria Villafañe y Viñals (1830– 1915) [in Spanish], Revista Ciencias Matemáticas (Havana) 19 (2) (2001), 120–132. Follows José Maria Villafañe y Viñals from his appointment as professor of descriptive geometry at the Escuela Preparatoria of Santiago (Cuba) to his appointment as professor of calculus at the Universidad Central (Madrid), describing the institutional setting of 19th-century Spanish mathematics along the way. (GVB) #31.4.117 Lloyd, E. Keith. Redfield’s contributions to enumeration, MATCH 46 (2002), 214–233. The problem of enumerating chemical isomers was worked on by Cayley and followed up by Pólya in 1937. However, J. Howard Redfield had anticipated Pólya’s result in the only paper published in his lifetime, in 1927. This and a second (rejected) paper “anticipated many of the major developments in the theory of enumeration made from the 1930s to the 1960s.” (GVB) #31.4.118 Lodge, Paul. Leibniz on divisibility, aggregates, and Cartesian bodies, Studia Leibnitiana 34 (1) (2002), 59–80. An explanation and argument for the validity of Leibniz’s critique of Descartes’s concep- tion of the body. (GVB) #31.4.119 Historia Mathematica 31 (2004) 502–530 519

Lützen, Jesper. Julius Petersen, Karl Weierstrass, Hermann Amandus Schwarz and Richard Dede- kind on hypercomplex numbers, Matematisk-fysiske Meddelelser. Det Kongelige Danske Videnskabernes Selskab 46 (2) (2001), 223–254. Focuses on the contributions of Petersen to the development of hypercomplex numbers. See the review by DoruStef ¸ anescu˘ in Mathematical Reviews 2004f:01013. (CJ) #31.4.120 Mancosu, Paolo. On the constructivity of proofs. A debate among Behmann, Bernays, Gödel, and Kaufmann, in Wilfried Sieg, Richard Sommer, and Carolyn Talcott, eds., Reﬂections on the Foundations of Mathematics (Urbana, IL: Association of Symbolic Logic, 2002), pp. 349–371. This debate, which also included Rudolf Carnap, took place in 1930 is made available here through archival material. (GVB) #31.4.121 Marcus, Solomon. See #31.4.125 and #31.4.137. Mawaldi, Moustafa. Méthode de l’analyse et de la synthèse de Kamal¯ al-D¯ın al-Faris¯ ¯ı, in Ekmeled- din Ihsano˙ glu˘ and Feza Günergun, eds., Science in Islamic Civilization (Istanbul: Research Centre for Islamic History, Art & Culture, IRCICA, 2000), pp. 193–199. Deals with al-Faris¯ ¯ı’s use of the ancient Greek techniques of analysis and synthesis to solve algebraic equations. See the review by Jan P. Hogendijk in Mathematical Reviews 2004b:01009. (GVB) #31.4.122 McCarthy, Daniel P.; and Byrne, John G. Al-Khwarizm¯ ¯ı’s sine tables and a Western table with the Hindu norm of R = 150, Archive for History of Exact Sciences 57 (3) (2003), 243–266. The authors review our present knowledge of the sine table of Ibn Mus¯ a¯ al-Khwarizm¯ ¯ı and note Ibn al-Muthanna’s¯ commentary on al-Khwarizm¯ ¯ı’s Z¯ıj, in which “the ‘sine instructions’ for the sine tables . . . was certainly normed for R = 150, and computed at intervals of 15◦.” The authors argue that those “sine instructions” were originally presented by al-Khwarizm¯ ¯ıinhisZ¯ıj. They also maintain that the sine table (R = 150, at intervals of 1◦) as found in the famous Toledan tables likely “represents a misguided ‘reconstruction’ of al-Khwarizm¯ ¯ı ...later annotators of manuscripts have sometimes understandably, but mistakenly, attributed . . . [this] sine table to al-Khwarizm¯ ¯ı.” See the review by S.M. Razaullah Ansari in Mathematical Reviews 2004d:01007. (ACL) #31.4.123 McCarty, D.C. Optics of thought: Logic and vision in Müller, Helmholtz, and Frege, Notre Dame Journal of Formal Logic 41 (4) (2000), 365–378. Frege’s treatment of binocular vision can be traced back to Müller, Helmholtz, and du Bois-Reymond. (GVB) #31.4.124 McConnell, J.C. See #31.4.37. Melville, Duncan J. See #31.4.131. Mendelson, E. See #31.4.34. Menger, Karl. Selecta mathematica, vol. 2, edited by Bert Schweizer, Abe Sklar, Karl Sigmund, Peter Gruber, Edmund Hlawka, Ludwig Reich and Leopold Schmetterer, Vienna: Springer-Verlag, 2003, x + 674 pp. Connected with the Vienna Circle and with the great intellectuals of his time, Karl Menger was a total mathematician. The second volume is rich and impressive in its diversity and deepness of ideas. It includes selections from Menger’s papers in different ﬁelds. See the review by Solomon Marcus in Mathematical Reviews 2004e:01065. (TBC) #31.4.125 520 Historia Mathematica 31 (2004) 502–530

Menzler-Trott, Eckart. Gentzens Problem. Mathematische Logik im nationalsozialistischen Deutsch- land, with an essay by Jan von Plato, Basel: Birkhäuser Verlag, 2001, xviii + 411 pp. The title of this book does not really convey its contents. Instead, it is a biography of the “external life” of Gerhard Gentzen (1909–1945). The author’s intention is to tell the story of Gentzen’s life to those interested in or already familiar with his fundamental contributions to mathematics and logic, and to make clear his position and circumstances as a mathematician under National Socialism. See the review by Joseph Dauben in Mathematical Reviews 2004e:01037. (TBC) #31.4.126 Michel, Alain. Thèses d’existence et travail mathématique [Existence arguments and mathematical work], in Michel Serfati, ed., De la Méthode: Recherches en Histoire et Philosophie des Mathématiques (Besançon: Presses Universitaires Franc-Comtoises, 2002), pp. 247–269. The author tries to substantiate the thesis that what philosophers of mathematics tend to view as merely abstract problems are in fact very precise problems faced by real mathematicians in their daily practice. See the review by Paloma Pérez-Ilzarbe in Mathematical Reviews 2004e:00004. (TBC) #31.4.127

Mirabolghassemi, Seyyed M.T.; and Bagheri, Mohammad. Abd al-Rahman¯ S. uf¯ ¯ı’s treatise on compass geometry [in Persian], Tarikh-e-Elm 1 (2003), 89–142. An edition of this late 10th-century A.D. text, entitled “Treatise on the construction of regular polygons by [compasses of] ﬁxed opening.” (GVB) #31.4.128 Mishchenko, A.S. The development of noncommutative geometry at Moscow University [in Russian], Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 2003 (3), 40–47. A survey of the results and methods produced by the Moscow topological school. (GVB) #31.4.129 Miyake, Katsuya. Some aspects of interactions between algebraic number theory and analytic number theory, in Shigeru Kanemitsu and Chaohua Jia, eds., Number Theoretic Methods (Dordrecht: Kluwer, 2002), pp. 263–299. Covers the contributions of number theorists such as Fermat, Dedekind, Weber, and Zolotarev. See the review by W. Narkiewicz in Mathematical Reviews 2004b:11001. (GVB) #31.4.130 Muldoon, Martin E. See #31.4.188. Muroi, Kazuo. Mathematical term tak¯ıltum and completing the square in Babylonian mathematics, Historia Scientiarum (2) 12 (3) (2003), 254–263. Against the recent readings of Eleanor Robson and Jens Høyrup, the author argues that the term tak¯ıltum “means completing the square in the solution of a quadratic equation. It actually denotes the identity a2 + 2ab + b2 = (a + b)2, and has nothing to do with squaring a number.” See the review by Duncan J. Melville in Mathematical Reviews 2004d:01002. (ACL) #31.4.131 Myrvold, Wayne C. On some early objections to Bohm’s theory, International Studies in the Philoso- phy of Science 17 (1) (2003), 7–24. The belief that Bohm’s theory was ignored by the physics community is contradicted by the existence of published criticisms by Einstein, Pauli, and Heisenberg. These criticisms are evaluated here. (GVB) #31.4.132 Nabonnand, Philippe. Les débats autour des applications des mathématiques dans les réformes de l’enseignement secondaire au début du vingtième siècle [The debates concerning mathematics applications in the reforms of secondary teaching at the beginning of the twentieth century], in #31.4.35, pp. 229–249. (GVB) #31.4.133 Historia Mathematica 31 (2004) 502–530 521

Nakane, Michiyo; and Fraser, Craig G. The early history of Hamilton–Jacobi dynamics 1834–1837, Centaurus 44 (3–4) (2002), 161–227. Hamilton’s focus in this time was to solve the n-body problem in physical astronomy, while Jacobi was more interested in the mathematical implications of Hamil- ton’s work for the solution of PDEs. See the review by Antonino Drago in Mathematical Reviews 2004b:01025. (GVB) #31.4.134 Narkiewicz, W. See #31.4.130. Naylor, Ron. Galileo’s physics for a rotating earth, in José Montesinos and Carlos Solís, eds., Phi- losophy on a Wide Scale [in Italian] (La Orotava: Fundación Canaria Orotava de Historia de la Ciencia, 2001), pp. 337–355. Galileo developed a theory of tides that he put forward as the principal physical evidence for the rotation of the earth. However his “conservatism regarding the fundamental nature of circular motion” caused him to adhere to a theory which became difﬁcult to defend in the face of physical evidence. He eventually abandoned his rotational theory and accepted the common view that tidal phe- nomena were produced by the moon. See the review by Douglas M. Jesseph in Mathematical Reviews 2004d:01015. (ACL) #31.4.135 Niss, Mogens. Applications of mathematics “2000”, in #31.4.35, pp. 271–284. (GVB) #31.4.136 Nunes, Pedro. Petri Nonii salaciensis opera [in Latin], with foreword in Portuguese and English by João Filipe Quieró, Coimbra: Univ. de Coimbra, 2002, xliv + 307 pp. This is a facsimile edition of four texts by the 16th-century mathematician: two dealing with navigation, one of the movement of boats with oars, and a collection of annotations to Peurbach’s Theoricae novae planetarum. See the review by Solomon Marcus in Mathematical Reviews 2004b:01055. (GVB) #31.4.137 O’Hara, James G. See #31.4.113. Palmieri, Paolo. Galileo did not steal the discovery of Venus’ phases: A counter-argument to West- fall, in José Montesinos and Carlos Solís, eds., Philosophy on a Wide Scale [in Italian] (La Orotava: Fundación Canaria Orotava de Historia de la Ciencia, 2001), pp. 433–444. Argues against Westfall that Galileo did not steal the idea from Castelli that the phases of Venus could provide a test between the geocentric and heliocentric hypotheses; unfortunately the author seems unaware that his argument has already been made in earlier publications. See the review by Owen Gingerich in Mathematical Reviews 2004b:01018. (GVB) #31.4.138 Palmieri, Paolo. Mental models in Galileo’s early mathematization of nature, Studies in History and Philosophy of Science 34A (2) (2003), 229–264. Outstanding article on Galileo’s use of the Eudoxan theory of ratio and proportion (Euclid, Book V) in his development of mathematical physics. See the review by William R. Shea in Mathematical Reviews 2004f:01005. (CJ) #31.4.139 Pambuccian, Victor V. See #31.4.7. Panza, Marco. See #31.4.53. Parker, Willard. See #31.4.43. Pasles, Paul C. See #31.4.38. 522 Historia Mathematica 31 (2004) 502–530

Passell, Nicholas. See #31.4.185. Paunic,´ Djura. History of measure theory, in E. Pap, ed., Handbook of Measure Theory,vol.1 (Amsterdam: North-Holland, 2002), pp. 1–26. Deals with the development of measure theory, including Egyptian and Greek material, to today. See the review by Joseph Max Rosenblatt in Mathematical Reviews 2004b:28003. (GVB) #31.4.140 Peckhaus, Volker. See #31.4.182. Pepe, Luigi. Bicentennial of the birth of Abel. Genius and moderation: Abel in Berlin and in Paris [in Italian], Lettera Matematica Pristem 46 (2002), 44–55. Recounts the story of Abel’s groundbreaking 1826 work and his attempt to have it published and recognized by established European mathematicians. See the review by Richard Davitt in Mathematical Reviews 2004f:01035. (CJ) #31.4.141 Pérez-Ilzarbe, Paloma. See #31.4.114 and #31.4.127. Pesic, Peter. Abel’s Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability, Cambridge, MA: MIT Press, 2003, viii + 203 pp. A popular account of Abel’s proof that the general quintic polynomial cannot be solved by radicals. (GVB) #31.4.142 Plotnitsky, Arkady; and Reed, David. Discourse, mathematics, demonstration, and science in Galileo’s Discourses concerning two new sciences, Conﬁgurations 9 (1) (2001), 37–64. This is a very general discussion of Galileo’s Discourses Concerning Two New Sciences. See the review by William R. Shea in Mathematical Reviews 2004e:01028. (TBC) #31.4.143 Pogliani, Lionello. Magic squares and the mathematics of thermodynamics, MATCH. Communica- tions in Mathematical and in Computer Chemistry 47 (2003), 153–166. Points out a connection of a Chinese “magic graph” to a present “thermodynamic magic square.” See the review by Rong Si Chen in Mathematical Reviews 2004b:05047. (GVB) #31.4.144 Pons, Anaclet. Those other mathematicians [in Spanish], La Gaceta de la Real Sociedad Matemática Española 6 (1) (2003), 27–37. Curiosity and the desire for knowledge are the main forces that led from superstition to mathematics. See the review by Capi Corrales-Rodrigáñez in Mathematical Reviews 2004d:01016. (ACL) #31.4.145 Prasad, Ramashis. See #31.4.111. Prokhorov, Dmitri Valentinovic.´ See #31.4.175. Quieró, João Filipe. See #31.4.137. Rashed, Roshdi. Histoire de l’analyse combinatoire, in Ekmeleddin Ihsano˙ glu˘ and Feza Günergun, eds., Science in Islamic Civilization (Istanbul:˙ Research Centre for Islamic History, Art & Culture, IR- CICA, 2000), pp. 151–166. A translation into French of the German article abstracted in #29.1.148. (GVB) #31.4.146 Rashed, Roshdi. Al-Quh¯ ¯ı et al-Sijz¯ı: Sur la compass parfait et le trace continu des sections coniques, Arabic Sciences and Philosophy 13 (1) (2003), 9–43. A text by the 10th-century geometer al-Sijz¯ıis presented, with comments on changes to the study of conic sections in his time. (GVB) #31.4.147 Historia Mathematica 31 (2004) 502–530 523

Rashid, Salim. See #31.4.71. Rav, Yehuda. See #31.4.88. Raynaud, Dominique. Ibn al-Haytham sur la vision binoculaire: Un précurseur de l’optique phys- iologique, Arabic Sciences and Philosophy 13 (1) (2003), 79–99. A survey of the extent of Ibn al- Haytham’s knowledge of the mechanisms of binocular vision. (GVB) #31.4.148 Read, Stephen. The liar paradox from John Buridan back to Thomas Bradwardine, Vivarium 40 (2) (2002), 189–218. Three related solutions to the liar paradox proposed by 14th-century scholars (the two in the title and Albert of Saxony) are discussed and compared. See the review by Mary J. Sirridge in Mathematical Reviews 2004b:01015. (GVB) #31.4.149 Reddi, C.A. See #31.4.16. Redmond, Don. See #31.4.46. Reed, David. See #31.4.143. Reich, Karin. Chinesische Mathematiker zwischen 1934 und 1941 in Hamburg [Chinese mathematicians between 1934 and 1941 in Hamburg], Mitteilungen der Mathematischen Gesellschaft in Hamburg 21 (2) (2002), 27–44. Before 1934 very few Chinese mathematicians pursued studies in Hamburg; after 1934 many did, including Shiing-Shen Chern and Ho-Jui Chang. (GVB) #31.4.150 Reich, Karin. Die Rezeption Diophants im 16. Jahrhundert [The reception of Diophantus in the 16th century], NTM (N.S.) 11 (2) (2003), 80–89. A summary of the recovery and reception of Diophantus’s Arithmetica in Western Europe during the late Renaissance. It identiﬁes the references, texts, editions, and uses of the work from its rediscovery by Regiomontanus in 1462 to the end of the 16th century. See the review by Warren Van Egmond in Mathematical Reviews 2004d:01008. (ACL) #31.4.151 Reich, Ludwig. See #31.4.125. Reichelt, Yngvar. See #31.4.93. Reinboud, Weia. See #31.4.17. Remmert, Volker R. Ungleiche Partner in der Mathematik im “Dritten Reich”: Heinrich Behnke und Wilhelm Süss [Unequal partners in mathematics in the “Third Reich”: Heinrich Behnke and Wilhelm Süss], Mathematische Semesterberichte 49 (1) (2002), 11–27. The partnership between the two men is presented in the context of the reorganization of the publication of mathematical journals and Behnke’s support for his friend Cartan. (GVB) #31.4.152 Rice, Adrian C.; and Wilson, Robin J. The rise of British analysis in the early 20th century: The role of G.H. Hardy and the London Mathematical Society, Historia Mathematica 30 (2) (2003), 173–194. A reevaluation of Hardy’s inﬂuence on the British mathematical research community in the early 20th century, especially with respect to analysis, with reference to Hardy’s relationship with the LMS. (GVB) #31.4.153 524 Historia Mathematica 31 (2004) 502–530

Roberts, John T. Leibniz on force and absolute motion, Philosophy of Science 70 (3) (2003), 553– 573. Argues that Leibniz was committed to a stronger space–time structure than “so-called Leibnizian space–time.” (GVB) #31.4.154

Robinson, P.M. Denis Sargan: Some perspectives, Econometric Theory 19 (3) (2003), 481–494. Dis- cusses some of the previous holders of the Tooke chair of economic science and statistics and relates one of Sargan’s papers to modern issues in semiparametric econometrics. (GVB) #31.4.155

Rosenblatt, Joseph Max. See #31.4.140.

Rosenfeld, Boris A. Tashkent manuscripts on mathematical atomism, in Ekmeleddin Ihsano˙ glu˘ and Feza Günergun, eds., Science in Islamic Civilization (Istanbul: Research Centre for Islamic History, Art & Culture, IRCICA, 2000), pp. 179–184. Two manuscripts, probably copies of 18th-century works by Mawlawi Sadiq and Mawlana Abd al-Jalil, present atomist views of geometry by 9th- and 10th-century mathematicians. See the review by Leon Harkleroad in Mathematical Reviews 2004b:01012. (GVB) #31.4.156

Rosenfeld, Boris. See also #31.4.3.

Saari, Donald G.; and Barney, Steven. Consequences of reversing preferences, Mathematical Intel- ligencer 25 (4) (2003), 17–31. A geometric analysis of those election procedures that permit the same ranking for a profile (a listing that specifies the number of voters whose preferences are given by each complete transitive ranking of the candidates) as for the profile where each voter’s preference order is reversed. Positional methods, e.g., Borda’s, plurality, approval, and the single transferable vote are examined as well as pairwise methods, e.g., Condorcet’s and Dodgson’s. (FA) #31.4.157

Sachs, Mendel. Cornelius Lanczos—Discoveries in the quantum and general relativity theories, Fon- dation Louis de Broglie. Annales 27 (1) (2002), 85–91. Sachs notes C. Lanczos’s proof of the mathematical equivalence of Heisenberg’s and Schrödinger’s representations of quantum mechanics and discusses Lanczos’s theory of the dynamics of isolated particles in general relativity. See the review by H. Treder in Mathematical Reviews 2004d:01038. (ACL) #31.4.158

Sayyad, Mohammad Reza. Mathematical modeling for the calculation of the conventional lunar Hejira calendar [in Persian], Tarikh-e-Elm 1 (2003), 27–38. Discusses a computerized mathematical model written by the author for the calculation of the conventional lunar Hejira calendar. (GVB) #31.4.159

Schappacher, Norbert. Politisches in der Mathematik: Versuch einer Spurensicherung [Political aspects of mathematics: Attempt at the collection of evidence], Mathematische Semesterberichte 50 (1) (2003), 1–27. This article focuses on an interpretation of Hermann Weyl’s 1918 Das Continuum as a “mathematical-literary processing of World War I.” (GVB) #31.4.160

Schattschneider, Doris; and Emmer, Michele, eds. M.C. Escher’s Legacy: A Centennial Celebration, Berlin: Springer-Verlag, 2003, xvi + 458 pp., with CD-ROM. A collection of papers emerging from two conferences held in honor of Escher’s centenary in 1998, in Rome and Ravello. (GVB) #31.4.161 Historia Mathematica 31 (2004) 502–530 525

Schinzel, A. A survey of achievements in number theory in the 20th century [in Polish], Wiadomosci Matematyczne 38 (2002), 79–88. A list of 53 of the most important results in number theory in the 20th century. (GVB) #31.4.162 Schlote, Karl-Heinz. Hypercomplex numbers in the work of Caspar Wessel and Hermann Gün- ther Grassmann: Are there any similarities?, Matematisk-fysiske Meddelelser. Det Kongelige Danske Videnskabernes Selskab 46 (2) (2001), 205–222. Considers contributions of Wessel and Grassmann to hypercomplex numbers. See the review by DoruStef ¸ anescu˘ in Mathematical Reviews 2004f:01014. (CJ) #31.4.163 Schlote, Karl-Heinz. See also #31.4.85. Schmetterer, Leopold. See #31.4.125. Schneider, Ivo. See #31.4.57. Schubring, Gert. E.H. Dirksens Beiträge zu den Grundlagen der Analysis [E.H. Dirksen’s contributions to the foundations of analysis], NTM (N.S.) 11 (2) (2003), 90–99. A survey of the scholarship on this Frisian mathematician, who was a proponent of Cauchy’s work. See the review by E.J. Barbeau in Mathematical Reviews 2004b:01026. (GVB) #31.4.164 Schubring, Gert. L’Enseignement Mathématique and the first international commission (IMUK): The emergence of international communication and cooperation, in #31.4.35, pp. 47–65. (GVB) #31.4.165 Schubring, Gert. See also #31.4.35. Schücking, Engelbert. See #31.4.106. Schuster, John. See #31.4.65. Schweizer, Bert. See #31.4.125. Scimone, Aldo. Two hundred years after Gauss’s great work, Disquisitiones Arithmeticae, Lettera Matematica Pristem 41 (2001), 48–57. The first of two articles; this one deals with the social and mathematical conditions under which this book arose. See the review by Capi Corrales-Rodrigáñez in Mathematical Reviews 2004b:01027. (GVB) #31.4.166 Seneta, Eugene. Karamata’s characterization theorem, Feller, and regular variation in probability theory, Institut Mathématique. Publications (Beograd) (N.S.), 71 (85) (2002), 79–89. Describes and proves Karamata’s basic theorem, and then describes in parallel the biographies of Karamata and Feller. See the review by Wilfried Hazod in Mathematical Reviews 2004c:60006. (GVB) #31.4.167 Serfati, Michel, ed. De la Méthode: Recherches en Histoire et Philosophie des Mathématiques,Be- sançon: Presses Universitaires Franc-Comtoises, 2002, 356 pp. A collection of 10 papers on topics from the 17th century to the present. The papers are being abstracted separately. (GVB) #31.4.168 Serfati, Michel. Le développement de la pensée mathématique du jeune Descartes (L’éveil d’un mathematician) [The development of the mathematical thought of the young Descartes (The awakening 526 Historia Mathematica 31 (2004) 502–530 of a mathematician)], in Michel Serfati, ed., De la Méthode: Recherches en Histoire et Philosophie des Mathématiques (Besançon: Presses Universitaires Franc-Comtoises, 2002), pp. 39–104. Covers the period from Descartes’s meeting with Beeckman in 1618 to his departure for the Netherlands in 1629. (GVB) #31.4.169 Serre, Jean-Pierre. See #31.4.93. Se¸¸ sen, Ramazan. See #31.4.94. Shea, William R. Galileo the Copernican, in José Montesinos and Carlos Solís, eds., Philosophy on a Wide Scale [in Italian] (La Orotava: Fundación Canaria Orotava de Historia de la Ciencia, 2001), pp. 41–59. An expository paper which deals with the extent to which Galileo’s telescope was capable of convincing others of his claims about the Moon and planets. See the review by Donald Cook in Mathematical Reviews 2004b:01019. (GVB) #31.4.170 Shea, William R. See also #31.4.139, #31.4.143, #31.4.177, and #31.4.178. Sheynin, Oscar B. Nekrasov’s work on probability: The background, Archive for History of Ex- act Sciences 57 (4) (2003), 337–353. Nekrasov’s exchanges with contemporary Russian figures such as A.A. Markov are highlighted. See the review by William J. Adams in Mathematical Reviews 2004b: 01047. (GVB) #31.4.171 Sheynin, Oscar B. On the history of Bayes’s theorem, The Mathematical Scientist 28 (1) (2003), 37–42. Concludes that Bayes was the author of the results in the 1763/1764 work The Doctrine of Chances presented to the Royal Society by his friend Richard Price. (GVB) #31.4.172 Shokurov, V.V. See #31.4.30. Siegmund, David. Herbert Robbins and sequential analysis, Annals of Statistics 31 (2) (2003), 349– 365. Herbert Robbins was a major figure in sequential analysis from 1952 to 1980. One of three historical articles in this issue of Annals of Statistics devoted to the memory of Robbins; see also #31.4.50 and #31.4.109. (GVB) #31.4.173 Siegmund-Schultze, Reinhard. The late arrival of academic applied mathematics in the United States: A paradox, theses, and literature, NTM (N.S.) 11 (2) (2003), 116–127. Drawn from a larger, unpublished work by the author, this is a study of why applied mathematics arrived as an academic research subject later (around 1940) in the United States than in Germany in spite of the fact that the U.S. had been influenced earlier by Germany in its pursuit of pure mathematics. There have been several theses put forward to explain this “paradox” but the author believes that no one of them alone suffices and that instead the explanation lies in a more systemic “belated modernisation” for the whole of science and the educational system in the U.S. (ACL) #31.4.174 Sigmund, Karl. See #31.4.125. Simonov, R.A. The problem of the origin of Old-Russian digits characters [in Russian], Voprosy Istorii Estestvoznaniya i Tekhniki 2002 (4), 726–744. The Old Russian “letter” numeration appeared as a variant of the Byzantine “letter” digit system adapted to conditions of the Old-Russian writing culture. Sources are examined from the 11th through 17th centuries, comparing them with South Slavonic, Greek Historia Mathematica 31 (2004) 502–530 527 and Byzantine documents. See the review by Dmitri Valentinovic´ Prokhorov in Mathematical Reviews 2004d:01001. (ACL) #31.4.175 Singmaster, David. See #31.4.76. Sirridge, Mary J. See #31.4.149. Siu, Man-Keung. Learning and teaching of analysis in the mid-20th century: A semipersonal obser- vation, in #31.4.35, pp. 179–190. (GVB) #31.4.176 Sklar, Abe. See #31.4.125. Sklar, Lawrence. See #31.4.97. Sonar, Thomas. William Gilberts Neigungsinstrument. I. Geschichte und Theorie der magnetischen Neigung [William Gilbert’s dip instrument. I. History and theory of magnetic declination], Mitteilungen der mathematischen Gesellschaft in Hamburg 21 (2) (2002), 45–68. William Gilbert developed a theory of magnetic declination and described a dip instrument in his De Magnete published in Latin in 1600. This article discusses the history of the instrument in the light of information provided by Thomas Blundeville in English in The Theory of the Seven Planets that appeared in 1602. See also #31.4.178. See the review by William R. Shea in Mathematical Reviews 2004e:01024. (TBC) #31.4.177 Sonar, Thomas. William Gilberts Neigungsinstrument. II. Die Berechnung einer Neigungstabelle [William Gilbert’s dip instrument. II. The calculation of a declination table], Mitteilungen der mathematischen Gesellschaft in Hamburg 21 (2) (2002), 69–78. The author describes how Henry Briggs, the inventor of logarithms, made a table that could be used to find the height of the pole when the magnetic declination was known. See also #31.4.177. See the review by William R. Shea in Mathematical Reviews 2004e:01025. (TBC) #31.4.178 Spagnolo, Filippo. See #31.4.186. Speed, T.P. John W. Tukey’s contributions to analysis of variance, Annals of Statistics 30 (6) (2002), 1649–1665. The author discusses 15 key papers by Tukey and represents a guide to solved problems in the field and to open problems and ideas. According to Speed, much of Tukey’s work in this area is underappreciated, and much of that which was appreciated at the time has been forgotten. In the author’s opinion Tukey was too far away from the world of linear models most statisticians inhabit. Further details of important contributions are given in the review by Jon Stene in Mathematical Reviews 2004d:62004. (ACL) #31.4.179 Sponsel, Alistair. Constructing a “revolution in science”: The campaign to promote a favourable reception for the 1919 solar eclipse experiments, British Journal of the History of Science 35 (4) (2002), 439–467. The public success of the 1919 experiments was partly due to a campaign by Eddington and Dyson to promote Einstein’s theory of relativity. (GVB) #31.4.180 Steen, Lynn Arthur. Analysis 2000: Challenges and opportunities, in #31.4.35, pp. 191–210. (GVB) #31.4.181 Stef¸ anescu,˘ Doru. See #31.4.4, #31.4.120, #31.4.163, and #31.4.192. 528 Historia Mathematica 31 (2004) 502–530

Stelzner, Werner. Compatibility and relevance: Bolzano and Orlov, Logic and Logical Philosophy 10 (2002), 137–171. This paper compares Orlov’s concept of compatibility with that of Bernard Bolzano. Both, for instance, regarded compatibility as crucial for logical entailment. Further similarities in aims and methods are discussed, but significant differences in the resulting logical systems due to differences in their treatment of compatibility are also stressed. See the review by Volker Peckhaus in Mathematical Reviews 2004d:01024. (ACL) #31.4.182 Stene, Jon. See #31.4.179. Stöltzner, Michael. The principle of least action as the logical empiricist’s shibboleth, Studies in History and Philosophy of Science. B. Studies in History and Philosophy of Modern Physics 34 (2) (2003), 285–318. An investigation into the reasons that logical empiricists remained silent regarding the principle of least action in the years around 1900. (GVB) #31.4.183 Suchon,´ Wojciech. Vasil’iev: What exactly did he do?, Logic and Logical Philosophy 7 (1999), 131– 141. Appraises the legitimacy of claims that N.A. Vasil’iev was the founding father of three branches of logical calculi. (GVB) #31.4.184 Takeuti, Gaisi. Memoirs of a Proof Theorist: Gödel and other Logicians, translated from the Japanese by Mariko Yasugi and Nicholas Passell, River Edge, NJ: World Scientific Publishing, 2003, xviii + 135 pp. Contains English translations of 10 articles originally published in Japanese. No attempt is made to update or correct the material these contain by using more recent scholarship on Gödel, making this volume of somewhat questionable value on its subject. See the review by John W. Dawson Jr. in Mathematical Reviews 2004f:01037. (CJ) #31.4.185 Tattersall, James J. See #31.4.62. Toffalori, Carlo. See #31.4.114. Tordini, Samanta. See #31.4.114. Toscano, Elena; and Spagnolo, Filippo. An interpretive excursion into twentieth-century logic [in Italian], Quaderni di Ricerca in Didattica 11 (2002), 16 pp. (electronic). This review of 20th-century logic begins with 19th-century algebraic logic, especially by Boole and C.S. Peirce. Then it turns to the Bourbakists (who notoriously despised formal logic), and gives a table of categories, of which mathematical logic is “Grand logic.” See the review by Ivor Grattan-Guinness in Mathematical Reviews 2004e:01040. (TBC) #31.4.186 Treder, H. See #31.4.158. Tsamparlis, Michael. See #31.4.106. Tyulina, I.A. Professor Vladimir Vasil’evich Golubev—The first dean of the Department of Mechan- ics and Mathematics at Moscow State University [in Russian], Voprosy Istorii Estestvoznaniya i Tekhniki 2003 (2), 135–142. The department came into existence 70 years ago, along with six others. Under Gol- ubev’s leadership, it became one of the most renowned educational institutions of its kind in the world. (GVB) #31.4.187 Historia Mathematica 31 (2004) 502–530 529

Ul’yanov, P.L. On interconnections between the research of Russian and Polish mathematicians in the theory of functions, in Wiesław Zelazko,˙ ed., Fourier Analysis and Related Topics (Warsaw: Polish Academy of Sciences, 2002), pp. 119–130. A survey of 20th-century work on three problems in the theory of functions, concentrating particularly on Russian and Polish contributions. See the review by Martin E. Muldoon in Mathematical Reviews 2004b:42001. (GVB) #31.4.188 Ullrich, Peter. Die Weierstraßschen “analytischen Gebilde”: Alternativen zu Riemanns “Flächen” und Vorboten der komplexen Räume [The Weierstrassian “analytic conﬁgurations”: Alternatives to Riemann’s “surfaces” and forerunners of complex spaces], Jahresbericht der deutschen Mathematiker- Vereinigung 105 (1) (2003), 30–59. Weierstrass’s notion of “analytic conﬁgurations,” which may be seen as similar to Riemann’s “surfaces”, came close to the idea of a complex manifold. (GVB) #31.4.189 Unguru, Sabetai. See #31.4.61. Van Brummelen, Glen R. See #31.4.14 and #31.4.69. Van Egmond, Warren. See #31.4.55 and #31.4.151. Vasconcelos, Júlio C.R. Inertia as a theorem in Galileo’s Discorsi, in José Montesinos and Carlos Solís, eds., Philosophy on a Wide Scale [in Italian] (La Orotava: Fundación Canaria Orotava de Historia de la Ciencia, 2001), pp. 293–305. Argues that there is no principle of inertia in Galileo’s Discorsi, only a concept. (GVB) #31.4.190 Vermeulen, Corinna. See #31.4.21. Vicente, Jorge Lorenzo. See #31.4.117. Villegas, Miguel Angel Gómez. Comment: “Essay toward solving a problem in the doctrine of chances” [R. Soc. London Philos. Trans. 53 (1763), 370–418] by T. Bayes [in Spanish], Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales (España) 95 (1–2) (2001), 81–85. Discusses the background to the inverse probability problem and gives several opinions on the work by Bayes’s contemporaries. (GVB) #31.4.191 Vishnevski˘ı, V.V. The contribution of Bolyai, Gauss, and Lobachevski˘ı to the discovery of non- Euclidean geometry (on the 200th anniversary of the birth of Janos Bolyai) [in Russian], Izvestiya Vysshikh Uchebnykh Zavedeni˘ı. Matematika 2002 (11), 3–7; English translation in Russian Mathematics 46 (11) (2002), 1–5. A short account of the contributions of the discoverers of non-Euclidean geometry. The paper includes a listing of their publications and manuscripts on this subject and of short biographies and appropriate references, especially in Russian. See the review by DoruStef ¸ anescu˘ in Mathematical Reviews 2004d:01020. (ACL) #31.4.192 Von Plato, Jan. See #31.4.126. Wachsmuth, Amanda; Wilkinson, Leland; and Dallal, Gerard E. Galton’s bend: A previously undis- covered nonlinearity in Galton’s family stature regression data, American Statistician 57 (3) (2003), 190–192. Analysis of Galton’s regression data on heights of parents and children, showing that the relationship is actually nonlinear. See the review by David Bellhouse in Mathematical Reviews 2004f:62017. (CJ) #31.4.193 530 Historia Mathematica 31 (2004) 502–530

Wahlquist, Hugo D. See #31.4.106. Wiesław, Witold. Vilnius mathematics in the time of Adam Mickiewicz [in Polish], Roczniki Pol- skiego Towarzystwa Matematycznego. Seria II. Wiadomosci Matematyczne 38 (2002), 139–177. De- scribes the mathematics that was taught at Vilnius University from 1790 to 1820. (GVB) #31.4.194 Wilkinson, Leland. See #31.4.193. Wills, Jörg M. Kepler, Kugeln, Cluster, Katastrophen [Kepler, spheres, clusters, catastrophes], Math- ematische Semesterberichte 50 (1) (2003), 95–109. A discussion of the theory and applications of sphere packing, beginning with the classical problems of Kepler and Newton. (GVB) #31.4.195 Wilson, Robin J. See #31.4.89 and #31.4.153. Yasugi, Mariko. See #31.4.185. Yazdi, Hamid-Reza Giahi. The Z¯ıj Mutabar Sanjar¯ı: Its position and importance in the history of Islamic period astronomy [in Persian], Tarikh-e-Elm 1 (2003), 75–88. This article summarizes the various sections of this early 11th/12th-century A.D. z¯ıj by al-Khazin¯ ¯ı. (GVB) #31.4.196 Zardecki, Andrew. See #31.4.18.