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Historia Mathematica 27 (2000), 443–462 doi:10.1006/hmat.2000.2290, available online at http://www.idealibrary.com on

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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. Materials should be sent to Glen Van Brummelen, Bennington College, Bennington, VT 05201, U.S.A. (E-mail: gvanbrum@ bennington.edu). 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 translit- eration 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 Volumes1 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 Randy Elzinga (Hamilton, Canada), Hardy Grant (Ottawa, Canada), Ivor Grattan-Guinness (Middlesex, UK), Cal Jongsma (Sioux Center, IA), Albert Lewis (Indianapolis, IN), Gary Stoudt (Indiana, PA), David Zitarelli (Philadelphia, PA), and Glen Van Brummelen.

Abeles, Francine F. Betting Round aka Pari-Mutual Betting: A Note on C. L. Dodgson, in #27.4.159, pp. 176– 183. This paper relates that Dodgson discovered in 1856, and communicated in an unpublished letter of 1857, the “pari-mutuel” betting system often credited to Pierre Oller (1865). The system itself, and Dodgson’s reasoning in setting it out, are described in detail. (HG) #27.4.1

Abraham, George. See #27.4.157. Alexanderson, Gerald L. The Random Walks of George Polya´ , Mathematical Association of America, 2000, 320 pp., hardbound $41.95, softbound $29.95 ($32.95/$23.95 for MAA members). The first half of this book is a portrait of George Pólya,as teacher and mathematician. The second half contains eight papers on Pólya’s accomplishments: “Pólya’s Work in Probability” by K. L. Chung, “Pólya’s Work in Analysis” by Ralph P. Boas, “Comments on Number Theory” by D. H. Lehmer, “Pólya’s Geometry” by Doris Schattschneider, “Pólya’s Enumeration Theorem” by R. C. Read, “Pólya’s Contributions in Mathematical Physics” by M. M. Schiffer, “George Pólyaand Mathematics Education” by Alan H. Schoenfeld, and “Pólya’s Influence” (references to his work). (GVB) #27.4.2

Allaire, Patricia R.; and Cupillari, Antonella. Artemas Martin: An Amateur Mathematician of the Nineteenth Century and His Contribution to Mathematics, College Mathematics Journal 31 (2000), 22–34. A survey of Martin’s contributions to mathematics in the United States, especially the establishment of journals, number theory and other classical topics, probability, and calculus. (GVB) #27.4.3 Anacona, Maribel Patricia. See #27.4.7. Anapolitanos, Dionysios A. Leibniz: Representation, Continuity and the Spatiotemporal, Dordrecht: Kluwer, 1999, xii+195 pp., $96. Treats Leibniz’s metaphysics and the role played by mathematics in developing his philosophical ideas. See the review by Marcel Guillaume in Mathematical Reviews 2000f:01010. (CJ) #27.4.4

443 0315-0860/00 $35.00 Copyright C 2000 by Academic Press All rights of reproduction in any form reserved. 444 ABSTRACTS HMAT 27

Angelelli, Ignacio. See #27.4.151. Apollonius of Perga. Conics, Books I–III, trans. R. Catesby Taliaferro, revised edition William H. Donahue, ed., with a preface by Dana Densmore and William H. Donahue, and an introduction by Harvey Flaumenhaft, Santa Fe: Green Lion Press, 1998, xxxviii+284 pp., hardbound $42, paperbound $23.95. This English translation of the Conics is a revised edition of that of R. Catesby Taliaferro of 1939 which was also used in the Britannica Great Books series. J. Lennart Berggren in his detailed review, Mathematical Reviews 2000d:01005, welcomes it and deems it superior to that of Thomas Little Heath. (ACL) #27.4.5 Apostol, Tom. See #27.4.50. Appleman, Jacob M. The Life of Emil Post and his “Polyadic Groups,” in #27.4.159, pp. 184–201. Details of Post’s life, personality, and career, including glimpses of his work in mathematical logic. The motivation for his work on polyadic groups and his axiomatization of them are discussed at some length. (HG) #27.4.6 Arboleda, Luis Carlos; and Anacona, Maribel Patricia. Non-Euclidean Geometries in Colombia, The Euclidean Wager of Professor Julio Garavito (1865–1920) [in Spanish], Quipu: Revista Latinoamericana de Historia de las Ciencias y la Tecnolog´ıa 11 (1) (1994), 7–24. Argues that Garavito’s resistance to the acceptance of non-Euclidean geometries in early 20th-century Colombia was not due simply to tradition and intellectual backwardness, but had a deeper philosophical basis. (GVB) #27.4.7 Arkhangel’ski˘ı,A. V.; and Tikhomirov, V. M. Pavel Samuilovich Uryson (1898–1924) [in Russian], Uspekhi Matematicheskikh Nauk 53 (5) (1998), 5–26; English translation in Russian Mathematical Surveys 53 (5) (1998), 875–892. This substantial biography of the short-lived topologist includes a 72-item bibliography. See the review by Roman Duda in Mathematical Reviews 2000d:01017. (ACL) #27.4.8 Arthur, Richard. Cohesion, Division and Harmony: Physical Aspects of Leibniz’s Continuum Problem (1671– 1686), Perspectives on Science 6 (1–2) (1998), 110–135. On Leibniz’s notion of the continuum in connection with his views on space and motion. See the review by Detlef Laugwitz in Mathematical Reviews 2000f:01011. (CJ) #27.4.9 Arthur, Richard. The Transcendentality of and Leibniz’s Philosophy of Mathematics, in #27.4.159, pp. 13– 19. An account of an unpublished paper of 1676 in which Leibniz considers the possibility of proving that “the magnitude of a circle cannot be expressed by an equation of any degree.” The proof would attempt to argue that circumference and diameter “do not have even an infinitely small common measure.” (HG) #27.4.10 Austin, Bill; Barry, Don; and Berman, David. The Lengthening Shadow: The Story of Related Rates, Mathematics Magazine 73 (2000), 3–12. An examination of related problems in calculus textbooks, especially in the 19th century. (GVB) #27.4.11 Baltus, Christopher. Issues in the Early History of the Fundamental Theorem of Algebra, in #27.4.159, pp. 164– 175. This paper raises, without fully resolving, the question of whether the proofs of the FTA given respectively by (i) d’Alembert and (separately) by (ii) Euler, Lagrange, Foncenex, and Laplace can be said to weaken the common ascription of priority to the first of Gauss’s proofs. (HG) #27.4.12 Barbut, Marc. Machivel et la PraxéologieMathématique, Mathematiques´ Informatique et Sciences Humaines 146 (1999), 19–30. Discusses Machiavelli’s work as a pre-formal contribution to game theory. See the review by Warren Van Egmond in Mathematical Reviews 2000f:01008. (CJ) #27.4.13 Barrow-Green, June. Mathematics in Britain 1860–1940: The BRITMATH Database on the World Wide Web, in #27.4.159, pp. 271–285. The author describes the design and contents of the database and provides examples of its use in research, from answers to simple factual queries to the discovery of unexpected insights in three areas (geometry in Cambridge, the Smith’s prizes at Cambridge, “mathematics and the empire”). (HG) #27.4.14 Barry, Don. See #27.4.11. Bartle, R. G. See #27.4.154. Bashmakova, Isabella G.; and Smirnova, Galina S. The Origin and Development of Algebra [in Russian], in B. M. Gnedenko, ed., Outlines of the History of Mathematics [in Russian], Moscow: Izdatelstvo Moskovskogo HMAT 27 ABSTRACTS 445

Universiteta, 1997, pp. 94–246. This paper is a synopsis of the development of algebra from ancient times up to the 19th century. The description is focused on the main problems that stimulated progress, as well as on the fundamental ideas and methods which were used for solving these problems. See the review by F. Mendelson in Mathematical Reviews 2000e:01003. (GSS) #27.4.15

Beckers, Danny. See #27.4.46.

Bensa, Elisa; and Zanarini, Gianni. The Physics of Music: Origin and Development of Musical Acoustics in the XVIIth and XVIIIth Centuries [in Italian], Nuncius 14 (1999), 69–111. A revisitation of the history of musical acoustics from Galileo to the end of the 18th century, emphasizing consonance theories. (GVB) #27.4.16

Berger, Marcel. Riemannian Geometry during the Second Half of the Twentieth Century, American Mathematical Society, 2000, 182 pp., softbound, $34 ($27 for AMS members). A survey of recent developments in Riemannian geometry; contains a chapter on Riemannian geometry before 1950. (GVB) #27.4.17

Berggren, J. Lennart. Numbers at Work in Medieval Islam, Journal for the History of Arabic Science 11 (1–2) (1995/97), 45–51. The author describes the arithmetical technique of “ﬁnger reckoning,” concentrating on the representation of fractions and their use in social life. See the review by Jens Høyrup in Mathematical Reviews 2000e:01012. (GSS) #27.4.18

Berggren, J. Lennart. Geometric Methods in Medieval Islam: The Case of the Azimuth Circles, in #27.4.73, pp. 13–21. Surveys the variety of medieval geometric methods for drawing azimuth circles on the planispheric astrolabe. (GVB) #27.4.19

Berggren, J. Lennart. See also #27.4.5.

Berlinski, David. The Advent of the Algorithm: The Idea that Rules the World, Mathematical Association of America, 2000, 368 pp., $28. Covers the history and social impact of the algorithm from Leibniz to the middle of the 20th century. (GVB) #27.4.20

Berman, David. See #27.4.11.

Blay, Michel; and Festa, Egidio. Mouvement, Continu et Composition des Vitesses au XVIIe Si`ecle, Archives Internationales d’Histoire des Sciences 48 (1998), 65–118. Starting with Galileo’s mistake of taking the speed of a falling body as proportional to distance, this work considers the treatment of speed in the 17th century, especially through the contributions of Bonaventura Cavalieri, Giovanni Paolo Casati, and Pierre Varignon. See the review by Niccol`oGuicciardini in Mathematical Reviews 2000d:01010. (ACL) #27.4.21

Blinn, James F. See #27.4.50.

Boas, Ralph P. See #27.4.2.

Boger, George. Completion, Reduction and Analysis: Three Proof-Theoretic Processes in Aristotle’s Prior An- alytics, History and Philosophy of Logic 19 (1998), 187–226. Distinguishes between three interpretations of Aristotle’s notion of a sullogismos in the Prior Analytics. (GVB) #27.4.22

Boi, Luciano. La Probleme` Mathematique´ de l’Espace: Une Queteˆ de l’Intelligible, Berlin: Springer-Verlag, 1995, xxiv+526 pp. Extensive historical study of concepts and methods in nineteenth century geometry: the early development of non-Euclidean geometry, curvature, surfaces, Riemannian geometry, Beltrami, Helmholtz, and Clifford. See the review by Bernard Rouxel in Mathematical Reviews 2000f:01002. (CJ) #27.4.23

Bolzano, Bernard. Bernard Bolzano—Gesamtausgabe. Reihe II. Nachlass B. Wissenschaftliche Tagebucher.¨ Band 8. Teil 2, Bob van Rootselaar and Anna van der Lugt, eds., Stuttgart: Friedrich Frommann Verlag G¨unther Holzboog, 1999, 210 pp., DM 398. This volume transcribes the notes Bolzano kept on his readings between May 24, 1815 and February 8, 1816. Among the authors he was reading were Hobbes, Barrow, Sturm, Clairaut, and Boscovich. See the review by Joseph Warren Dauben in Mathematical Reviews 2000e:01044. (GSS) #27.4.24

Bottazzini, Umberto. See #27.4.144. 446 ABSTRACTS HMAT 27

Boutillier, David. The Prospects for Intuitionistic Conceptions of Mathematics, in #27.4.159, pp. 28–37. This paper (i) sets out to show that “Frege’s attempt to provide a characterization of arithmetic that explains how numerical terms refer” is inconsistent, (ii) considers a proposal by Hartry Field for explaining the application of mathematics, and (iii) considers “what happens to logicism if classical logic and mathematics is [sic] rejected.” (HG) #27.4.25

Br´eard,Andrea. Re-Kreation eines Mathematischen Konzeptes im Chinesischen Diskurs, Stuttgart: Franz Steiner Verlag,1999, xx+461 pp., DM 168. The author explains mathematical questions from Chinese primary sources and through detailed mathematical analysis, to give understandable answers to them. The work deals with insufﬁciently studied source materials, now making them accessible. See the review by Keizo Hashimoto in Mathematical Reviews 2000e:01011. (GSS) #27.4.26

Breger, Herbert. Gottfried Wilhelm Leibniz als Mathematiker, in Uberblicke¨ Mathematik 1996/97, 5–17. A summary of the mathematical career and achievements of Leibniz. The author contends that the foundations of the inﬁnitesimal calculations of Leibniz are neither vague nor contradictory but are misunderstood by modern readers. See the review by Willard Parker in Mathematical Reviews 2000e:01040. (GSS) #27.4.27

Breger, Herbert. See #27.4.71.

Bridges, Douglas S. See #27.4.85.

Brigaglia, Aldo; and Scimone, Aldo. Algebra and Number Theory [in Italian], in Simonetta di Sieno, Angelo Guerraggio, and Pietro Nastasi, eds., Italian Mathematics after Unity [in Italian], Milan: Marcos y Marcos, 1998, pp. 505–567. This survey of algebra and number theory in Italy from 1919 to 1936 provides an overview of the connections between Italian mathematicians and their interactions with the mathematics developed elsewhere. It includes Betti, Battaglini, Peano, Bianchi, Scorza, Cipolla, and Ricci. Note is especially taken of the lack of impact in Italy of the modern algebra of Emmy Noether and van der Waerden. Thirty-six photographs are included. A detailed review is given by H. Lausch in Mathematical Reviews 2000d:01015. (ACL) #27.4.28

Butzer, Paul L. Scholars of the Mathematical Sciences in the Aachen-Li`ege-MaastrichtRegion during the Past 1200 Years; An Overview, in Paul L. Butzer, H. Th. Jongen, and W. Oberschelp, eds., Charlemagne and his Heritage, Vol. 2, Turnhout: Brepols, 1998, pp. 43–90. This comprehensive biographical listing indicates the mathematical contributions made by natives of the heartland of the empire of Charlemagne. Jens Høyrup in his review, Mathematical Reviews 2000d:01018, takes the article to task for excessive modernizing in the descriptions of the pre-moderns. (ACL) #27.4.29

Cartwright, M. L. See #27.4.165.

Cercignani, Carlo. Ludwig Boltzmann: The Man Who Trusted Atoms, Oxford: Oxford Univ. Press, 1998, xviii+ 329 pp., $49.95. Gives quick information on Boltzmann’s work and relationships with other scientists. See the review by Wilfred Schroder in Mathematical Reviews 2000f:01023. (CJ) #27.4.30

Chabrier, Jean-Claude. Musical Science, in Roshdi Rashed and R´egisMorelon, eds., Encyclopedia of the History of Arabic Science, London: Routledge, 1996, Vol.2, pp. 581–613. Discusses medieval Arabic music and its relation to various Greek theories known to the Arabs. See the review by Christoph J. Scriba in Mathematical Reviews 2000f:01004. (CJ) #27.4.31

Charette, Francois. A Monumental Medieval Table for Solving the Problems of Spherical Astronomy for all Latitudes, Archives Internationales d’Histoire des Sciences 48 (1998), 11–64. Description and analysis of the largest astronomical table of the Middle Ages. See the review by Benno van Dalen in Mathematical Reviews 2000f:01005. (CJ) #27.4.32

Chatterji, S. D. See #27.4.165.

Chung, K. L. See #27.4.2.

Cipra, Barry. A Bicentennial for the Fundamental Theorem of Algebra, Math Horizons, November 1999, 5–7. A historical background to, and brief description of, Gauss’s doctoral dissertation on the Fundamental Theorem of Algebra. (GVB) #27.4.33 HMAT 27 ABSTRACTS 447

Cohen, Edward L. Calendars of the Dead-Sea-Scroll Sect, in #27.4.159, pp. 59–71. The Essenes who wrote the scrolls used two calendars, a 354-day lunar one and a (much more complicated) 364-day solar one. These are here described in detail, with special attention to the problem of adjusting the 364-day calendar to the actual length of a year. (HG) #27.4.34 Cohen, Edward L. Adoption and Reform of the Gregorian Calendar, Math Horizons, February 2000, 5–11. Describes a number of innovations, proposed or realized, to calendars from 1582 to the present. (GVB) #27.4.35 Cohen, I. Bernard. Newton’s Determination of the Masses and Densities of the Sun, Jupiter, Saturn, and the Earth, Archive for History of Exact Sciences 53 (1998), 83–95. The author gives a careful analysis of the determinations of the masses and densities of the planets and the sun on the same scale as the mass and density of the Earth in Newton’s Principia. The differences in the three editions of the Principia are detailed and discussed. See the review by Massimo Galuzzi in Mathematical Reviews 2000e:01021. (GSS) #27.4.36 Cooke, Roger. See #27.4.107. Cordes, Heinz; Jensen, Arne; Kuroda, S. T.; Ponce, Gustavo; Simon, Barry; and Taylor, Michael. Tosio Kato (1917–1999), Notices of the American Mathematical Society 47 (2000), 650–657. A memorial of Tosio Kato surveying his work in a number of different areas of mathematics and physics including Schrodinger operators, atomic Hamiltonians and self-adjointness, scattering theory, perturbation theory, nonlinear evolution equations, and others. (RE) #27.4.37 Corrigan, Joe. See #27.4.50. Corry, Leo. The Influence of David Hilbert and Hermann Minkowski on Einstein’s Views over the Interrelation Between Physics and Mathematics, Endeavor 22 (3) (1998), 95–97. Argues that Hilbert and Minkowski influenced Einstein’s change in his view of mathematics from that of a mere tool, to the source of scientific creativity. (GVB) #27.4.38 Corry, Leo. From Mie’s Electromagnetic Theory of Matter to Hilbert’s Unified Foundations of Physics, Studies in History and Philosophy of Modern Physics 30 (2) (1999), 159–183. Describes the importance of Mie’s electromagnetic theory of matter for Hilbert’s development of Einstein’s theory of general relativity. See the review by H. Treder in Mathematical Reviews 2000f:01020. (CJ) #27.4.39 Craik, Alex D. D. Geometry Versus Analysis in Early 19th-Century Scotland: John Leslie, William Wallace, and Thomas Carlyle, Historia Mathematica 27 (2000), 133–163. Scottish mathematicians led the introduction of “continental” analysis into Britain, although they continued to emphasize Euclidean geometry in their courses. Eventually the tensions led to a dispute over the teaching of astronomy. (GVB) #27.4.40 Crépel,P. See #27.4.60. Cuomo, Serafina. Pappus of Alexandria and the Mathematics of Late Antiquity, Cambridge, UK: Cambridge Univ. Press, 2000, 234 pp., hardbound, $59.95. Attempts to improve Pappus’s reputation by placing him in the context of his time. (GVB) #27.4.41 Cupillari, Antonella. See #27.4.3. Dauben, Joseph Warren. Abraham Robinson: The Creation of Nonstandard Analysis, Princeton, NJ: Princeton Univ. Press, 1998, 579 pp., hardbound $97.50, softbound $29.95. Follows Robinson’s odyssey from Hitler’s Germany through Palestine and wartime Europe to the USA; also explains and explores the revolutionary achievement of nonstandard analysis. (GVB) #27.4.42 Dauben, Joseph Warren. See also #27.4.24. Dauben, Joseph Warren; and Lewis, Albert C., eds. The History of Mathematics from Antiquity to the Present: A Selective Annotated Bibliography, revised edition on CD-ROM, Providence, RI: American Mathematical Society, 2000, $49 ($39 for AMS members). A revised and updated edition of Dauben’s 1985 bibliography, containing twice as many entries; now searchable by computer and contains Internet links. (GVB) #27.4.43 Day, Peter W. See #27.4.106. 448 ABSTRACTS HMAT 27

De Gandt, Fran¸cois. See #27.4.71. De Leeuw, Karl. Cryptology and Statecraft in the Dutch Republic, doctoral dissertation, Univ. of Amsterdam, 2000, 216 pp. Available through the Institute for Programming Research and Algorithmics. Comprising an extensive general introduction followed by six papers (four in English, two in Dutch) published during the 1990s in historical and cryptographical journals. Covers material little noticed in the history of mathematics, in contrast to the story for the mid-20th century (Turing and all that). (IGG) #27.4.44 Deakin, Michael A. B. See #27.4.65. Dellian, Ed. Nochmals: Die Newtonische Konstante. Bemerkungen zu Isaac Newtons Lehre von der Absoluten Bewegung [Once Again: the Newtonian Constant. Remarks on Isaac Newton’s Theory of Absolute Motion], Philosophia Naturalis 36 (1) (1999), 19–34. In this work the author maintains that during the eighteenth century mechanics was developed according to principles which differ dramatically from those of Newton. According to Newton force is proportional to change in momentum and the author speculates about the constant of proportionality implied and hints at the relationships that might occur between this “Newtonian constant” and the velocity of light according to special relativity. See the review by NiccolòGuicciardini in Mathematical Reviews 2000e:01022. (GSS) #27.4.45 Dennis, John; Fauvel, John; Singmaster, David; Eagle, Ruth; Liebeck, Pam; and Beckers, Danny. “A Most Horrible Infamy”: The Keele Saga Continues, BSHM Newsletter 41 (2000), 11–19. An update on the sale of invaluable works from the Turner Collection at the University of Keele, including information on its dispersal and selling price. The piece by Danny Beckers on the Keele multiplier effect describes a similar sale held in the Netherlands last year. (DEZ) #27.4.46 Densmore, Dana. See #27.4.5. Detlefsen, Michael. Constructive Existence Claims, in Matthias Schirn, ed., The Philosophy of Mathemat- ics Today, New York: Oxford Univ. Press, 1998, pp. 307–335. In this article the author examines the fundamental differences between Brouwer’s and Hilbert’s epistemological conceptions of the nature of the exhi- bition of an object as proof of its existence. The author concludes by stating that Brouwer was “a kind of mathematical ‘existentialist.’” See the review by Victor V. Pambuccian in Mathematical Reviews 2000e:00006. (GSS) #27.4.47 Devlin, Keith. See #27.4.49. Dobson, Geoffrey J. Newton’s Errors with the Rotational Motion of Fluids, Archive for History of Exact Sciences 54 (1999), 243–254. Analysis of Newton’s slightly flawed treatment of rotational motion of fluids. See the review by NiccolòGuicciardini in Mathematical Reviews 2000f:01012. (CJ) #27.4.48 Donahue, William H. See #27.4.5. Doxiadis, Apostolos. Uncle Petros and Goldbach’s Conjecture, New York: Bloomsbury, 2000, 208 pp., hardbound, $19.95. This translation of a 1992 Greek novel about a family’s obsession with proving Goldbach’s conjecture contains various references to its history. It achieved notoriety through its publishers’ offer of a $1 million prize to the first person to prove the conjecture in the next two years. See the review by Keith Devlin at MAA Online [http://www.maa.org/reviews/petros.html]. (GVB) #27.4.49 Duda, Roman. See #27.4.8. Eagle, Ruth. See #27.4.46. Early History of Mathematics (videotape), Tom Apostol, James F. Blinn, and Joe Corrigan, producers, Pasadena, CA: California Institute of Technology, 2000, 30 mins., VHS/PAL, $34.90. Outlines a variety of developments in the early history√ of mathematics, including Babylonian calendars, the Pythagorean Theorem, estimates of , the irrationality of 2, ancient astronomy and trigonometry, and the creation of analytic geometry, giving rise eventually to the birth of calculus. Available at http://www.projectmathematics.com. (GVB) #27.4.50 Epkenhaus, Martin. See #27.4.125. HMAT 27 ABSTRACTS 449

Fauvel, John. See #27.4.46. Ferguson, Kitty. Measuring the Universe: Our Historic Quest to Chart the Horizons of Space and Time,New York: Walker & Co., 1999, 342 pp., hardbound, $27. A popular history of various attempts to measure astronomical quantities, from Eratosthenes to Stephen Hawking. Describes the social contexts at the cost of the mathematics. (GVB) #27.4.51 Ferrari, Jean. See #27.4.71. Ferraro, Giovanni. Functions, Functional Relations, and the Laws of Continuity in Euler, Historia Mathematica 27 (2000), 107–132. An analysis of the notions of functions, their aspects, and continuity in Euler’s mathematics. (GVB) #27.4.52

Ferreirós,José. Labyrinth of Thought: A History of Set Theory and its Role in Modern Mathematics, Boston: Birkhäuser, 1999, 464 pp., hardbound, $115. This discussion of the development of set theory from 1850 to 1950 concentrates more on the development of research programmes than on technical results. (GVB) #27.4.53

Festa, Egidio. See #27.4.21.

Flaumenhaft, Harvey. See #27.4.5.

Fossa, John. An Introduction to Platonic Mathematics, in #27.4.159, pp. 307–312. This paper presents in detail a geometrical interpretation of the “nuptial number” passage in Republic 546, an interpretation which “explains how the Nuptial Number determines those times that are propitious for human procreation.” (HG) #27.4.54

Fowler, David. Inventive Interpretations, Revue d’Histoire des Mathematiques´ 5 (1999), 149–153. This note discusses the lack of an arithmetic basis in extant Greek geometry, and suggests that our reconstruction of an early geometry based on arithmetical procedures, borrowed from ancient Babylon, reflects historians’ modern cultural perceptions of geometry more than it does the Greek evidence. (GVB) #27.4.55 Francis, Richard L. See #27.4.97. Franzen, Winfried. See #27.4.71. Galuzzi, Massimo. See #27.4.36 and #27.4.61. a Garding, Lars. A Happy Collaboration, Asian Journal of Mathematics 3 (1) (1999), xlix–liv. The forward elementary solution of a hyperbolic differential operator requires algebraic topology and algebraic geometry. The author tells the very interesting story of his collaboration with the topologist Bott and the algebraic ge- ometer Atiyah and the results they found. See the review by M. Zerner in Mathematical Reviews 2000e:01038. (GSS) #27.4.56 Garro, Ibrahim. Limits, Asymptotes and Infinities, Old and New, in #27.4.159, pp. 72–97. Discussion of both the historical significance (e.g., introduction of “noneuclidean concepts”), and the modern generalization and resolution (e.g., in terms of nonarchimedean fields), of three paradoxes from medieval Arabic geometry. The paper touches at a number of points on the “methodological and philosophical differences between Greek and Arabic mathematics.” (HG) #27.4.57 Gaskin, Richard. Russell and Richard Brinkley on the Unity of the Proposition, History and Philosophy of Logic 18 (1997), 139–150. Describes Russell’s attempts to understand the unity of the proposition, and finds anticipations of his difficulties in the writings of the 14th-century philosopher Richard Brinkley. (GVB) #27.4.58 Gazalé,Midhat J. Number: From Ahmes to Cantor, Princeton: Princeton Univ. Press, 2000, 272 pp., hardbound, $29.95. A companion and successor to Gazalé’s Gnomon: From Pharaohs to Fractals (#27.2.67), this popular book covers a variety of cultures, combining history, mathematics, and a little computer science. (GVB) #27.4.59 Gil, Thomas. See #27.4.71. Gingerich, Owen. See #27.4.117. 450 ABSTRACTS HMAT 27

Godard, Roger; and Cr´epel,P. An Historical Study of the Median, in #27.4.159, pp. 207–218. This survey begins in the 18th century but focuses mainly on the 19th, especially the work of the “English School” (Galton, Edgeworth); it also treats brieﬂy some 20th-century developments. One section covers the 19th-century study of the statistics of sorted observations. (HG) #27.4.60 Goldenbaum, Ursula. See #27.4.71.

Goodstein, David L.; and Goodstein, Judith R. Feynman’s Lost Lecture. The Motion of Planets Around the Sun, with CD-ROM, New York: Norton, 1996, 191 pp. The focus of this book–video package is Feynman’s lecture giving a proof of the law of ellipses for planetary motion. Feynman was evidently unaware that the method of proof had also been used by J. C. Maxwell. A comparison is given of this method and the route that Newton himself took. See the detailed review by Massimo Galuzzi in Mathematical Reviews 2000d:01011a/2000d:01011b. (ACL) #27.4.61 Goodstein, David L.; and Goodstein, Judith R. La Conferencia Perdida de Feynman: El Movimiento de los Planetas Alrededor del Sol [in Spanish], trans. Antonio-Prometeo Moya, Barcelona: Tusquets Editores, 1998, 207 pp. A translation into Spanish of #27.4.61. (GVB) #27.4.62 Goodstein, Judith R. See #27.4.61 and #27.4.62.

Grabinsky, Guillermo. The Weierstrass Continuous Nondifferentiable Function [in Spanish], Miscelanea´ Matematica´ 25 (1997), 29–38. The author discusses the original proof of Weierstrass that the function is continuous and nowhere differentiable on an interval. Other historical facts are included. See the review by Volodymyr K. Maslyuchenko in Mathematical Reviews 2000e:26006. (GSS) #27.4.63 Grafton, Anthony. Cardano’s Cosmos: The Worlds and Works of a Renaissance Astrologer, Cambridge, MA: Harvard Univ. Press, 1999, 284 pp., hardbound, $36. Concentrates mostly on Cardano’s astrology as a path to his world view, dealing only in passing with his mathematics. (GVB) #27.4.64 Grant, Hardy. Mathematics and the Liberal Arts II, College Mathematics Journal 30 (1999), 197–203. A sketch of the history of the liberal arts tradition from the 12th century to the present, emphasizing the role of the four mathematical arts: arithmetic, geometry, astronomy, and music. See the review by Michael A. B. Deakin in Mathematical Reviews 2000e:01047. (GSS) #27.4.65 Grassmann, Hermann. Extension Theory, American Mathematical Society/London Mathematical Society, 2000, 403 pp., softbound, $75 ($45 for AMS members). An English translation of a work that contains “a detailed development of the inner product and its relation to the concept of angle, the ‘theory of functions’ from the point of view of extension theory, and Grassmann’s contribution to the Pfaff problem.” (GVB) #27.4.66 Grattan-Guinness, Ivor. See #27.4.87.

Grau, Conrad. See #27.4.71.

Gray, Jeremy. Linear Differential Equations and Group Theory from Riemann to Poincare´, 2nd edition, Boston: Birkh¨auser, 1999, 384 pp., hardbound, $64.95. This study of the origins of geometric function theory in the 19th century has been expanded, and the appendices enriched with historical accounts of the Riemann–Hilbert problem, the uniformization theorem, Picard–Vessiot theory, and the hypergeometric equation in higher dimensions. (GVB) #27.4.67 Gray, Jeremy. See also #27.4.68.

Guicciardini, Niccol`o. Reading the Principia: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736, Cambridge: Cambridge Univ. Press, 1999, 285 pp., hardbound, $74.95. An account of the reception of the Principia, arguing that its acceptance was spurred by Continental mathematicians’ rewriting of its ideas from its original geometrical framework into the language of calculus (which Newton had tried to avoid in the Principia due to a dislike of algebra in matters of physics). See the review by Jeremy Gray at MAA Online [http://www.maa.org/reviews/readnewton.html]. (GVB) #27.4.68 Guicciardini, Niccol`o. See also #27.4.21, #27.4.45, and #27.4.48. HMAT 27 ABSTRACTS 451

Guillaume, Marcel. See #27.4.4. Hagengruber, Ruth. See #27.4.71. Hardy, G. H. See #27.4.165. Hashagen, Ulf. Mathematik und Technik im Letzten Drittel des 19. Jahrhunderts—Eine Bayerische Perspektive, in Friedrich Naumann, ed., Carl Julius von Bach (1847–1931), Stuttgart: Wittwer, 1998, pp. 169–184. A description of the debate about mathematical education at the technical universities in Germany at the end of the 19th century, focusing on the role of mathematician Walter von Dyck and the situation at the Technical University in Munich. See the review by Karl-Heinz Schlote in Mathematical Reviews 2000e:01031. (GSS) #27.4.69 Hashimoto, Keizo. See #27.4.26.

Hayashi, Takao. The Caturacintaman¯ . i of Giridharabhat.t.a: A Sixteenth-Century Sanskrit Mathematical Treatise, SCIAMVS 1 (2000), 133–208. An edition and translation of a work that contains similar topics and organization to Bh¯askaraII’s L¯ılavat¯ ı¯, such as arithmetical operations, mixtures, series, and plane figures. (GVB) #27.4.70 Hayashi, Takao. See also #27.4.158. Hecht, Hartmut, ed. Pierre Louis Moreau de Maupertuis. Eine Bilanz nach 300 Jahren, Berlin: Berlin-Verlag, 1999, 543 pp., DM 108. A collection of papers, mostly in German and French, in commemoration of Maupertuis’ 300th birthday. Titles include: Irene Passeron, “Maupertuis, Passeur d’Intelligibilité.De la cyclo¨ıdeàl’Ellipso¨ıd Aplati en Passant par le ‘Newtonianisme’: AnnéesParisiennes”; Conrad Grau, “Maupertuis in Berlin”; Mario Howald-Haller, “Maupertuis’ Messungen in Lappland”; Ilse Jahn, “Maupertuis Zwischen Präformations-und Epigenesistheorie. Sein Beitrag zu biologischen Fragen des 18. Jahrhunderts”; Eckhard Höfner, Non-historische ‘Ursprungs’-Modelle im 18. Jahrhundert: Zu Problemen der Origine-Konstruktionen in Maupertuis’ Sprachre- flexion und bei anderen Denkern der Epoche”; Thomas Gil, “Implizite Sozialphilosophie. Maupertuis’ Sozial- philosophische Argumentationen in den Schriften ‘Uber¨ den Urprung und die Funktion der Menschlichen Sprache”’; Winfried Franzen, “Bemerkungen zu Maupertuis’ ‘Essai de Philosophie Morale”’; Lukas Sosoe, “Mon- tesquieu et Maupertuis: Sources Fran¸caisesde l’Utilitarisme”; Ruth Hagengruber, “Emilie du Châteletan Mauper- tuis: Eine Metaphysik in Briefen”; Hartmut Hecht, “Gemeinsame Denkmotive bei Leibniz und Maupertuis”; Jean Ferrari, “Kant, Maupertuis et le Principe de la Moindre Action”; Helmut Pulte, “Mannigfaltigkeit der Regeln und Einheit der Prinzipien: Maupertuis und die Entmetaphysierung Teleologischen Denkens”; Renate Wahsner, “Uber¨ den ‘Ungrund der Neutonischen Begriffe und Sätze’.Eine Metaphysische Diskussion ‘Uber¨ eine Neue Physik”’; Fran¸coisde Gandt, “1744: Maupertuis et d’Alembert entre Mécaniqueet Métaphysique”;Dieter Suisky, “Uber¨ eine Differenz in der Begründungdes Wirkungsprinzips bei Maupertuis und Euler”; Matthias Schramm, “Zur Entste- hung des Prinzips der Kleinsten Aktion”; David Speiser, “Pierre Louis Moreau de Maupertuis (1698–1759)”; Herbert Breger, “Uber¨ den von Samuel Königveröffentlichten Brief zum Prinzip der Kleinsten Wirkung”; Ursula Goldenbaum, “Die Bedeutung der ‘Offentlichen Debatte’ überdas Jugement der Berliner Akademie fürdie Wis- senschaftsgeschichte. Eine Kritische Sichtung hartnäckigerVorurteile”; H.-H. von Borzeszkowski, “Der Episte- mologische Gehalt des Maupertuisschen Wirkungsprinzips”; RüdigerThiele, “Ist die Natur Sparsam? Betrachtun- gen zum Prinzip von Maupertuis aus Mathematikhistorischer Sicht”; and Heinz Lübbig,“Das Wirkungsprinzip von Maupertuis und Feynmans Wegintegral der Quantenphase.” (GVB) #27.4.71 Hill, Katherine. John Wallis and Isaac Barrow: Tradition and Innovation and the State of Mathematics, Endeavor 22 (3) (1998), 117–120. Wallis’s and Barrow’s works reveal a tension between traditional geometric modes of thought and the emerging algebraic techniques. (GVB) #27.4.72 Histoire des Mathematiques´ Arabes, Proceedings of the 3rd Maghreb Colloquium held in Tipaza, December 1– 3, 1990, 2 vols., Algiers: Association Algérienned’Histoire des Mathématiques,1998, Vol. 1 (Arabic): 112 pp., Vol.2 (French and English): 280 pp. The 25 papers in this collection deal with a variety of topics in the mathematical sciences in medieval Islam. Some of the papers will be abstracted separately. (GVB) #27.4.73 Höfner, Eckhard. See #27.4.71. Hogendijk, Jan P. Al-Nayr¯ız¯ı’s Mysterious Determination of the Azimuth of the Qibla at Baghd¯ad, SCIAMVS 1 (2000), 49–70. Al-Nayr¯ız¯ı’s determination of the direction of Mecca from Baghdad, the first extant correct method 452 ABSTRACTS HMAT 27 complete with geometric proof, nevertheless resulted in a hopelessly poor value, due to a numerical instability at a vital stage of his calculation; this may explain the lack of popularity of his method. Includes an edition and translation of the text. (GVB) #27.4.74

Howald-Haller, Mario. See #27.4.71.

Høyrup, Jens. See #27.4.18, #27.4.29, and #27.4.142.

Ingraham, R. L. See #27.4.103.

Jackson, Allyn. Mathematics in Barcelona: Time Past, Time Future, Notices of the American Mathematical Society 47 (2000), 554–560. Mathematically speaking, the country of Spain is still in early stages of growth. This article surveys the growth of mathematics in Spain during the dictatorship of Francisco Franco, which began after the Spanish Civil War (1936–1939) and lasted until his death in 1975. The article focuses mainly on the recent mathematical development in the region of Catalonia after the death of Franco. It also speculates on the future of mathematics in Barcelona which is in Catalonia. (RE) #27.4.75

Jahn, Ilse. See #27.4.71.

Jensen, Arne. See #27.4.37.

Jesseph, Douglas. Leibniz on the Foundations of the Calculus: The Question of the Reality of Inﬁnitesimal Magnitudes, Perspectives on Science 6 (1–2) (1998), 6–40. On the changing status of inﬁnitesimals in Leibniz’s writings. See the review by Detlef Laugwitz in Mathematical Reviews 2000f:01013. (CJ) #27.4.76

Katz, Victor J., ed. Using History to Teach Mathematics: An International Perspective, Mathematical Association of America, 2000, 300 pp., paperbound, $32.95 ($25.95 for MAA members). This diverse collection of papers on the use of history in mathematics teaching is the outcome of a 1996 conference on history and pedagogy of mathematics. The papers will be abstracted in future issues. (GVB) #27.4.77

Katz, Victor J. See also #27.4.128, #27.4.129, and #27.4.130.

Kennedy, Edward S. Mathematical Geography, in Roshdi Rashed and R´egisMorelon, eds., Encyclopedia of the History of Arabic Science, Vol. 1, London: Routledge, 1996, pp. 185–201. Beginning with the Arabic translations of Marinus of Tyre and Ptolemy, made by the end of the ninth century, this work surveys what is known of Arabic/Islamic cartographic techniques. The most notable names are al-B¯ır¯un¯ı and al-Zarqalluh (Azarquiel). George Saliba in his review, Mathematical Reviews 2000d:01008, refers to his own researches that conclude that European scientists did not require Latin translations in order to beneﬁt from such Arabic sources. (ACL) #27.4.78

Kjeldsen, Tinne Hoff. The Origin of Nonlinear Programming, in #27.4.159, pp. 219–237. A classic 1950 paper by Kuhn and Tucker is widely regarded as founding the mathematical theory of nonlinear programming. The author sets this paper in its historical and mathematical context, and argues that the support of Kuhn and Tucker by the (U.S.) Ofﬁce of Naval Research exerted an “enormous” inﬂuence. (HG) #27.4.79

Kleiner, Israel. From Fermat to Wiles: Fermat’s Last Theorem Becomes a Theorem, Elemente der Mathematik 55 (2000), 19–37. The mathematical story of Fermat’s Last Theorem, roughly evenly split between the period from Fermat to the early 20th century, and modern developments leading to Wiles’s proof. (GVB) #27.4.80

Knobloch, Eberhard. Analogy and the Growth of Mathematical Knowledge, in E. Groshold and H. Breger, eds., The Growth of Mathematical Knowledge, Dordrecht: Kluwer, 2000, pp. 295–314. The role of analogy in the expansion of mathematical knowledge is explored, using examples especially from the mathematics of Clavius, Kepler, John Bernoulli, and Leibniz. (GVB) #27.4.81

Knobloch, Eberhard. See also #27.4.89. Koch, Helmut. Mathematik in der DDR, Mitteilungen der Deutschen Mathematiker-Vereinigung, 1999 (2), pp. 34–41. Contains reminiscences of a renowned number theorist on the topic. See the review by Michael Otte in Mathematical Reviews 2000f:01025a. (CJ) #27.4.82 HMAT 27 ABSTRACTS 453

Kreyszig, Erwin. On the Evolution of Engineering Mathematics, in #27.4.159, pp. 122–128. Three case studies— Euler and his theory of ships and turbines, Monge and descriptive geometry, Hamilton and the “war” between quaternions and vectors—are presented in support of the claim that “the history of engineering mathematics is a worthwhile domain for further research” and would enrich the teaching of mathematics to “engineers, physicists and computer scientists.” (HG) #27.4.83 Krull, Wolfgang. Gesammelte Abhandlungen/Collected Works, Paulo Ribenboim, ed., Berlin: Walter de Gruyter, 1999, 2 vols., 1252 pp., hardbound, DM 548. Contains almost all the papers published between 1921 and 1973 by Wolfgang Krull, an outstanding scholar in abstract commutative algebra. Includes essays by Paulo Ribenboim, H. Schöneborn,H.-J. Nastold, and J. Neukirch. (GVB) #27.4.84 Kuroda, S. T. See #27.4.37. Kushner, Boris A. Markov’s Constructive Analysis; A Participant’s View, Theoretical Computing Science 219 (1–2) (1999), 267–285. An essay on the history and fundamentals of those areas of mathematics begun by Markov in the late 1940s; written by a leading expert in the subject. See the review by Douglas S. Bridges in Mathematical Reviews 2000f:03188. (CJ) #27.4.85 Kvasz, Ladislav. On Classification of Scientific Revolutions, Journal of General Philosophy of Science 30 (1999), 201–232. The question whether Kuhn’s theory of scientific revolutions could be applied to mathematics provokes the author to consider whether there are different kinds of scientific revolutions. He classifies three kinds: idealization, re-presentation, and objectivization. (GVB) #27.4.86 Laserna, Mario. Introduction to the Theory of Science in Hobbes, Revista de la Academia Colombiana de Ciencias Exactas, Fisicas y Naturales 23 (1999), 97–128. Describes the principal features of Hobbes’ epistemology and the role of mathematics in his approach. See the review by Ivor Grattan-Guinness in Mathematical Reviews 2000f:01006. (CJ) #27.4.87 Lassak, Marek. The Auerbach–Banach–Mazur–Ulam Problem on the Packing of a Potato Sack [in Polish], Wiadomsci´ Matematyczne 34 (1998), 49–59. The author gives a history of the four proofs of the theorem that states that for any sequence of convex sets of diameter a and volume b there exists a cube of radius f (a, b) in which the above sets can be packed. See the review by Andrezej Szczepanski in Mathematical Reviews 2000e:52020. (GSS) #27.4.88 Lauenstein, Hajo. Arithmetik und Geometrie in Raffaels Schule von Athen, Frankfurt: Peter Lang, 1998, 228 pp., $45.95. Provides a new interpretation of Raphael’s “School of Athens” using the tablets held by Pythagoras and Euclid; the golden section and Pythagorean proportionality are prominent in this analysis. See the review by Eberhard Knobloch in Mathematical Reviews 2000f:01009. (CJ) #27.4.89 Laugwitz, Detlef. See #27.4.9 and #27.4.76. Lausch, H. See #27.4.28. Lavers, Gregory. Set Theory and Category Theory as Foundations for Mathematics, in #27.4.159, pp. 38–52. A critique of the arguments of (i) Jean-Pierre Marquis, that “category theory can be a foundation for mathematics,” and (ii) John Mayberry, that “set theory is actually the foundation for mathematics.” Both claims are here reduced to weaker ones. (HG) #27.4.90 Laverty, David G. What is Mathematics About?, in #27.4.159, pp. 20–27. The author urges that “we should attempt to provide an analysis of the concept of number such that one is able to grasp the totality of objects falling under this concept,” and argues against the view of Michael Dummett that this is impossible. (HG) #27.4.91 Leahy, Andrew. See #27.4.145. Ledermann, Walter. Memoir: Two Mathematical Cultures, BSHM Newsletter 41 (2000), 5–10. The author describes the two different mathematical cultures he encountered in the 1930s as a student at both the University of Berlin and St. Andrews. (DEZ) #27.4.92 Lehmer, D. H. See #27.4.2. 454 ABSTRACTS HMAT 27

Lemmermeyer, Franz. Reciprocity Laws: From Euler to Eisenstein, New York: Springer-Verlag, 2000, 487 pp., hardbound, $79.95. A history of the law of quadratic reciprocity and its various extensions. Deals mostly with 19th-century “higher reciprocity laws”; the author promises a second volume to cover more recent history, from Kummer to Artin. (GVB) #27.4.93

Lewis, Albert C. See #27.4.43 and #27.4.162.

Li, Wenlin; and Martzloff, Jean-Claude. Aper¸cusur les Echanges´ Math´ematiquesentre la Chine et la France (1880–1949), Archive for History of Exact Sciences 53 (1998), 181–200. Describes the beginning of Chinese integration into the international mathematical community by sending its students abroad. (GVB) #27.4.94

Liebeck, Pam. See #27.4.46.

Lingard, David. The History of Mathematics: An Essential Component of the Mathematics Curriculum at all Levels, BSHM Newsletter 41 (2000), 64–69. The author provides examples of cases where the introduction of historical material from books, videos, and TV programs is used to enhance student motivation and achievement in the school curriculum. (DEZ) #27.4.95

Lipsch¨utz-Yevick, Miriam. A Sequel to Semiotic Impediments to Formalization (1), in #27.4.159, pp. 53–58. The paper cited in the title of this one (Semiotica 120, 1/2 (1998), 109–128) concludes that “there is a big gap between what formalism pretends to do and what is actually possible.” The present paper argues for the complementary position that “it is impossible to formulate a semiotically unambiguous representation of arithmetic in a ‘formal system’ in Hilbert’s sense.” (HG) #27.4.96

Lobachevsky, N. I. Nascent Non-Euclidean Geometry: Revisiting Geometric Research on the Theory of Parallels, (trans. from German), Quantum 9 (5) (1999), 20–25. A reprint of the ﬁrst part of Lobachsvki’s 1840 treatise. See the review by Richard L. Francis in Mathematical Reviews 2000d:01013. (ACL) #27.4.97

Logofet, D. O. See #27.4.98.

Lotka, Alfred J. Analytical Theory of Biological Populations, trans. David P. Smith and HélèneRossert, New York: Plenum, 1998, xxxii+220 pp., $49.50. These first English translations of two monographs on population dynamics of 1934 and 1939 by Alfred Lotka include an introduction by the translators and a short biography. See the review by D. O. Logofet in Mathematical Reviews 2000d:92024. (ACL) #27.4.98

L¨ubbig, Heinz. See #27.4.71.

Lützen, Jesper. Mechanistic Images in Geometric Form: Hertz’s Principles of Mechanics, in #27.4.159, pp. 1–11. The author urges that “applied mathematics” is usually “a complicated process in which mathematics and another scientific field interact mutually,” transforming both. The paper illustrates this by showing that in Hertz’s application of differential geometry to mechanics, “the mathematical formalism changed some aspects of his physical ideas and conversely the mechanics left important imprints on the mathematical formalism.” (HG) #27.4.99

Maor, Eli. e: The Story of a Number, Princeton, NJ: Princeton Univ. Press, 1998, 232 pp., $14.95. A popular account of the occurrences of the number e in history. (GVB) #27.4.100

Maor, Eli. June 8, 2004—Venus in Transit, Princeton, NJ: Princeton Univ. Press, 2000, 176 pp., $22.95. Tells historical stories related to the ﬁve Venus transits across the face of the sun that have been observed by humans, in preparation for the ﬁrst such event since 1882. (GVB) #27.4.101

Martzloff, Jean-Claude. See #27.4.94.

Maslyuchenko, Volodymyr K. See #27.4.63.

Mawhin, J. Henri Poincaré,ou les Mathématiquessans Œillères[Henri Poincaré,or Mathematics without Blinders], Revue des Questions Scientifiques 169 (4) (1998), 337–365. This paper is a biography of Poincaré and describes his work on automorphic functions, the qualitative theory of differential equations, the n-body problem, and algebraic topology, as well as his writings on the philosophy of science. See the review by F. Smithies in Mathematical Reviews 2000e:01033. (GSS) #27.4.102 HMAT 27 ABSTRACTS 455

Mehra, Jagdish; and Rechenberg, Helmut. Planck’s Half-Quanta: A History of the Concept of Zero-Point En- ergy, Foundations of Physics 29 (1999), 91–132. This article traces the evolution of quantum mechanics from Planck’s introduction in 1900 to Heisenberg and Schrodinger’s modern formulation in 1925. This article gives a detailed history of the experimental and theoretical efforts during this period. See the review by R. L. Ingraham in Mathematical Reviews 2000e:81003. (GSS) #27.4.103 Melville, Duncan J. Interpreting Texts in a History of Mathematics Class, in #27.4.159, pp. 298–306. Taking scholarly conjecture about the Babylonian tablet Plimpton 322 as example, the author outlines and argues for an approach to teaching history of mathematics that exposes students to historians’ “differing interpretations” and “differing modes of discourse.” (HG) #27.4.104 Mendell, Henry. Reflections on Eudoxus, Callipus and their Curves: Hippopedes and Callippopedes, Centau- rus 40 (1998), 177–275. The author presents useful historical theses, including proposed corrections of modern commentators who would detect errors in Eudoxus’ study of planetary motion. The author sees the figure eight curve generated by the two innermost spheres, the hippopede, as playing a more pervasive role in his astronomy than is generally realized. See the review by A. G. Molland in Mathematical Reviews 2000e:01010. (GSS) #27.4.105 Mendelson, F. See #27.4.15. Meyerstein, F. Walter. Is Movement an Illusion? Zeno’s Paradox: From a Modern Viewpoint, Complexity 4 (4) (1999), 26–30. Outlines analyses of Zeno’s paradox by Plato and Aristotle and then discusses various more modern approaches to resolving the difficulty. See the review by Peter W. Day in Mathematical Reviews 2000f:00007. (CJ) #27.4.106 Molland, A. G. See #27.4.105. Monastyrsky, M. Riemann, Topology and Physics, 2nd edition, trans. Roger Cooke, Boston: Birkhäuser, 1999, 256 pp., hardbound, $54.95. This book is divided into two parts: the first, an account of Riemann’s life and work; the second, a description of interactions between physics and topology. The second edition contains a new chapter and various improvements and corrections. (GVB) #27.4.107 Moore, Gregory H. The Influence of Klein’s Erlanger Programm: A Reappraisal, in #27.4.159, pp. 112–121. This paper argues, contrary to assertions in older histories (Boyer, Bell) that “EP” had very little influence for decades after its promulgation in 1872, despite a number of translations in the early 90s. A final section discusses “the inadequacy of EP as a definition of geometry.” (HG) #27.4.108 Moya, Antonio-Prometeo. See #27.4.62. Muller, Ralf. Die Dynamische Logik des Erkennens von Charles S. Pierce,Würzburg: Königshausen& Neumann, 1999, xii+278 pp., DM 78. Interpretation of C. S. Peirce’s logic and semiotics as logic of cognition; advantages of Peirce’s approach compared to others are discussed. See the review by Roman Murawski in Mathematical Reviews 2000f:01018. (CJ) #27.4.109 Murawski, Roman. See #27.4.109. Muroi, Kazuo. Quadratic Equations in the Susa Mathematical Text No. 21, SCIAMVS 1 (2000), 3–10. Recon- structs the quadratic equations and the methods of solution presented in this text, dated to the 16th century BC. (GVB) #27.4.110 Nabonnand, Philippe. La Correspondance entre Henri PoincareetG´ osta¨ Mittag-Leffler, Basel: Birkhäuser, 1999, 421 pp., sFr. 228. An edition, with commentary, of the correspondence between Mittag-Leffler and Poincaré.This is the first of four planned volumes of Poincaré’s correspondence. (GVB) #27.4.111 Nakane, Michiyo. Some Aspects of Mathematisation in the Construction of the Hamilton–Jacobi Theory, in #27.4.159, pp. 238–247. This paper describes Hamilton’s elaboration of the theory in optics and dynamics and Jacobi’s derivation of a mathematical theory from the physical one. The author proposes conceptual and termino- logical distinctions typified by these two examples. (HG) #27.4.112 Narasimhan, V. S. See #27.4.158. 456 ABSTRACTS HMAT 27

Nastasi, Pietro. The Institutional Context [in Italian], in Simonetta di Sieno, Angelo Guerraggio, and Pietro Nastasi, eds., Italian Mathematics after Unity [in Italian], Milan: Marcos y Marcos, 1998, pp. 817–943. Lengthy essay on the institutional and sociological aspects of Italian mathematics between the two World Wars, with some reference to the preceding half century. See the review by Luigi Pepe in Mathematical Reviews 2000f:01021. (CJ) #27.4.113

Nastasi, Pietro. See also #27.4.144.

Nastold, H.-J. See #27.4.84.

Ne’eman, Yuval. De l’Autogéométrisationde la Physique, Les Relations entre les Mathématiqueset la Physique Théorique,in Les Relations entre les Mathematiques´ et la Physique Theorique´ , Bures-sur-Yvette: Institut des Hautes Etudes´ Scientifiques, 1998, pp. 145–152. The author considers two geometrizations in the history of physics: the geometrization of gravitational physics and conservation laws in the works of Einstein, Minkowski, and Noether and the geometrization of quantum physics in the works of Weyl. See the review by Arne Schirrmacher in Mathematical Reviews 2000e:81004. (GSS) #27.4.114

Netz, Reviel. The Origins of Mathematical Physics: New Light on an Old Question, Physics Today 53 (6) (2000), 32–37. Besides telling the story of the Archimedes Palimpsest, Netz argues that Archimedes considered the objects that he studied in his mathematical physics to be geometric in nature, not physical. (GVB) #27.4.115

Neuwirch, J. See #27.4.84.

Nilsson, Ulf S. See #27.4.119.

Nobre, Sergio. History of Mathematics in Brazil, BSHM Newsletter 41 (2000), 32–35. An account of events leading up to the founding of the Brazilian Society for the History of Mathematics (SBHMat) in 1999. There are discussions of the Society’s relations with Portuguese historians, the Brazilian Society for the History of Science, and mathematical societies, as well as a list of master’s and doctoral theses written since 1997. (DEZ) #27.4.116

North, John. The Norton History of Astronomy and Cosmology, New York: Norton, 1995, xxviii+697 pp. This book is a popular, wide-ranging survey of astronomy, but not mathematical astronomy, from ancient times to the present. See the review by Owen Gingerich in Mathematical Reviews 2000e:01005. (GSS) #27.4.117

Otte, Michael. See #27.4.82 and #27.4.143.

Ozdural,¨ Alpay. Mathematics and Arts: Connections Between Theory and Practice in the Medieval Islamic World, Historia Mathematica 27 (2000), 171–201. Uses two works, one by the 10th-century mathematician Abu ‘l-Waf¯a’and another by an anonymous 13th-century author, to illustrate how mathematicians communicated to artisans the geometry useful to the latter’s work. (GVB) #27.4.118

Ozsváth,István. Working with Engelbert, in Alex Harvey, ed., On Einstein’s Path: Essays in Honor of Engelbert Schucking¨ , New York: Springer-Verlag, 1999, pp. 339–351. The author discusses parts of his almost 40 years of collaboration with Engelbert Schückingon relativistic cosmology and embedding models into higher Euclidean spaces. The author includes many historical comments. See the review by Ulf S. Nilsson in Mathematical Reviews 2000e:83001. (GSS) #27.4.119

Pambuccian, Victor V. See #27.4.47.

Parker, Willard. See #27.4.27.

Passeron, Irene. See #27.4.71.

Pechenkin, A. A. The Importance of the Strasbourg Period in L. I. Mandelstam’s Life for his Further Work in Science, NTM 7 (1999), 93–104. Discusses education and research interests of a leading Soviet physicist, whose ensemble interpretation of quantum mechanics is related to von Mises’ understanding of probability. See the review by Arne Schirrmacher in Mathematical Reviews 2000f:01024. (CJ) #27.4.120 HMAT 27 ABSTRACTS 457

Peckhaus, Volker. 19th Century Logic Between Philosophy and Mathematics, Bulletin of Symbolic Logic 5 (6) (1999), 433–450. Considers the philosophers’ and the mathematicians’ interests and roles in the development of modern logic in the 19th century. (GVB) #27.4.121 Pepe, Lugi. See #27.4.113. Pettersson, J. S. Indus Numerals on Metal Tools, Indian Journal of History of Science 34 (2) (1999), 89–108. Nine numerical inscriptions on metal tools are found to be based on an octal number system, and the expressions are found not to relate to weights. (GVB) #27.4.122

Pingree, David. Amr.talahar¯ı of Nity¯ananda, SCIAMVS 1 (2000), 209–217. This 17th-century collection of astronomical tables in Sanskrit is “a bold but flawed experiment in melding together Indian, Jewish, Islamic, and Christian calendaric and astronomical elements.” (GVB) #27.4.123 Ponce, Gustavo. See #27.4.37. Puchta, Susann. Die Stellung des Ingenieurs und Technikwissenschaftlers Carl Julius von Bach zur Mathematik—Ein Beitrag zum Wirken von Bachs bei der Entwicklung der Technikwissenschaften, in Friedrich Naumann, ed., Carl Julius von Bach (1847–1931), Stuttgart: Wittwer, 1998, pp. 195–208. A study of Carl von Bach’s commitment to the mathematical training of engineers at German technical universities at the end of the 19th century. At a time when many engineers demanded a restriction of the teaching of abstract mathematics, von Bach held the view that there must be a well-balanced relation between theory and practice and promoted understanding between technical scientists and engineers. See the review by Karl- Heinz Schlote in Mathematical Reviews 2000e:01046. (GSS) #27.4.124 Pulte, Helmut. See #27.4.71. Radloff, Ivo. Abels Unmöglichkeitsbeweis im Spiegel der Modernen Galoistheorie [Abel’s Impossibility Proof as Reflected in Modern Galois Theory], Mathematische Semesterberichte 45 (1998), 127–139. Abel’s proof translated into modern language and notation in the context of modern group theory. See the review by Martin Epkenhaus in Mathematical Reviews 2000e:12004. (GSS) #27.4.125 Ramskov, Kurt. Sources for Danish Mathematics, Historia Mathematica 27 (2000), 164–170. Summarizes publications on Danish mathematics and describes a new archive of mathematical materials at the Institute for Mathematical Sciences at the University of Copenhagen. (GVB) #27.4.126 Ransom, Peter. Manx Sundials, BSHM Newsletter 41 (2000), 44–47. Descriptions of three sundials from the Isle of Man. (DEZ) #27.4.127 Rashed, Roshdi. Algebra, in Roshdi Rashed and RégisMorelon, eds., Encyclopedia of the History of Arabic Science, Vol.2, London: Routledge, 1996, pp. 349–375. The author gives an introduction to the current knowledge on the history of algebra in Islam from the 9th through the 13th century, including hard-to-find material on al-Karaj¯ı, al-Samaw’al, al-Khayy¯am,and al-T. ¯us¯ı.See the review by Victor J. Katz in Mathematical Reviews 2000e:01014. (GSS) #27.4.128 Rashed, Roshdi. Combinatorial Analysis, Numerical Analysis, Diophantine Analysis and Number Theory, in Roshdi Rashed and RégisMorelon, eds., Encyclopedia of the History of Arabic Science, Vol.2, London: Routledge, 1996, pp. 376–417. The author discusses the contributions made by Islamic mathematicians including al-F¯aris and Ibn al-Bann¯a’in combinatorics, al-K¯ash¯ıon numerical solutions to polynomial equations, Ab¯uK¯amil and al-Karaj¯ıin indeterminate analysis, and Ibn Qurra in number theory. See the review by Victor J. Katz in Mathe- matical Reviews 2000e:01015. (GSS) #27.4.129 Rashed, Roshdi. Infinitesimal Determinations, Quadrature of Lunules and Isoperimetric Problems, in Roshdi Rashed and RégisMorelon, eds., Encyclopedia of the History of Arabic Science, Vol. 2, London: Routledge, 1996, pp. 418–446. The author discusses some of the most advanced mathematical work of Islamic mathematicians, including the work of Ibn Qurra on areas, Ibn al-Haytham on the volume of a paraboloid formed by revolving a parabola around a line perpendicular to its axis and the quadrature of lunes, and the work of al-Kh¯azinand Ibn al-Haytham on isoperimetric problems. See the review by Victor J. Katz in Mathematical Reviews 2000e:01016. (GSS) #27.4.130 458 ABSTRACTS HMAT 27

Read, R. C. See #27.4.2. Rechenberg, Helmut. See #27.4.103. Remmert, Volker. Mathematicians at War. Power Struggles in Nazi Germany’s Mathematical Community: Gustav Doetsch and Wilhelm Süss, Revue d’Histoire des Mathematiques´ 5 (1999), 7–60. A discussion of several interactions between the German mathematical community and the Nazi regime, especially those involving Wilhelm Süss, president of the Deutsche Mathematiker Vereinigung during World War II, and his Freiberg colleague Gustav Doetsch. (GVB) #27.4.131 Ribenboim, Paolo. See #27.4.84. Rice, Adrian. Extending Euler: A Little-Known Episode in the Prehistory of Quaternions, in #27.4.159, pp. 143– 163. An account of work by John Thomas Graves (1826) which generalized Euler’s definitive 1749 paper on logarithms of negative and complex numbers. Graves’s paper was later an important stimulus toward Hamilton’s quaternions: awareness of the algebraic closure of the complex numbers helped open the way for hypercomplex systems defined as such. (HG) #27.4.132 Richards, Joan L. Angles of Reflection, Mathematical Association of America, 2000, 272 pp., hardbound, $23.95. A personal account of Richards’s research on the life and work of Augustus De Morgan, during which her nine- year-old son was diagnosed with a brain tumor. The interaction between deep familial crisis and her academic work led to a deepened perspective on the relations between life, family, and work, both in personal and in historical figures’ lives. (GVB) #27.4.133 Robson, Eleanor. Mathematical Cuneiform Tablets in Philadelphia. I. Problems and Calculations, SCIAMVS 1 (2000), 11–48. Catalogues and analyzes the “interesting” Babylonian mathematical cuneiform tablets, most originating in Nippur, in the University of Pennsylvania Museum of Archaeology and Anthropology. (Parts II and III of the study will present tablets copied by scribes as part of the rote learning process, containing arithmetical tables and metrological lists and tables.) (GVB) #27.4.134 Rosińska,Gra˙zyna. Decimal Positional Fractions: Their Use for the Surveying Purposes (Ferrara, 1442), Kwartal- nik Historii Nauki i Techniki 40 (4) (1995), 17–32. A study of the surveying instrument described by 15th-century mathematician Giovanni Bianchini in his Compositio instrumenti, concentrating on its use of decimal positional fractions, which is “surely superior to” that of Simon Stevin. (GVB) #27.4.135 Rosińska,Gra˙zyna. The “Fifteenth-Century Roots” of Modern Mathematics: The Unit Segment, its Function in Bianchini’s De Arithmetica, Bombelli’s L’Algebra ..., and Descartes’ La Geometrie,´ Kwartalnik Historii Nauki i Techniki 41 (3–4) (1996), 53–70. Traces various uses and concepts of the unit segment, especially in the works mentioned in the title. (GVB) #27.4.136 Rosińska,Gra˙zyna. The “Italian Algebra” in Latin and How it Spread to Central Europe: Giovanni Bianchini’s De Algebra (ca. 1440), Organon 26–27 (1997–1998), 133–145. A summary of the contents of Bianchini’s Algebra, one of the three treatises in his Flores Almagesti that comprised the mathematical introduction to his astronomy. (GVB) #27.4.137 Rosińska,Gra˙zyna. The Euclidean Spatium in Fifteenth-Century Mathematics, Kwartalnik Historii Nauki i Techniki 43 (1) (1998), 27–41. Considers Giovanni Bianchini’s notions of number and the arithmetic of the natural numbers, their relations to the Greek concept of Euclidean space, and his anticipation of negative numbers. (GVB) #27.4.138 Rossert, Hélène. See #27.4.98. Rouxel, Bernard. See #27.4.23. Rubinstein, Rheta; and Schwartz, Randy. Arabic from A (Algebra) to Z (Zero), Math Horizons, September 1999, 16–18. Describes various Arabic influences in modern mathematics, especially terms derived from Arabic words. (GVB) #27.4.139 Saliba, George. Arabic Planetary Theories After the Eleventh Century AD, in Roshdi Rashed and RégisMorelon, eds., Encyclopedia of the History of Arabic Science, London: Routledge, 1996, Vol. 1, pp. 58–127. Detailed but HMAT 27 ABSTRACTS 459 accessible survey of medieval Islamic planetary astronomy, much of it not readily available before. See the review by Glen R. Van Brummelen in Mathematical Reviews 2000f:01006. (CJ) #27.4.140 Saliba, George. See also #27.4.78. Sarnak, Peter. Ralph Phillips (1913–1998), Notices of the American Mathematical Society 47 (2000), 561– 563. A memorial of Ralph Phillips surveying his lifetime achievements including his work in functional analysis and semigroups, partial differential equations, dissipative and hyperbolic systems, and automorphic forms. (RE) #27.4.141 Schappacher, Norbert. “Wer war Diophant?” Mathematische Semesterberichte 45 (1998), 141–156. The author shows how four different eras have each constructed their different ideas of the content of Diophantos’s Arithmetica, from the nondeterminate algebraic view of early Islamic times to the algebraic–geometrical view that can be seen in the modern West. See the review by Jens Høyrup in Mathematical Reviews 2000d:01004. (ACL) #27.4.142 Schattschneider, Doris. See #27.4.2. Schiffer, M. M. See #27.4.2. Schirrmacher, Arne. See #27.4.114 and #27.4.120. Schlote, Karl-Heinz; and Wussing, Hans. Hans Wussing—Auskünfte der Wissenschaftsgeschichte in der Ehehemaligen DDR [Information on the History of Science in the Former GDR], NTM 7 (1999), 65–82. An interview with Hans Wussing, the most prominent historian of mathematics from the former GDR. See the review by Michael Otte in Mathematical Reviews 2000f:01026. (CJ) #27.4.143 Schlote, Karl-Heinz. See also #27.4.69 and #27.4.124. Schoenfeld, Alan H. See #27.4.2. Schöneborn,H. See #27.4.84. Schramm, Matthias. See #27.4.71. Schroder, Wilfred. See #27.4.30. Schwartz, Randy. See #27.4.139. Scimone, Aldo. See #27.4.28. Scinà,Domenico. Elogio di Francesco Maurolico [in Italian], Umberto Bottazzini and Pietro Nastasi, eds., Rome: Salvatore Sciascia Editore, 1994, 187 pp., L 25,000. Reprint of the Elogio di Francesco Maurolico (1494– 1575) originally published in 1808 with commentary by Umberto Bottazzini and Pietro Nastasi. See the review by William R. Shea in Mathematical Reviews 2000e:01019. (GSS) #27.4.144 Scriba, Christoph J. See #27.4.31. Seife, Charles. Zero: The Biography of a Dangerous Idea, New York: Viking Press, 2000, 248 pp., softbound, $24.95. A popular account of the history of the concept of zero, distinguishing itself from Robert Kaplan’s recent The Nothing that Is: A Natural History of Zero (#27.2.102) by following the story into physics rather than philosophy. See the review by Andrew Leahy at MAA Online [http://www.maa.org/reviews/zero2.html]. (GVB) #27.4.145 Seltman, Muriel. Thomas Harriot and the Solution of the Cubic, in #27.4.159, pp. 129–142. The author sets out the solution techniques found in Harriot’s Artis Analyticae Praxis and in the “indescribable muddle” of his manuscripts, and sees in his approach a great advance on such predecessors as Cardano and Viète.Indeed the Praxis marks “the ushering in of an era,” because “Harriot thought symbolically.” (HG) #27.4.146 Serfati, Michel. Descartes et la Constitution de l’Ecriture´ Symbolique Mathématique, Revue d’Histoire des Sciences 51 (2–3) (1998), 237–289. The author shows that Descartes is easier to read than his predecessors because of his invention of an effective symbolic representation. The author also examines the “diophanto-cossic” 460 ABSTRACTS HMAT 27 symbolic system in comparison. See the review by William R. Shea in Mathematical Reviews 2000e:01025. (GSS) #27.4.147

Sesiano, Jacques. Une Introduction a` l’Histoire de l’Algebre` , Lausanne: Presses Polytechniques et Universitaires Romandes, 1999, viii+168 pp., sFr. 39. This book is an outgrowth of a series of lectures on the history of algebra. It is not a comprehensive history of algebra, but a basic introduction to the types of problems that illustrate the earlier forms of algebra that should be useful for an instructor who is looking for examples to enliven a course on elementary algebra with problems drawn from actual historical texts. See the review by Warren Van Egmond in Mathematical Reviews 2000e:01007. (GSS) #27.4.148

Shea, William R. See #27.4.144 and #27.4.147.

Sheynin, Oscar. The Discovery of the Principle of Least Squares, Historia Scientarium (2) 8 (3) (1999), 249–264. A new interpretation is given of Gauss’s discovery of the principle of least squares. Reference is made to a letter from Gauss to the British Astronomer Royal of 9 May 1802. See the review by Zeno G. Swijtink in Mathematical Reviews 2000d:01014. (ACL) #27.4.149

Shore, Steven N. Blue Sky and Hot Piles: The Evolution of Radiative Transfer Theory from Atmospheres to Nuclear Reactors, in #27.4.159, pp. 248–270. A survey of the development, over the past century, of techniques for treating the transfer of light through an absorbing and scattering medium, with emphasis on how techniques for treating photons have been adapted in other ﬁelds for speciﬁc transfer issues, in particular the transfer of neutrons in nuclear reactors. (HG) #27.4.150

Sieg, Wilfried. Hilbert’s Programs: 1917–1922, Bulletin of Symbolic Logic 5 (1) (1999), 1–44. Hilbert’s unpublished lectures, 1917–1922, are seen by the author as countering the view of Hilbert as a dogmatic formalist. They show, for example, Hilbert’s emphasis on the need for semantic justiﬁcations. See the review by Ignacio Angelelli in Mathematical Reviews 2000d:01016. (ACL) #27.4.151

Simon, Barry. See #27.4.37.

Singmaster, David. Mathematical Gazetteer of Britain #14: Institutions Further Out, BSHM Newsletter 41 (2000), 35–43. Descriptions of institutions near London with items of mathematical interest, including a detailed discussion of the Royal Observatory at Greenwich. (DEZ) #27.4.152

Singmaster, David. See also #27.4.46.

Smirnova, Galina S. See #27.4.15.

Smith, David P. See #27.4.98.

Smithies, F. See #27.4.102.

Snobelen, Stephen D. On Reading Isaac Newton’s Principia in the 18th Century, Endeavor 22 (4) (1998), 159– 163. Describes the efforts of 18th-century popularizers of the Principia to make the work accessible to a wider audience, and the resulting transformation of Newton’s ideas. (GVB) #27.4.153

Sosoe, Lukas. See #27.4.71. Speiser, David. See #27.4.71. Stahl, Saul. Real Analysis: A Historical Approach, New York: Wiley, 1999, xiv+269 pp., hardbound, $64.95. A junior–senior university textbook in real analysis that attempts to provide motivation for rigor through historical examples. The reviewer in Mathematical Reviews 2000d:26001, R. G. Bartle, believes that this book would make an excellent precursor to a “serious course” in analysis. (ACL) #27.4.154

Stedall, Jackie. “In Serche of Englands Antiquitees”: A Millennial Journey, BSHM Newsletter 41 (2000), 1–4. An account of the author’s trek on the eve of the third millennium retracing the path taken by the medieval mathematician, astronomer, and physician Simon Bredon (c. 1300–1372) on his walk from Winchcombe to Oxford in the 1320s. (DEZ) #27.4.155 HMAT 27 ABSTRACTS 461

Sugiura, Mitsuo. On the Space Problem of Helmholtz, in Surikaisekikenky¯ usho¯ Koky¯ uroku¯ 1064 (1998), pp. 6– 14. The author gives a brief history of Helmholtz’s space problem and four characterizations of the orthogonal group of a positive deﬁnite quadratic form, one of which is connected with the Iwasawa decomposition of GL(n, R). See the author’s summary in Mathematical Reviews 2000e:01034. (GSS) #27.4.156

Suisky, Dieter. See #27.4.71.

Swerdlow, Noel M. Acronychal Risings in Babylonian Planetary Theory, Archive for History of Exact Sciences 54 (1999), 49–65. Treats motion of the three superior planets, giving a better understanding of Babylonian planetary astronomy. See the review by George Abraham in Mathematical Reviews 2000f:01001. (CJ) #27.4.157

Swijtink, Zeno G. See #27.4.149.

Szczepanski, Andrezej. See #27.4.88.

Taliaferro, R. Catesby. See #27.4.5.

Tantrasan. graha. Chapter VIII, trans. V. S. Narasimhan, Indian Journal of History of Science 34 (2) (1999), supplement, 8 pp. Revised edition of the author’s own translation with many improvements. See the review by Takao Hayashi in Mathematical Reviews 2000e:01017. (GSS) #27.4.158

Tattersall, James J., ed. Proceedings of the Canadian Society for the History and Philosophy of Mathematics, Vol. 12, Toronto: Univ. of Toronto, 1999, paperbound, 312 pp. This volume contains most of the papers delivered at the 25th annual meeting of the Canadian Society for History and Philosophy of Mathematics, held jointly with the British Society for History of Mathematics, in July 1999. Papers by Francine F. Abeles, Jacob M. Appleman, Richard Arthur, Christopher Baltus, June Barrow-Green, David Boutillier, Edward L. Cohen, John Fossa, Ibrahim Garro, Roger Godard and P. Crépel,Tinne Hoff Kjeldsen, Erwin Kreyszig, Gregory Lavers, David G. Laverty, Miriam Lipschütz-Yevick, Jesper Lützen,Duncan J. Melville, Gregory H. Moore, Michiyo Nakane, Adrian Rice, Muriel Seltman, Steven N. Shore, RüdigerThiele, Robert Thomas, and David E. Zitarelli are abstracted separately. (GVB) #27.4.159

Taylor, Michael. See #27.4.37.

Thiele, R¨udiger. Early Calculus of Variations and the Concept of the Function, in #27.4.159, pp. 98–111. After a brief summary of the history of the function concept, the author identiﬁes as an important episode in that history, and discusses in detail, the work of Johann and Jakob Bernoulli (1697ff.) on generalizations of “Dido’s” isoperimetric problem. (HG) #27.4.160

Thiele, R¨udiger. See also #27.4.71.

Thomas, Robert. What Phenomena did Euclid Write About?, in #27.4.159, pp. 202–206. An “introductory” sketch of Euclid’s Phenomena and of Autolykos’s two works (A Rotating Sphere and Risings and Settings), with particular attention to the balance in each between pure mathematics and “observables.” The author suggests that the Phenomena “might form a useful exercise for the study of ancient applied mathematics.” (HG) #27.4.161

Tikhomirov, V. M. See #27.4.8.

Tobies, Renate. Mathematik als Programm. Zum 150. Geburtstag von Felix Klein, Mitteilungen der Deutschen Mathematiker-Vereinigung 1999 (2), 15–21. The degree to which David Hilbert and Felix Klein supported each other is documented. This is put in the context of the rather negative opinion of Felix Klein held by a number of Berlin mathematicians. See the review by Albert C. Lewis in Mathematical Reviews 2000d:01020. (ACL) #27.4.162

Treder, H. See #27.4.39.

Uhrin, Bela. See #27.4.163.

Van Brummelen, Glen R. See #27.4.140.

Van Dalen, Benno. See #27.4.32. 462 ABSTRACTS HMAT 27

Van der Lugt, Anna. See #27.4.24. Van Egmond, Warren. See #27.4.13 and #27.4.148. Van Rootselaar, Bob. See #27.4.24. Vencovska, Alena. See #27.4.164. Volkert, Klaus. Die Lehre vom Flächeninhaltebener Polygone: Einige Schritte in der Mathematisierung eines Anschaulichen Konzeptes [The Theory of the Surface Area of Plane Polygons: Some Steps in the Mathematization of a Graphic Concept], Mathematische Semesterberichte 46 (1999), 1–28. A study of the notion of area of a plane polygon, discussing Euclid, Legendre, and multicongruence of polygons as studied by P. Gerwien and J. H. C. Duhamel. References to the foundations of geometry in the works of Euler, Bolyai, and Hilbert are also included. Also includes a comprehensive list of references and many historical notes. See the review by Bela Uhrin in Mathematical Reviews 2000e:52005. (GSS) #27.4.163 Von Borzeszkowski, H.-H. See #27.4.71. Wahsner, Renate. See #27.4.71. Wefelscheid, H. See #27.4.165. Wójtowicz, Krzysztof. Heuristic Arguments in Set Theory [in Polish], Wiadomsci´ Matematyczne 34 (1998), 61– 82. A summary of arguments for and against adding to ZF various axioms which are independent of ZF. Included is the discussion of the axiom of choice by Zermelo, Borel, Baire, Lebesgue, and Hadamard; a discussion of the axiom of determinacy; a discussion of the continuum hypothesis by Gödel,Cohen, Freiling, and Friedman; and a discussion of the axiom of constructibility by Zermelo, Devlin, and Maddy. See the review by Alena Vencovska in Mathematical Reviews 2000e:03130. (GSS) #27.4.164 Wussing, Hans. See #27.4.143. Young, G. C.; and Young, W. H. Selected Papers, S. D. Chatterji and H. Wefelscheid, eds. Lausanne: Presses Polytechniques et Universitaires Romandes, 2000, 870 pp. Selection restricted to the main papers on Fourier analysis and related topics, and to Grace’s 1895 dissertation under Klein. Also includes respective obituaries by M. L. Cartwright and G. H. Hardy. All photoreprints. Also a bibliography, and introductory note by Chatterji. Published in the city where the Youngs lived for several years. (IGG) #27.4.165 Young, W. H. See #27.4.165. Zanarini, Gianni. See #27.4.16. Zerner, M. See #27.4.56. Zitarelli, David E. An Outline of the History of Mathematics in America, in #27.4.159, pp. 286–297. A description of the author’s undergraduate course on the history of mathematics in “America” (including Canada) to 1950. The course is organized around a six-stage periodization, from “Native Americans” to “Internationalism (1933–1950)”; this paper sketches the history of each of these subdivisions. (HG) #27.4.166