ABSTRACTS - COnnecting REpositoriesHMAT 29 ABSTRACTS 341 Agazzi, Evandro. The Relation of...

Historia Mathematica 29 (2002), 340–360doi:10.1006/hmat.2002.2364

ABSTRACTS

Edited by Glen Van Brummelen

The purpose of this department is to give sufficient information about the subject matter of eachpublication 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 shouldbe 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 publicationsthat 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 morejournals for this department.

In order to facilitate reference and indexing, entries are given abstract numbers which appear at theend 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, theabstracts 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 areabstracts by Francine Abeles (Kean, NJ), Djamil Aıssani (Bejaıa, Algeria), Timothy Carroll (Ypsilanti,MI), Hardy Grant (Ottawa, Canada), Patti Wilger Hunter (Westmont, CA), Herbert Kasube (Peoria, IL),Niwas Lawot (Bennington, VT), Elena Marchisotto (Northridge, CA), Hassan Noon (Bennington, VT),Peter Ross (Santa Clara, CA), Kevin VanderMeulen (Hamilton, Canada), David Zitarelli (Philadelphia,PA), and Glen Van Brummelen.

Abeles, Francine F. Game Theory and Politics: A Note on C. L. Dodgson, in #29.3.91, pp. 77–84. A descriptionof the political context and the mathematical content of an 1884 pamphlet in which Dodgson sought to specifyvoting arrangements that would promote fairness of proportional representation in national elections. His ideasstemmed from his earlier use of game theory in election analysis. (HG) #29.3.1

Abeles, Francine F. The Enigma of the Infinitesimal: Toward Charles L. Dodgson’s Theory of Infinitesimals,Modern Logic 8(3/4) (2000–2001), 7–19. A discussion of Dodgson’s inchoate theory of infinitesimals as elementsin a nonlinear (non-Archimedean) number system underlying a non-Euclidean geometry. The author provides acontext for Dodgson’s theory by surveying the main lines of thought about infinitesimals in analysis and geometryin the 19th century. (FA) #29.3.2

Abhyankar, K. D. Babylonian Source of Aryabha.ta’s Planetary Constants, Indian Journal of History of Science35(3) (2000), 185–188. The author argues that Aryabha.ta’s values of bhaga .nas were probably derived fromBabylonian planetary data. (GVB) #29.3.3

Abraham, George. See #29.3.181.

Ackerberg-Hastings, Amy. The Semi-Secret History of Charles Davies, in #29.3.91, pp. 85–96. A sketch ofthe life and work of an enormously prolific author of textbooks, and an influential teacher, to whom “historiansof mathematics have not paid much attention.” One section deals with “Davies and the professionalization ofAmerican mathematics.” (HG) #29.3.4

Agargun, A. Goksel; and Ozkan, E. Mehmet. A Historical Survey of the Fundamental Theorem of Arithmetic,Historia Mathematica 28 (2001), 207–214. This survey focuses on the work of Euclid, al-Farisı, Prestet, Euler,and Gauss. (GVB) #29.3.5

3400315-0860/02 $35.00

C© 2002 Elsevier Science (USA)All rights reserved.

HMAT 29 ABSTRACTS 341

Agazzi, Evandro. The Relation of Mathematics to the Other Sciences, in Evandro Agazzi and Gyorgy Darvas,eds., Philosophy of Mathematics Today, Dordrecht: Kluwer Academic, 1997, pp. 235–259. In efforts to discoverthe reason for the success of mathematics, mathematics is viewed as a system of theories on the one hand and as alanguage on the other hand. The views of Galileo, Kant, Einstein, Godel, and Hilbert illustrate the variation in therelation of mathematics to the sciences. See the review by Alvin M. White in Mathematical Reviews 2002c:00008.(TBC) #29.3.6

Aıssani, Djamil. See #29.3.13 and #29.3.159.

Amor Montano, Jose Alfredo. Set Theory in the XXth Century [in Spanish], Miscelanea Matematica 31 (2000),1–27. This paper gives an overview of the developments of set theory in the 20th century. See the review by IgnacioAngelelli in Mathematical Reviews 2002c:01035. (TBC) #29.3.7

Angelelli, Ignacio. See #29.3.7 and #29.3.195.

Arya, Shashi Prabha. Trends in Topology, The Mathematics Student 67(1–4) (1998), 113–140. An attempt toevaluate the relative importance, past and present, of the various branches of topology. (GVB) #29.3.8

Atiyah, Michael. Mathematics in the 20th Century, American Mathematical Monthly 108 (2001), 654–666.Based on the author’s Fields Lecture at the World Mathematical Year 2000 Symposium in Toronto, this paperrevolves around the themes “local to global,” “increase in dimensions,” “commutative to noncommutative,” and“linear to nonlinear,” as well as the dichotomy between geometry and algebra, common methods applied acrossmathematical disciplines, finite groups, and the impact of physics. (GVB) #29.3.9

Atkinson, Leigh. Where Do Functions Come From? The College Mathematics Journal 33(2) (2002), 107–112. With the aim of helping calculus students understand the importance of functions for modern mathematics,the author examines the changing understanding of motion and velocity from classical antiquity through the19th century, considering how this understanding contributed to the evolution of the concept of a function.(PWH) #29.3.10

Awodey, S.; and Carus, A. W. Carnap, Completeness, and Categoricity: The Gabelbarkeitssatz of 1928, Erkennt-nis 54(2) (2001), 145–172. An examination of Carnap’s typescript Investigations in General Axiomatics containedwithin his Nachlass, showing insights into the nature and motivation of his logicism. (GVB) #29.3.11

Badino, Massimiliano. See #29.3.155.

Baez, John C. The Octonions, Bulletin of the American Mathematical Society 39 (2002), 145–206. This surveyof octonions weaves occasional historical discussions into its mathematical exposition. (GVB) #29.3.12

Ballieu, Michel; and Aıssani, Djamil. The Mathematical Knowledge Available in Small Kabylie in the NineteenthCentury, Proceedings of the International Conference “Bejaıa and Its Region through the Ages: History, Society,Sciences, Culture,” Bejaıa: Gehimab Edition, 1997, pp. 252–260. This talk stresses the principal sources of interestin and the level of knowledge of mathematics in the 19th century in Little Kabylia. The recent discovery in theAth Urtilan area of a scholarly library of manuscripts—the Ulahbib collection—allows some conclusions througha method of mathematical analysis of social facts. (DA) #29.3.13

Baltus, Christopher. Gauss’s Second Proof of the Fundamental Theorem of Algebra, 1815, in #29.3.91,pp. 97–106. The proof in question is algebraic. The author provides a detailed exposition of Gauss’s argument,with sketches of earlier ventures in the same line and of later judgments and reworkings. (HG) #29.3.14

Bartle, Robert G. See #29.3.26.

Bartocci, Claudio. See #29.3.161.

Bartolini Bussi, Maria G. The Geometry of Drawing Instruments: Argument for a Didactical Use of Realand Virtual Copies, Cubo 3(2) (2001), 27–54. After a historical survey, the author discusses theoretical, practical,and pedagogical issues involved in the mechanical drawing of curves. A focus of the paper is Kempe’s Theorem(1876) on a general method of drawing plane curves by “linkwork.” Simulations using Cabri and Java are described.(HG) #29.3.15

342 ABSTRACTS HMAT 29

Bebbouchi, Rachid. Geometrical Reflexions of the Mathematician Eugene Dewulf in Bougie, Proceedings of theInternational Conference “Bejaıa and Its Region through the Ages: History, Society, Sciences, Culture,” Bejaıa:Gehimab Edition, 1997, pp. 269–273. This article presents work on left surfaces realized by the mathematicianEugene Dewulf, a founding member of the Mathematical Society of France, during his Algerian stay (1863–1872).(DA) #29.3.16

Bell, Ian. Demonstration in Aristotle’s Metaphysics, Apeiron 32(2) (1999), 75–108. Key passages in the Meta-physics are taken to indicate that there is one unified science which deals with being and also with being’s attributes.It is argued that in the Metaphysics the relations between the objects studied and the concepts of being and sub-stance are explained in terms of the proof-structures of Posterior Analytics. See the review by Albert C. Lewis inMathematical Reviews 2002c:01006. (TBC) #29.3.17

Bellissima, Fabio. Epimoric Ratios and Greek Musical Theory, in Maria Luisa Dalla Chiara, ed., Language,Quantum, Music, Dordrecht: Kluwer Academic, 1999, pp. 303–326. An investigation of arithmetical propertiesof epimoric ratios, which mathematically represent musical intervals of an octave, taking into account the Sectiocanonis of Euclid, as well as other Greek and Latin sources. See the review by Christoph J. Scriba in MathematicalReviews 2002b:01005. (EAM) #29.3.18

Bellissima, Fabio. A Problem of Fermat Relative to the Decomposition of the Epimoric Fractions, Physis 37(1)(2000), 167–180. Fermat had proposed that a method be found for determining the number of possible differentdecompositions of an epimoric ratio (which mathematically represents musical intervals of an octave) into threeepimoric factors. The author develops an algorithm which answers this proposal. See the review by Christoph J.Scriba in Mathematical Reviews 2002b:01006. (EAM) #29.3.19

Bellosta, Helene. See #29.3.124.

Benvenuto, Edoardo. Adhemar-Jean-Claude Barre de Saint-Venant: The Man, the Scientist, the Engineer, inGiornata Lincea, ed., Il Problema di de Saint-Venant: Aspetti Teorici e Applicativi [The Saint-Venant Problem:Theoretical and Practical Aspects], Rome: Accademia Nazionale dei Lincei, 1998, pp. 7–34. An introduction to deSaint-Venant and to his contributions to the mathematical theory of elasticity. See the review by Jesus Hernandezin Mathematical Reviews 2002b:01035. (EAM) #29.3.20

Berberan-Santos, Mario N. See #29.3.138.

Berestovskaya, N. V. History and Philosophy of Mathematics [in Russian], in A. K. Guts, ed., MathematicalStructures and Modeling No. 6 [in Russian], Omsk: Omskiı Gosudarstvennyı Univ., 2000, pp. 156–159. Considersthe appropriateness of the use of non-Euclidean mathematics in relativistic philosophies. (GVB) #29.3.21

Berggren, John Lennart. See #29.3.78 and #29.3.79.

Betsch, Gerhard. Sudwestdeutsche Mathematici aus dem Kreis um Michael Mastlin [Southwest German Math-ematicians from the Circle around Michael Mastlin], in Irmgard Hantsche, ed., Der “Mathematicus”: Zur En-twicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators, Bochum: UniversitatsverlagDr. N. Brockmeyer, 1996, pp. 121–150. Defining a mathematician as a practitioner of applied mathematics in itswidest sense, the author looks at the work of some mathematicians from the circle around M. Mastlin (1550–1631).J. Kepler, W. Schickart, G. Galgemair, W. Bachmayer, and M. Beger. See the review by Karl-Heinz Schlote inMathematical Reviews 2002c:01018. (TBC) #29.3.22

Bimbo, Katalin. See #29.3.108.

Bissel, K. The Role of A. A. Andronov in the Development of Automatic Control in Russia [in Russian],Avtomatica i Telemekhanika 2001(6), 5–17; translation in Automation and Remote Control 62(6) (2001), 863–874. A brief introduction to the work of Aleksandr Aleksandrovitch Andronov (1901–1952), beginning with hiswork in nonlinear dynamics, and its impact on Soviet research in automatic control theory. (EAM) #29.3.23

Boger, George. The Modernity of Aristotle’s Logic, in Demetra Sfendoni-Mentzou, Jagdish Hattiangadi, andDavid M. Johnson, eds., Aristotle and Contemporary Science, vol. II, New York: Peter Lang, 2001, pp. 97–112.


Argues that Aristotle’s logic is more modern than is usually supposed, particularly his distinction between syntaxand semantics. See the review by Leon Harkleroad in Mathematical Reviews 2002a:01005. (HEK) #29.3.24

Boh, Ivan. Four Phases of Medieval Epistemic Logic, Theoria 66(2) (2000), 129–144. Outlines the developmentof medieval discussions on epistemic logic during the 14th century. See the review by Paloma Perez-Ilzarbe inMathematical Reviews 2002b:03004. (EAM) #29.3.25

Bony, Jean-Michel; Choquet, Gustave; and Lebeau, Gilles. Le Centenaire de l’Integrale de Lebesgue [Centennialof the Lebesgue Integral], Comptes Rendus des Seances de l’Academie des Sciences. Serie I. Mathematique 332(2)(2001), 85–90. Contains a reprint of, and commentary on, a remarkable 2 1

2 -page note of Henri Lebesgue, in whichhe briefly defines measure, measurability of a function, and the Lebesgue integral. See the review by Robert G.Bartle in Mathematical Reviews 2002a:28001. (HEK) #29.3.26

Bottazzini, Umberto. See #29.3.55.

Bradley, James. The Soviet Concept of the Correlation of Forces, in Michael Stob, ed., Thirteenth ACMS Con-ference on Mathematics from a Christian Perspective, Grand Rapids: Calvin College, 2001, pp. 115–122. A studyof Soviet military work on the Lanchester equations and the correlation of forces. (GVB) #29.3.27

Brauer, G. U. See #29.3.146.

Bressoud, David. Was Calculus Invented in India? The College Mathematics Journal 33(1) (2002), 2–13. Dis-cussion of how Indian astronomers, sometime between 1350 and 1550, discovered the series for trigonometricfunctions. (PWH) #29.3.28

Brillinger, D. R. John Wilder Tukey (1915–2000), Notices of the American Mathematical Society 49(2) (2002),193–201. An account of many contributions of Tukey, a topologist and statistician who “revolutionize[d] the worldof the analysis of data.” (KVM) #29.3.29

Brouwer, L. E. J. The Foundations of Topology and the Topology of the Foundations, in L. M. Schoonhoven,ed., Gems from a Century of Science 1898–1997, Amsterdam: North-Holland, 1997, pp. 11–44. A reprint of aclassic paper by Brouwer. (GVB) #29.3.30

Burckel, R. B. See #29.3.205.

Cartier, Pierre. A Mad Day’s Work: From Grothendieck to Connes and Kontsevich. The Evolution of Concepts ofSpace and Symmetry, Bulletin of the American Mathematical Society 38 (2001), 389–408. Written on the occasionof the 40th anniversary of the Institut des Hautes Etudes Scientifiques in 1998, this paper deals with the natureof space and its points, the concept of a spectrum, points and representations, noncommutative geometry, internalsymmetries, and Grothendieck’s “broken dream” of unifying Galois theory and topology. (GVB) #29.3.31

Carus, A. W. See #29.3.11.

Casini, Paolo. D’Alembert (1717–1783) [in Italian], Bollettino della Unione Matematica Italiana. Sezione A. LaMatematica nella Societa e nella Cultura (8) 2(1) (1999), 11–16. This is an overview of the contributions of Jeand’Alembert to the Encyclopedie of 1751 and his 1752 “Essai sur la societe des gens de lettres et des grands.” Theauthor makes the interesting observation that the mathematician’s social status was rather unusual—the respectthat intellectuals accorded the science of mathematics guaranteed that mathematicians were highly esteemed, evenwhen many lacked the competence to judge their results. See the review by Douglas M. Jesseph in MathematicalReviews 2002c:01028. (TBC) #29.3.32

Catanese, Fabrizio. Hilbert at the Georg August Universitat Gottingen: Yesterday and Today [in Italian], Matem-atiche (Catania) 55 (2000), suppl. 1, 7–24. Discusses Hilbert in the context of the development of mathematicsat Gottingen, and includes the Italian versions of two of his manuscripts. See the review by Doru Stefanescu inMathematical Reviews 2002b:01039. (EAM) #29.3.33

Chaber, Jozef. See #29.3.77.

Chambers, Llewelyn G. See #29.3.203.

Choquet, Gustave. See #29.3.26.


Christianidis, Jean. Readers of Diophantus in Byzantium, Neusis 9 (2000), 117–131. Commentaries and glosseson Diophantus’s Arithmetica by Byzantine scholars help to clarify aspects of Diophantus’s thought which are notevident in the original text. (GVB) #29.3.34

Cizmar, Jan. The Origins and Development of Mathematical Notation (A Historical Outline), Quaderni diRicerca in Didattica 9 (2000), 105–124. This survey of mathematical notation emphasizes “the decisive role ofEuropean mathematics in the elaboration of the modern notation in the main branches of elementary and highermathematics.” (GVB) #29.3.35

Closs, Michael P. Mesoamerican Mathematics, in #29.3.41, pp. 205–238. (GVB) #29.3.36

Cohen, Edward. Simon Newcomb and the Leap-Year Problem, in #29.3.91, pp. 107–120. A brief scientificbiography of Newcomb and an exposition of the “arithmetic of the leap year,” including a formula, due toNewcomb, for the length of a solar year as a function of time elapsed since the beginning of the Christian era.(HG) #29.3.37

Cohen, Hermann. Le Principe de la Methode Infinitesimale et son Histoire, with introduction, translation andnotes by Marc de Launay, Paris: J. Vrin, 1999, 191 pp., 135 F. The first French translation of the classical book byHermann Cohen (1852–1918). The author discusses the book within the context of Cohen’s entire work, notablywith respect to Cohen’s critique of Kant. See the review by Pierre Crepel in Mathematical Reviews 2002b:01004.(EAM) #29.3.38

Colmez, Pierre; and Serre, Jean-Pierre, eds. Correspondance Grothendieck–Serre, Paris: Societe Mathematiquede France, 2001, xii+288 pp., 39 . Contains a large part of the mathematical correspondence between Grothendieckand Serre, particularly in algebraic geometry during the years 1955–1965. (GVB) #29.3.39

Crepel, Pierre. See #29.3.38 and #29.3.92.

Crowley, J. See #29.3.109.

D’Ambrosio, Ubiratan. A Historiographical Proposal for Non-Western Mathematics, in #29.3.41, pp. 79–92.(GVB) #29.3.40

D’Ambrosio, Ubiratan; and Selin, Helaine, eds. Mathematics across Cultures: The History of Non-WesternMathematics, Dordrecht: Kluwer, 2000, xx+479 pp., $217. This collection contains 6 articles on the connectionbetween mathematics and culture and 15 papers focusing on particular cultures. It “provides the teacher withnumerous examples by which to convince students that, indeed, every culture has mathematics.” The papersare listed in these abstracts as #29.3.36, #29.3.40, #29.3.49, #29.3.61, #29.3.63, #29.3.90, #29.3.99, #29.3.112,#29.3.128, #29.3.144, #29.3.151, #29.3.156, #29.3.173, #29.3.176, #29.3.179, #29.3.197, #29.3.199, #29.3.200,#29.3.201, #29.3.202, and #29.3.208. See the review by Victor J. Katz in Mathematical Reviews 2002a:01001.(HEK) #29.3.41

D’Ambrosio, Ubiratan. See also #29.3.165.

Dauben, Joseph. Review of Georges Ifrah, The Universal History of Numbers and The Universal History ofComputing, part 1, Notices of the American Mathematical Society 49(1) (2002), 32–38. Dauben outlines thedeficiencies and mistakes in Ifrah’s books. See also #29.3.43. (KVM) #29.3.42

Dauben, Joseph. Review of Georges Ifrah, The Universal History of Numbers and The Universal History ofComputing, part 2, Notices of the American Mathematical Society 49(2) (2002), 211–216. Dauben outlines thedeficiencies and mistakes in Ifrah’s books. See also #29.3.42. (KVM) #29.3.43

Dauben, Joseph W. See also #29.3.58 and #29.3.104.

De Smet, Rudolf; and Verelst, Karin. Newton’s Scholium Generale: The Platonic and Stoic Legacy—Philo,Justus Lipsius and the Cambridge Platonists, History of Science 39(123, part 1) (2001), 1–30. This is a comparisonbetween Newton’s text and some works by the Alexandria-born Jewish Platonist Philo (c. 20 BC–AD 50), bythe Cambridge Platonists Henry More (1614–1687) and Ralph Cudworth (1617–1688), and by the neo-stoicBrabant humanist Justus Lipsius (1547–1606). The author shows that some of the passages in Newton’s Scholium


Generale are similar to the passages in the above listed authors’ works. See the review by Niccolo Guicciardini inMathematical Reviews 2002c:01029. (TBC) #29.3.44

Dejnozka, Jan. Origin of Russell’s Early Theory of Logical Truth as Purely General Truth: Bolzano, Peirce,Frege, Venn, or MacColl? Modern Logic 8(3/4) (2000–2001), 21–30. A discussion of the most likely influenceson this early theory of Bertrand Russell and the effect (negative) of the delayed publication in 1994 of his 1905paper, “Necessity and Possibility,” on the development of modal logic. The author claims that Russell’s earliestpublished statements of implied modal logic appeared in the journal Mind in 1906 and 1908 as responses to thework of H. MacColl. (FA) #29.3.45

Del Centina, Andrea. The Manuscript of Abel’s Parisian Memoir Found in Its Entirety, Historia Mathematica29 (2002), 65–69. This memoir on transcendental functions was lost after printing. In 1952 all but eight pageswere found; the author discovered the remaining pages in 2000. (GVB) #29.3.46

Di Girolamo, Giulia. The Archimedean Influence in Galileo’s Theoremata [in Italian], Physis 36(1) (1999),21–54. In Galileo’s Theoremata Galileo found centers of gravity for several solids. Galileo refers to his motivationas a flawed attempt by Fredrici Commandino to use the Archimedean methods from De planorum aequilibriis.See the review by Victor V. Pambuccian in Mathematical Reviews 2002c:01019. (TBC) #29.3.47

Dieks, Dennis. See #29.3.126.

Dudley, Underwood. The World’s First Mathematics Textbook, Math Horizons, April 2002, 8–11. The Rhindpapyrus, which dates to 1650 BC in Egypt, is organized much like most modern mathematics texts, as a set ofquestions followed by their solutions. It presents techniques to solve various practical arithmetic problems of theday, in particular those involving multiplication with reciprocals or fractions. (HN) #29.3.48

Eglash, Ron. Anthropological Perspectives on Ethnomathematics, in #29.3.41, pp. 13–22. (GVB) #29.3.49

Einstein, Albert. The Collected Papers of Albert Einstein, Vol. 8, edited by Robert Schulmann, A. J. Kox, MichelJanssen, and Jozsef Illy, Princeton, NJ: Princeton Univ. Press, part A lxxii+590 pp., part B xxx+528 pp. The secondinstallment of Einstein’s correspondence comprises the first five Berlin years (1914 to 1918). There are letters byand to H. A. Lorentz, W. de Sitter, K. Schwarzschild, and the mathematicians D. Hilbert, F. Klein, T. Levi-Civita,and H. Weyl. There are also letters that are important to Einstein’s justification of his theory of gravitation as aphysical theory of space–time geometry. See the review by H. Treder in Mathematical Reviews 2002c:01047a/b.(TBC) #29.3.50

Etnyre, John B. See #29.3.60.

Ferraro, Giovanni. Rigor and Proof in the Mid-Eighteenth Century [in Italian], Physis 36(1) (1999), 137–163. This is an investigation of the standards of rigor in mathematical analysis between 1740 and 1770, drawingheavily on material from Euler. See the review by Victor V. Pambuccian in Mathematical Reviews 2002c:01030.(TBC) #29.3.51

Figa-Talamanca, Alessandro. How to “Objectively” Evaluate the Quality of Scientific Research: The Case of theImpact Factor [in Italian], Bollettino della Unione Matematica Italiana. Sezione A. La Matematica nella Societa enella Cultura (8) 2(3) (1999), 249–281. This article contains an extensive analysis of the ways in which scientistsadapt their habits of publication, citation, choice of journal, etc., to the method based on the number of times thatthe publication in question is cited in other publications during the first two years. See the review by Eduard Glasin Mathematical Reviews 2002c:01048. (TBC) #29.3.52

Fine, Kit. Cantorian Abstraction: A Reconstruction and Defense, Journal of Philosophy 95(12) (1998), 599–634. Seeks to show the coherence and relative plausibility (but not necessarily the correctness) of Cantor’sand Dedekind’s account of number and order type. See the review by Yehuda Rav in Mathematical Reviews2002b:01031. (EAM) #29.3.53

Frankenstein, Marilyn. See #29.3.140.

Franklin, James. The Science of Conjecture: Evidence and Probability before Pascal, Baltimore/London:Johns Hopkins Univ. Press, 2001, xiii+497 pp., $55. A historical study of rational methods of dealing with


uncertainty, including scientific fields, but also rhetorical, legal, social, philosophical, religious, and other perspec-tives. (GVB) #29.3.54

Freguglia, Paolo. Studies on the Foundations of Mathematics in the Second Half of the Nineteenth Century, withParticular Emphasis on the Situation in Italy [in Italian], Matematiche (Catania) 55 (2000), suppl. 1, 161–205.The core of the paper is an account of Veronese’s work on the foundations of multidimensional geometry andPeano’s axiomatic approach to the geometry of position. See the review by Umberto Bottazzini in MathematicalReviews 2002c:01033. (TBC) #29.3.55

Friedman, Michael. Reconsidering Logical Positivism, Cambridge, UK: Cambridge Univ. Press, 1999, xx+252pp., $19.95. A collection of essays that attempts to reappraise dispassionately the origins, motivations, and truephilosophical aims of the logical positivist movement. In particular, the author argues that its main innovationwas a new conception of a priori knowledge and its role in empirical science. See the review by Eduard Glas inMathematical Reviews 2002a:00005. (HEK) #29.3.56

Friedman, Michael. Geometry, Construction, and Intuition in Kant and His Successors, in Gila Sher and RichardTieszen, eds., Between Logic and Intuition, Cambridge, UK: Cambridge Univ. Press, 2000, pp. 186–218. Adiscussion of the meaning given to spatial intuition by Kant, Helmholtz, Poincare, and Weyl. See the review byVictor V. Pambuccian in Mathematical Reviews 2002b:00005. (EAM) #29.3.57

Gasser, James, ed. A Boole Anthology: Recent and Classical Studies in the Logic of George Boole, Dordrecht:Kluwer, 2000, xii+336 pp., $144. A collection of papers which survey Boole’s mathematical and philosophicalaccomplishments, some of which emerged from a conference on Boole in Lausanne in 1997. See the review byJoseph W. Dauben in Mathematical Reviews 2002a:03004. (HEK) #29.3.58

Gatto, Romano. The Debate about Methods and Vincenzo Flauti’s Challenge to the Mathematicians of theKingdom of Naples [in Italian], Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche (4) 67 (2000),181–233. A detailed account of an episode in the long debate between the synthetic and analytic viewpoints ingeometry, during the period between 1771 and 1839. See the review by Victor V. Pambuccian in MathematicalReviews 2002b:01027. (EAM) #29.3.59

Geiges, Hansjorg. A Brief History of Contact Geometry and Topology, Expositiones Mathematicae 19(1) (2001),25–53. This article gives an overview of the historical origins of contact geometry beginning with Sophus Lie in1872 and continuing through the present. See the review by John B. Etnyre in Mathematical Reviews 2002c:53129.(TBC) #29.3.60

Gerdes, Paulus. On Mathematical Ideas in Cultural Traditions of Central and Southern Africa, in #29.3.41,pp. 313–343. (GVB) #29.3.61

Giacardi, Livia. The Corrado Segre Archive, Historia Mathematica 28 (2001), 296–301. The University ofTurin has within its manuscript collection about 40 books of lecture notes and other materials by Corrado Segre,the founder of the Italian school of algebraic geometry; these could provide a rich source for historical studies.(GVB) #29.3.62

Gilsdorf, Thomas E. Inca Mathematics, in #29.3.41, pp. 189–203. (GVB) #29.3.63

Glas, Eduard. See #29.3.52 and #29.3.56.

Godard, Roger. A Study of the Interpolation Theory from Lagrange up to 1950s, in #29.3.91, pp. 121–133.This survey covers Lagrange interpolation, Hermite interpolation, the calculus of finite differences, approximationtheory, the treatment of errors, interpolation of periodic functions, and piecewise interpolation. (HG) #29.3.64

Gottwald, Siegfried. See #29.3.71.

Gray, Jeremy J. The Hilbert Challenge, Oxford: Oxford Univ. Press, 2000, xii+315 pp. This book examinesthe reasons behind the long-lived success of Hilbert’s 23 problems. The reviewer states “this should be the firstplace for a twenty-first century student to turn who wishes to know just what the Hilbert problems are and how andwhy they proved so influential.” See the review by Albert C. Lewis in Mathematical Reviews 2002c:01037.(TBC) #29.3.65


Gray, Jeremy J. Weierstrass, Luzin, and Induction, American Mathematical Monthly 108 (2001), 865–870. Thisreflection on Luzin’s long-running disagreement with Weierstrass about analysis centers on the tension betweenintuition and representation of mathematical concepts and contains criticisms of Laugwitz’s earlier paper on Luzin(#28.2.115). (GVB) #29.3.66

Gregory, Andrew. Aristotle, Dynamics and Proportionality, Early Science and Medicine 6(1) (2001), 1–21.Explains Aristotle’s seemingly disparate comments on bodies in motion in terms of his project to establish acoherent theory of change in general, not just dynamics. (GVB) #29.3.67

Grier, David Alan. Dr. Veblen Takes a Uniform: Mathematics in the First World War, American MathematicalMonthly 108 (2001), 922–931. Discusses Veblen’s work on ballistics in 1918 while he served at the AberdeenProving Ground in Maryland, as well as the effect of military service on mathematicians during the First WorldWar. (GVB) #29.3.68

Griffin, Nicholas. Russell, Logicism, and “If–Thenism,” in #29.3.91, pp. 134–146. This paper argues that whileRussell in The Principles of Mathematics held that all mathematical statements are conditional in form, his “if–thenism” is not “remotely like” that ascribed to him by Putnam. The author also claims that the if–thenism inPrincipia Mathematica represents, in part, “a failure of Russell’s logicist hopes.” (HG) #29.3.69

Gross, Mark. See #29.3.149.

Guicciardini, Niccolo. See #29.3.44.

Hafner, Johannes. Bolzano’s Criticism of Indirect Proofs, Revue d’Histoire des Sciences 52(3–4) (1999),385–398. An attempt to clarify the nature of Bolzano’s discomfort with indirect proofs in mathematics.(GVB) #29.3.70

Hansen, Frank-Peter. Geschichte der Logik des 19. Jahrhunderts: Eine Kritische Einfuhrung in die Anfangeder Erkenntnis- und Wissenschaftstheorie [History of Logic in the 19th Century: A Critical Introduction to theBeginnings of Epistemology and Science Theory], Wurzburg: Konigshausen & Neumann, 2000, 201 pp. This is nota history of mathematical logic, but rather “a critical introduction to the beginnings of epistemology and sciencetheory” with a focus on German philosophy. See the review by Siegfried Gottwald in Mathematical Reviews2002c:01034. (TBC) #29.3.71

Harkleroad, Leon. See #29.3.24.

Hayashi, Takao. A Set of Rules for the Root-Extraction Prescribed by the Sixteenth-Century Indian Mathemati-cians, Nılaka .ntha Somastuvan and Sankara Variyar, Historia Scientiarum 9(2) (1999), 135–153. The commentariesof these two Indian mathematicians contain useful clues to the achievements of the Madhava school. This paperdiscusses the square root of the sum of two squares, the square root of the difference of two squares, and theirapplication to root-extraction by place-value notation and to the approximation of roots of nonsquare numbers.See the review by A. I. Volodarskiı in Mathematical Reviews 2002a:01013. (HEK) #29.3.72

Hayashi, Takao. Govindasvamin’s Arithmetic Rules Cited in the Kriyakramakarı of Sankara and Naraya .na,Indian Journal of History of Science 35(3) (2000), 189–231. The author discusses Govindasvamin’s arithmeticrules in Sanskrit collected from the Kriyakramakarı together with his English translation and commentary. Seethe review by Pradip Kumar Majumdar in Mathematical Reviews 2002b:01015. (EAM) #29.3.73

Hayashi, Takao. See also #29.3.98.

He, Kun. See #29.3.183.

Hentschel, Klaus. Das Brechungsgesetz in der Fassung von Snellius. Rekonstruktion seines Entdeckungspfadesund eine Ubersetzung seines Lateinischen Manuskriptes sowie Erganzender Dokumente [The Law of Refractionin the Version Due to Snellius. Reconstruction of His Path of Discovery and a Translation of the Latin Manuscriptand Supplementary Documents], Archive for History of Exact Sciences 55(4) (2001), 297–344. A translation of,and commentary on, the manuscript containing the law of refraction named after Snell. The author argues thatSnell’s previous geodetic work, his knowledge of previous literature in optics, and his interest in Ibn al-Haytham’swork led him to his discovery. (HEK) #29.3.74


Herbenick, Raymond. Aristotle on Mathematical Ethics, in Demetra Sfendoni-Mentzou, Jagdish Hattiangadiand David M. Johnson, eds., Aristotle and Contemporary Science, vol. II, New York: Peter Lang, pp. 239–251.Sketches Aristotle’s matrix of exactness in subject matter and in method, assessing its significance in view ofrecent moral development psychology. Includes a summary of recent secondary literature regarding the prob-lem of mathematical ethics. See the review by Eberhard Knobloch in Mathematical Reviews 2002b:01048.(EAM) #29.3.75

Hernandez, Jesus. See #29.3.20.

Heyde, C. C. See #29.3.102.

Hill, Victor E. IV. President Garfield and the Pythagorean Theorem, Math Horizons, February 2002, 9–11, 15.President Garfield’s proof of the Pythagorean Theorem is an example of geometrical intuition at its best. Althoughthe proof seems to be a mere geometrical curiosity, it is quite elegant and worthy of recognition. (NL) #29.3.76

Hodel, R. E. A History of Generalized Metrizable Spaces, in C. E. Aull and R. Lowen, eds., Handbook ofthe History of General Topology, vol. 2, Dordrecht: Kluwer, 1998, pp. 541–576. This survey focuses on 1950–1980 and contains a long bibliography. See the review by Jozef Chaber in Mathematical Reviews 2002a:54001.(HEK) #29.3.77

Hogendijk, Jan P. Traces of the Lost Geometrical Elements of Menelaus in Two Texts of al-Sijzı, Zeitschrift furGeschichte der Arabisch-Islamischen Wissenschaften 13 (1999–2000), 129–164, 9 (Arabic paging). The authorpublishes new evidence from two texts by the 10th-century Islamic geometer Abu Sa‘ıd al-Sijzı to show thatMenelaus’s lost book, Geometrical Elements, was a collection of elementary theorems and problems on straightlines, circles, and triangles in the plane. See the review by John Lennart Berggren in Mathematical Reviews2002b:01013. (EAM) #29.3.78

Hogendijk, Jan P. Al-Nayrızı’s Own Proof of Euclid’s Parallel Postulate, in Menso Folkerts and Richard Lorch,eds., Sic Itur ad Astra, Wiesbaden: Harrassowitz, 2000, pp. 252–265. The article gives an edited Arabic text andEnglish translation of and commentary on al-Nayrızı’s commentary on Euclid’s Elements. The author shows howal-Nayrızı’s proof influenced Thabit ibn Qurra and then in turn other Islamic mathematicians. See the review byJohn Lennart Berggren in Mathematical Reviews 2002c:01014. (TBC) #29.3.79

Hogendijk, Jan P. See also #29.3.148.

Horstmann, Frank. Ein Baustein zur Kepler-Rezeption: Thomas Hobbes’ Physica Coelestis [A Building Blockin the Appreciation of Kepler: Thomas Hobbes’ Physica Coelestis], Studia Leibnitiana 30(2) (1998), 135–160.In this treatise Hobbes demonstrates a debt to Kepler and modifies Kepler’s explanation of why the earth’s orbitis eccentric, namely, that the earth consists of two parts, one well-disposed to, and the other hostile to, the sun.(GVB) #29.3.80

Hugly, Philip; and Sayward, Charles. Did the Greeks Discover the Irrationals? Philosophy 74(288) (1999),169–176. The authors discuss the Greek discovery of irrationals by geometric considerations. Their thesis is thatthe results of Greek mathematicians do not entail the existence of irrational numbers. See the review by DoruStefanescu in Mathematical Reviews 2002c:01008. (TBC) #29.3.81

Hupp, Ingrid. Arithmetik- und Algebralehrbucher Wurzburger Mathematiker des 18. Jahrhunderts [Arithmeticand Algebra Textbooks by Wurzburg Mathematicians of the 18th Century], Munich: Institut fur die Geschichteder Naturwissenschaften, 1998, viii+172 pp. The author analyzes textbooks of the three mathematicians FranzHuberti (1715–1789), Franz Trentel (1730–1804), and Andreas Metz (1767–1839), who lectured as professorsof mathematics at the University of Wurzburg. See the review by Karl-Heinz Schlote in Mathematical Reviews2002c:01031. (TBC) #29.3.82

Illy, Jozsef. See #29.3.50.

Information About the Institute’s Activities 2000, Berlin: Max-Planck-Institut fur Wissenschaftsgeschichte, 2001,54 pp. A pamphlet summarizing the research activity at the Max Planck Institute for the History of Science for2000. (GVB) #29.3.83


Ivanov, N. V. See #29.3.174 and #29.3.186.

Izuhara, Ritsuko. A Study on Baien’s Diagrams, “Gengo-zu,” in Terms of Symmetry, Forma 15(2) (2000),163–172. The symmetries in Japanese philosopher Baien Miura’s diagrams suggest that he was representingthree-dimensional images on a two-dimensional surface. (GVB) #29.3.84

Jaffard, Stephane. Decompositions en Ondelettes [Wavelet Decompositions], in Jean-Paul Pier, ed., Developmentof Mathematics 1950–2000, Basel: Birkhauser, 2000, pp. 609–634. Treats the development and applications ofwavelet expansions by means of important examples and their history. The author first explores the significance ofunconditional bases and later focuses on signal processing. See the review by Lars F. Villemoes in MathematicalReviews 2002b:42053. (EAM) #29.3.85

Janssen, Michel. See #29.3.50.

Janssen, Theo M. V. Frege, Contextuality and Compositionality, Journal of Logic, Language and Information10(1) (2001), 115–136. In the Grundlagen period Frege followed a strict form of the context principle; as timewent on he moved toward compositionality, but eventually was forced to reject it. (GVB) #29.3.86

Jesseph, Douglas M. See #29.3.32.

Joel, J. S. See #29.3.119 and #29.3.127.

Johnson, Warren P. The Curious History of Faa di Bruno’s Formula, American Mathematical Monthly 109(2002), 217–234. This formula, which the author describes as the best answer to the question “what is the mthderivative of a composite function?” began its life in real analysis and has appeared in many fields and with manyvariants. (GVB) #29.3.87

Kak, Subash. Yamatarajabhanasalagam: An Interesting Combinatoric Sutra, Indian Journal of History of Science35(2) (2000), 123–127. Considers the history of a sutra that describes all combinations of a binary sequence oflength 3. (GVB) #29.3.88

Katz, Victor J. See #29.3.41.

Kheddaoui, Abdelkader. Sciences of Calculation in Bougie (Mathematical Study) [in Arabic], in Proceedingsof the International Conference “Bejaıa and Its Region through the Ages: History, Society, Sciences, Culture,”Bejaıa: Gehimab Edition, 1997, pp. 224–236. This article tries to encircle the elements of the sciences of calculationknown in Bougie in medieval times. (DA) #29.3.89

Kim, Soo Hwan. Development of Materials for Ethnomathematics in Korea, in #29.3.41, pp. 455–465.(GVB) #29.3.90

Kinyon, Michael K., ed. Proceedings of the Canadian Society for the History and Philosophy of Mathe-matics, Vol. 13, 2000, paperbound, 215 pp. This volume contains most of the papers delivered at the 26th annualmeeting of the CSHPM, held at McMaster University, Hamilton, Ontario, in June 2000. The papers are ab-stracted separately as #29.3.1, #29.3.4, #29.3.14, #29.3.37, #29.3.64, #29.3.69, #29.3.95, #29.3.97, #29.3.101,#29.3.103, #29.3.106, #29.3.113, #29.3.116, #29.3.121, #29.3.150, #29.3.154, #29.3.180, #29.3.192, #29.3.193,and #29.3.198. (HG) #29.3.91

Knobloch, Eberhard. See #29.3.75.

Koriako, Darius. Kants Philosophie der Mathematik, Hamburg: Felix Meiner Verlag, 1999, viii+363 pp., DM128. The 11th work in a series begun in 1987 thoroughly exploring Kant’s philosophy of mathematics. See thereview by Pierre Crepel in Mathematical Reviews 2002b:01028. (EAM) #29.3.92

Korte, Bernhard. Vojtech Jarnik’s work in combinatorial optimization, Discrete Mathematics 235(1–3) (2001),1–17. Discusses two of Jarnik’s papers from 1930 and 1934 concerning the minimal spanning tree problemand the Euclidean Steiner tree problem. See the review by Xueliang Li in Mathematical Reviews 2002b:01041.(EAM) #29.3.93


Kosinski, Antoni A. Cramer’s Rule Is Due to Cramer, Mathematics Magazine 74 (2001), 310–312. Argues thatColin Maclaurin’s Treatise of Algebra does not contain a proof of Cramer’s Rule and that Cramer himself deservesthe credit. (GVB) #29.3.94

Kox, A. J. See #29.3.50.

Kreyszig, Erwin. “Modern” Starts, in #29.3.91, pp. 23–43. The title refers to the birth of “ideas, concepts andareas” that make 20th-century mathematics “distinctly different” from what went before. The author concentrateson topology and functional analysis and their “give-and-take.” A brief coda compares modernism in mathematicsand in the visual arts. (HG) #29.3.95

Kunitzsch, Paul. Schriftenverzeichnis, in Menso Folkerts and Richard Lorch, eds., Sic Itur Ad Astra: Studienzur Geschichte der Mathematik un Naturwissenschaften. Festschrift fur den Arabisten Paul Kunitzsch zum 70Geburtstag, Wiesbaden: Harrassowitz Verlag, 2000, pp. 7–29. A brief biography and bibliography of historianPaul Kunitzsch. (GVB) #29.3.96

Kunoff, Sharon. A Commentary on the First Hebrew Geometry and Its Relationship to the First Arabic Geometry,in #29.3.91, pp. 147–153. The title refers to a Hebrew manuscript dated ca. 150 and to al-Khwarizmı’s geometryof ca. 820. A comparison shows that al-Khwarizmı drew heavily on, while adding to, the Hebrew material. Thegrounds for the dating of the Hebrew text (by Gandz) are set out. (HG) #29.3.97

Laforge, Christophe. L’Arithmetique Vedique. I. Veda et Nikhilam Soutra [Vedic Arithmetic. I. Veda andNikhilam Sutra], Revue des Questions Scientifiques 170(4) (1999), 355–368. This is the first of a series ofpapers meant to be a French introduction to the so-called “Vedic mathematics” of Bharati K.r.s .na Tirthaji.This paper deals with multiplication. See the review by Takao Hayashi in Mathematical Reviews 2002c:01016.(TBC) #29.3.98

Langermann, Y. Tzvi; and Simonson, Shai. The Hebrew Mathematical Tradition, in #29.3.41, pp. 167–188.(GVB) #29.3.99

Laubenbacher, Reinhard; McGrath, Gary; and Pengelley, David. Lagrange and the Solution of Numerical Equa-tions, Historia Mathematica 28 (2001), 220–231. Lagrange’s algorithm for detecting, isolating, and approximatingall real and complex roots of polynomial equations was guaranteed to converge (unlike Newton’s method) andforeshadowed later techniques in geometry and abstract algebra. (GVB) #29.3.100

Lavers, Gregory. Carnap, Godel and Friedman on Analyticity, in #29.3.91, pp. 154–158. According to the author,Michael Friedman holds that Carnap, in The Logical Syntax of Language, seeks to present a “perspective fromwhich a scientifically minded philosopher could make sense of what is at issue” in debates over the foundations ofmathematics. This paper argues against Friedman’s view that Carnap fails in this attempt because “the definitionof analytic must be made within an indefinite meta-language.” (HG) #29.3.101

Le Cam, Lucien. La Statistique Mathematique depuis 1950 [Mathematical Statistics since 1950], in Jean-PaulPier, ed., Development of Mathematics 1950–2000, Basel: Birkhauser, 2000, pp. 735–761. A survey of the devel-opment of most topics within mathematical statistics since 1950. See the review by C. C. Heyde in MathematicalReviews 2002a:62001. (HEK) #29.3.102

Lebeau, Gilles. See #29.3.26.

Lehoux, Daryn. On the Alleged Zodiacal Calendar in Geminus and Miletus I, in #29.3.91, pp. 44–47. The authorargues, contrary to an “old claim,” that the Germinus and Miletus I parapegmata did not use zodiacal calendars.In particular, their divisions are not compatible with those of the only zodiacal calendar known from antiquity, theDionysian. (HG) #29.3.103

Leibniz, Gottfried Wilhelm. Die Grundlagen des Logischen Kalkuls, edited and with commentary by FranzSchupp with the cooperation of Stephanie Weber, Hamburg: Felix Meiner Verlag, 2000, lxxxvi+289 pp., DM98. A dual-language (Latin–German) edition of 10 manuscripts from the collection of Leibniz manuscripts inHanover; these texts are often preliminary drafts, and thus represent Leibniz at work. Topics include logicalcalculus, identity calculus, arithmetic calculus, plus–minus calculus, concept and statement calculi, the adequacycriterion, negation of concepts and statements, intensional and extensional interpretations, disjunctive inclusion,


and the interpretation of diagrams, among others. See the review by Joseph W. Dauben in Mathematical Reviews2002a:01039. (HEK) #29.3.104

Lenstra, H. W. Solving the Pell Equation, Notices of the American Mathematical Society 49(2) (2002), 182–192. Before describing the efficiency of methods of solution for Pell’s equation, Lenstra outlines a history of theequation, including the cattle problem of Archimedes. (KVM) #29.3.105

Lewis, Albert C. The Contrasting Views of Charles S. Peirce and Bertrand Russell on Cantor’s TransfiniteParadise, in #29.3.91, pp. 159–166. The author describes how Peirce and Russell sought in Cantor’s theory oftransfinite numbers rigorous support for their respective attacks on the problems posed by space, the continuum,the infinitely great, and the infinitely small. (HG) #29.3.106

Lewis, Albert C. See also #29.3.17, #29.3.65, #29.3.141, and #29.3.166.

Li, Xueliang. See #29.3.93.

Lorentz, G. G. Who Discovered Analytic Sets? Mathematical Intelligencer 23(4) (2001), 28–32. Using recentlyavailable information about priority questions from the Soviet Academy of Sciences found in a “lost” bookcontaining the complete reports of N. N. Luzin’s 1936 trial, the author analyzes the contributions of P. S. Alexandrov,F. Hausdorff, Luzin, and M. Suslin to the discovery of A-sets and the related theory of Borel sets in the period1915–1923. (FA) #29.3.107

Maenpaa, Petri. From Backward Reduction to Configurational Analysis, in Michael Otte and Marco Panza,eds., Analysis and Synthesis in Mathematics, Dordrecht: Kluwer, 1997, pp. 201–226. The author investigatesinterpretations of the methods called analysis and synthesis in Greek geometry and compares his reconstruction ofGreek mathematics with other reconstructions that use first-order logic as their formal framework. See the reviewby Katalin Bimbo in Mathematical Reviews 2002c:01009. (TBC) #29.3.108

Majumdar, Pradip Kumar. See #29.3.73.

Manteuffel, T.; and Crowley, J. SIAM Turns Fifty, Notices of the American Mathematical Society 49(2) (2002),309. The authors reflect on the past of the SIAM organization in this letter to the editor. (KVM) #29.3.109

Marchini, Carlo. Myths, Magic, Displays, Theorems, Definitions [in Italian], Rivista di Matematica della Uni-versita di Parma (6) 3∗ (2000), 123–141. A short history of theorems and definitions from ancient Greece tomodern times, intended to demystify the words for students. (GVB) #29.3.110

Martı i Artigas, Joan. The Prehistory of Computer Science [in Catalan], Butlletı de la Societat Catalana deMatematiques 15(2) (2000), 37–50. This survey divides the prehistory of computer science into four periods usingthe dates 1452, 1642, and 1880. The “proper historic period” begins in 1970. (GVB) #29.3.111

Martzloff, Jean-Claude. Chinese Mathematical Astronomy, in #29.3.41, pp. 373–407. (GVB) #29.3.112

McCague, Hugh. The Mathematics of Building and Analysing a Medieval Cathedral, in #29.3.91, pp. 167–174.An overview of both the “practical geometry” of the medieval masons and the modern mathematical and statisticalmethods which seek to recover the specific pattern(s) embodied in a given cathedral. The spiritual and symbolicelements in the designs are also discussed. (HG) #29.3.113

McGrath, Gary. See #29.3.100.

McKinzie, Mark; and Tuckey, Curtis. Higher Trigonometry, Hyperreal Numbers, and Euler’s Analy-sis of Infinities, Mathematics Magazine 74 (2001), 339–368. Contains a modern account of Euler’s seriesarguments in Introductio in analysin infinitorum, “sensitively rehabilitated to contemporary tastes for rigor.”(GVB) #29.3.114

McLeod, Mary C.; and Schotch, Peter K. Remarks on the Modal Logic of Henry Bradford Smith, Journal ofPhilosophical Logic 29(6) (2000), 603–615. Smith, a contemporary of C. I. Lewis, took an approach to modallogic that did not lend itself as well to the received “possible worlds” semantics. (GVB) #29.3.115

McMurran, Shawnee. See #29.3.190.


Melville, Duncan J. Third-Millennium Mathematics: A Brief Survey, in #29.3.91, pp. 175–187. A description,restricted geographically to “core Mesopotamia,” of developments in a period which “few except experts study” butin which “abstract numbers” and sexagesimal place-value numeration were introduced and in fact “mathematicscame into being.” (HG) #29.3.116

Melville, Duncan J. Weighing Stones in Ancient Mesopotamia, Historia Mathematica 29 (2002), 1–12. Proposesa procedure for determining the solutions to problems on Old Babylonian mathematical tablet YBC 4652 anddiscusses the underlying pedagogy of the document. (GVB) #29.3.117

Mendelson, E. See #29.3.189.

Mishchenko, A. S. The Hirzebruch Formula: 45 Years of History and the Current State [in Russian], Algebra iAnaliz 12(4) (2000), 16–35; translation in St. Petersburg Mathematical Journal 12(4) (2001), 519–533 This is anexpository paper devoted to the 45-year history and the modern state of the Hirzebruch formula, which gives anexpression for the signature of an oriented manifold in terms of its Pontryagin classes. See the review by EvgeniiV. Troitskii in Mathematical Reviews 2002c:57049. (TBC) #29.3.118

Mlodinow, Leonard. Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace, New York:Free Press, 2001, xii+306 pp. This enjoyably written book gives a history of geometry linked around five particularpeople, with others discussed as appropriate. The five are Euclid (axiomatization), Descartes (use of coordinates),Gauss (non-Euclidean geometries), Einstein (relativity), and Witten (string theory). See the review by J. S. Joel inMathematical Reviews 2002c:01002. (TBC) #29.3.119

Mollin, Richard A. A Brief History of Factoring and Primality Testing B. C. (Before Computers), MathematicsMagazine 75 (2002), 18–28. This survey covers contributions by Eratosthenes, Ibn al-Banna, Fibonacci, Cataldi,Mersenne, Fermat, Euler, Gauss, Landry, Lucas, and Lehmer. (GVB) #29.3.120

Moore, Gregory H. Editing Mathematicians: The Cases of Kurt Godel and Bertrand Russell, in #29.3.91, pp. 188–195. The author raises a number of questions about the editing of collected works of modern (post-1800) mathe-maticians (what should editors aim for? what should they include?), considers some possible answers, and urgesthat editors “adopt a more sophisticated explanatory role” than has been common in the past. (HG) #29.3.121

Moore, Gregory H. Hilbert on the Infinite: The Role of Set Theory in the Evolution of Hilbert’s Thought, HistoriaMathematica 29 (2002), 40–64. Hilbert produced no set-theoretic results, but his advocacy had a profound effecton the new field. (GVB) #29.3.122

Mueller, William. Mathematical Wunderkammern, American Mathematical Monthly 108 (2001), 785–796. Wun-derkammern, or “wonder cabinets,” contained physical representations of mathematical concepts. This paper sur-veys wunderkammern from the 17th to the late 19th century and speculates on the cultural and philosophicalfactors that led to their growth and demise. (GVB) #29.3.123

Muldoon, Martin E. See #29.3.143.

Mushtaq, Q. Introduction: The Mathematicians and Their Heritage, in C. E. Bosworth and M. S. Asimov, eds.,History of Civilizations of Central Asia, vol. IV, Paris: UNESCO, 2000, pp. 177–182. In a few pages seven centuriesof the history of mathematical sciences in the Islamic world are presented. There are inaccuracies in this paper.See the review by Helene Bellosta in Mathematical Reviews 2002c:01015. (TBC) #29.3.124

Naik, Prahallad Chandra. Date of Birth of Samanta Chandra Sekhar, Indian Journal of History of Science 35(2)(2000), 149–160. The date of birth of this renowned traditional Indian astronomer is determined to be December13, 1835. (GVB) #29.3.125

Ne’eman, Yuval. Pythagorean and Platonic Conceptions in XXth Century Physics, in N. Alon, J. Bourgain,A. Connes, M. Gromov, and V. Milman, eds., GAFA 2000, Basel: Birkhauser, 2000, pp. 383–405. The author startswith a characterization of ancient Greek science and identifies five “meta-themes” suggested by the Greeks. Hethen claims that these profound and visionary ideas become prominent in 20th century physics. See the review byDennis Dieks in Mathematical Reviews 2002c:00019. (TBC) #29.3.126

Novikov, Sergey P. Classical and Modern Topology: Topological Phenomena in Real World Physics, in N. Alon,J. Bourgain, A. Connes, M. Gromov, and V. Milman, eds., GAFA 2000, Basel: Birkhauser, 2000, pp. 406–424.


The two main sections, as indicated in the title, contain (1) a history of topology in the second half of the 20thcentury and (2) the author’s work on the boundary between topology and physics. See the review by J. S. Joel inMathematical Reviews 2002c:01043. (TBC) #29.3.127

Orey, David Clark. The Ethnomathematics of the Sioux Tipi and Cone, in #29.3.41, pp. 239–252.(GVB) #29.3.128

Otte, Michael. See #29.3.160.

Ozkan, E. Mehmet. See #29.3.5.

Pagli, Paolo. The Logical Law of Contraposition and Euclid’s Elements [in Italian], Physis 37(1) (2000), 1–19.Contains commentaries on several instances of the appearance of a statement and its contrapositive in the Elements.See the review by Victor V. Pambuccian in Mathematical Reviews 2002a:01008. (HEK) #29.3.129

Pambuccian, Victor V. See #29.3.47, #29.3.51, #29.3.57, #29.3.59, #29.3.129, #29.3.139, and #29.3.187.

Pasles, Paul. Digging for Squares, Math Horizons, April 2002, 17–19. A popular account of the author’s searchfor the magic squares created by Benjamin Franklin. (GVB) #29.3.130

Paul, Siegfried. Die Moskauer Mathematische Schule um N. N. Lusin [The Moscow Mathematical School aroundN. N. Luzin], Bielefeld: B. Kleine Verlag GmbH, 1997, 238 pp. This book contains a description of the growthand development of the Moscow mathematical school, with special reference to the role played by N. N. Luzinand the campaign against him in the summer of 1936. See the review by F. Smithies in Mathematical Reviews2002c:01049. (TBC) #29.3.131

Pedley, T. J. James Lighthill and His Contributions to Fluid Mechanics, in John L. Lumley, Stephen H. Davis, andHelen L. Reed, eds., Annual Review of Fluid Mechanics, Vol. 33, Palo Alto, CA: Annual Reviews, 2001, pp. 1–41.Summarizes the life of Lighthill and his research in acoustics, traffic flow, and biological fluid mechanics andgives a brief description of the work of his thesis students. See the review by Thomas H. Sonar in MathematicalReviews 2002b:01042. (EAM) #29.3.132

Pelletier, Francis Jeffry. Did Frege Believe Frege’s Principle? Journal of Logic, Language and Information 10(1)(2001), 87–114. There are actually two theses known as Frege’s principle. This paper is an investigation into theextent to which Frege really believed them. (GVB) #29.3.133

Pengelley, David. See #29.3.100.

Pepe, Luigi. See #29.3.147.

Perez-Ilzarbe, Paloma. See #29.3.25.

Pesic, Peter. The Validity of Newton’s Lemma 28, Historia Mathematica 28 (2001), 215–219. The validityof this lemma, in Book I of the Principia, was questioned by Derek Whiteside; Pesic argues that Whiteside’scounterexamples would not have been admitted as valid curves by Newton. (GVB) #29.3.134

Piccuti, Ettore. Leonardo Da Pisa e il suo Liber Abaci [in Italian], Proceedings of the International Conference“Bejaıa and Its Region Through the Ages: History, Society, Sciences, Culture,” Bejaıa: Gehimab Edition, 1997,pp. 274–281. In this paper the author tries to determine the influence of Arabian mathematics in Leonardo of Pisa’sLiber Abaci. (DA) #29.3.135

Plofker, Kim. The “Error” in the Indian “Taylor Series Approximation” to the Sine, Historia Mathematica 28(2001), 283–295. Discusses a Sanskrit commentary on a medieval approximation to the sine that resembles aTaylor series that sheds light on its apparent inaccuracy, and emphasizes that the this work was rooted in geometricapproximation rather than notions of calculus or analysis. (GVB) #29.3.136

Poggendorff, Johann Christian. Biographisch–Literarisches Handworterbuch der Exakten Naturwissenschaften[Biographical–Literary Lexicon of the Exact Natural Sciences], Berlin: WILEY-VCH Verlag Berlin GmbH, 2000,6 CD-ROMs, 1277.21. This new electronic edition of the renowned Poggendorff database contains all volumesfrom the first volume (which appeared in 1863) to the current VIII/1. (GVB) #29.3.137


Pogliani, Lionello; and Berberan-Santos, Mario N. Constantin Caratheodory and the Axiomatic Thermody-namics, Journal of Mathematical Chemistry 28(1–3) (2000), 313–324. Axiomatic thermodynamics, a creation ofCaratheodory, centers around certain properties of Pfaffian differential equations. (GVB) #29.3.138

Posy, Carl J. Immediacy and the Birth of Reference in Kant: The Case for Space, in Gila Sher and RichardTieszen, eds., Between Logic and Intuition, Cambridge, UK: Cambridge Univ. Press, 2000, pp. 155–185. The authorshows how the three characteristics Kant assigns to human intuition give rise to his view that the representationof space is pure intuition. See the review by Victor V. Pambuccian in Mathematical Reviews 2002c:01032.(TBC) #29.3.139

Powell, Arthur B.; and Frankenstein, Marilyn. In Memoriam Dirk Jan Struik: Marxist Mathematician, Historianand Educator, For the Learning of Mathematics 21(1) (2001), 40–43. Surveys Struik’s life and his major mathe-matical, historical, and political interests. Includes some anecdotes from the authors’ personal acquaintances withStruik. (PR) #29.3.140

Pritchard, Paul. Metaphysics � 15 and Pre-Euclidean Mathematics, Apeiron 30(1) (1997), 49–62. The authorproposes that Aristotle’s Metaphysics � 15 can be understood as a reference to a pre-Euclidean theory of ratio.See the review by Albert C. Lewis in Mathematical Reviews 2002b:01009. (EAM) #29.3.141

Pulkkinen, Jarmo. Russell and the Neo-Kantians, Studies in History and Philosophy of Science 32A(1) (2001),99–117. Discusses the debate between logicists and neo-Kantian philosophers at the beginning of the 20th century.The author analyzes Russell’s 1949 book (A Critical Exposition of the Philosophy of Leibniz), comparing it toE. Cassirer’s 1902 work (Leibniz System in seinen Wissenschaftlichen Grundlagen) and discusses the neo-Kantiancriticisms of Russell’s definition of natural number. See the review by Hourya Sinaceur in Mathematical Reviews2002b:00011. (EAM) #29.3.142

Puppi, Giampietro. Vito Volterra and the Physics of His Time [in Italian], in International Conference in Memoryof Vito Volterra [in Italian], Rome: Accademia Nazionale dei Lincei, 1992, pp. 257–270. A discussion of some ofVolterra’s work, particularly the periodic motions of the terrestrial pole, electrical discharges in gases, the flux ofmechanical energy, addresses and proposals, and mathematical ecology (species competition, predator–prey) andits consequences (basic dynamics of the laser phenomenon, autocatalytic chemical reactions). See the review byMartin E. Muldoon in Mathematical Reviews 2002a:01032. (HEK) #29.3.143

Puttaswamy, T. K. The Mathematical Accomplishments of Ancient Indian Mathematicians, in #29.3.41,pp. 409–422. (GVB) #29.3.144

Qu, An Jing. Methods for Determining the Intercalary Month in a Chinese Calendar-Making System: A Problemof Probability [in Chinese], Journal of Northwest University 30(6) (2000), 465–469. A study of the three methodsfor intercalating leap months in the Chinese calendar, each of which predicts only a possible position of a leapmonth. (GVB) #29.3.145

Ramırez Rodrıguez, Marıa Eva. Abel’s Study of the Binomial Series [in Spanish], Epsilon 16(3) (2000), 351–375. Abel’s proof of the binomial expansion of (1 + x)µ, where x is a complex number such that |x | < 1 and µ

is an arbitrary complex number, is presented. Cauchy’s fallacious proof of the same result is also presented. Seethe review by G. U. Brauer in Mathematical Reviews 2002c:40006. (TBC) #29.3.146

Rashed, Roshdi. Pierre Fermat et les Debuts Modernes de l’Analyse Diophantienne, Historia Scientiarum 9(1)(1999), 3–16. Distinguishing Fermat’s arithmetic research as belonging to two different traditions—that of Eu-clidean and neo-Pythagorean arithmetic and that of Diophantine analysis—the author focuses on a theorem ofFermat concerning prime numbers and his work in the latter tradition. See the review by Luigi Pepe in MathematicalReviews 2002b:01024. (EAM) #29.3.147

Rav, Yehuda. See #29.3.53.

Rebstock, Ulrich. The Kitab al-Kafı fı Mukhta.sar (al- .hisab) al-Hindı of al- .Sardafı, Zeitschrift fur Geschichte derArabisch-Islamischen Wissenschaften 13 (1999/00), 189–204. A summary and analysis of the arithmetical treatiseof this late 10th-century Yemeni mathematician. Also discusses a 14th-century commentary by al- .Hamilı, whichcontains an iterative procedure for extracting square roots—its earliest occurrence in manuscripts thus far studied.See the review by Jan P. Hogendijk in Mathematical Reviews 2002a:01011. (HEK) #29.3.148


Reid, Miles. Twenty-Five Years of 3-Folds—An Old Person’s View, in Alessio Corti and Miles Reid, eds.,Explicit Birational Geometry of 3-Folds, Cambridge, UK: Cambridge Univ. Press, 2000, pp. 313–343. Treatsdifferent aspects of the birational theory of 3-folds, leading to the development of Mori theory, The authorincludes autobiographical tidbits which give a personal context for the discoveries. See the review by Mark Grossin Mathematical Reviews 2002b:14001. (EAM) #29.3.149

Rice, Adrian. A Gradual Innovation: The Introduction of Cauchian Calculus into Mid-Nineteenth-Century Britain, in #29.3.91, pp. 48–63. The career of Cauchy’s limit-based methods, in a context dominatedby the algebraic approach of Lagrange, “provides an excellent illustration of the predominance of algebraistsover analysts (in the modern sense), and applied over pure, among nineteenth-century British mathematicians.”(HG) #29.3.150

Ritter, James. Egyptian Mathematics, in #29.3.41, pp. 115–136. (GVB) #29.3.151

Rius, Monica. La Alquibla en al-Andalus y al-Magrib al-Aq.sa [The Qibla in Andalus and the Maghrib],Barcelona: Univ. of Barcelona, 2000, 418 pp. This study of the qibla in Andalus and the Maghrib contains acritical edition of the 14th-century treatise Kitab al-Qibla, by Abu‘Alı al-Ma.smudı. (GVB) #29.3.152

Roberts, David Lindsay. E. H. Moore’s Early Twentieth-Century Program for Reform in Mathematics Edu-cation, American Mathematical Monthly 108 (2001), 689–696. E. H. Moore’s failed efforts to improve mathe-matics education centered around the “laboratory method” and might be seen as a forerunner of reform today.(GVB) #29.3.153

Robitaille, Ariane. Can We Learn Something about Combinatorics from Review Journals? in #29.3.91,pp. 196–203. The author tracks the emergence of combinatorics as an independent branch of mathematics byscrutiny of Mathematical Reviews and Zentralblatt fur Mathematik from 1950 to 1980. The clues are changingsystems of classification, numbers of items on combinatorics, and the journals which published those items.(HG) #29.3.154

Robotti, Nadia; and Badino, Massimiliano. Max Planck and the “Constants of Nature,” Annals of Science 58(2)(2001), 137–162. A reconstruction of the process that introduced the constants of nature into the black-bodyradiation law of Planck in 1900, beginning with the constants given by Wien in 1896 and those given by Planckin 1899. The relationship between these three pairs of constants is explored, as well as the impact of Planck’sconsiderations of constants on the formulation of his famous law. (EAM) #29.3.155

Robson, Eleanor. The Uses of Mathematics in Ancient Iraq, 6000–600 BC, in #29.3.41, pp. 93–113.(GVB) #29.3.156

Robson, Eleanor. Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322, Historia Mathemat-ica 28 (2001), 167–206. Robson presents an analysis of this notorious Babylonian tablet that rejects explanationsin terms of trigonometry and generating functions in favor of regular reciprocal pairs. Robson contextualizesthe tablet, “perhaps thereby knocking it off its pedestal” to take its place within a broader study of cuneiformmathematics. (GVB) #29.3.157

Robson, Eleanor. Words and Pictures: New Light on Plimpton 322, American Mathematical Monthly 109 (2002),105–120. This paper, based on an address at the Joint Mathematics Meetings in New Orleans in 2001, arguesfor a respect for cultural context when deciphering contributions of ancient mathematical texts, and presents a“historically, culturally, and linguistically convincing interpretation” of the numbers on this ancient Babyloniantablet. (GVB) #29.3.158

Rouxel, Bernard; and Aıssani, Djamil. The Geometrician Albert Ribaucour in Bougie, Proceedings of the In-ternational Conference “Bejaıa and Its Region Through the Ages: History, Society, Sciences, Culture,” Bejaıa:Gehimab Edition, 1997, pp. 261–268. The object of this paper is to determine the mathematical contribution ofRibaucour during his Algerian stay (in particular, his conflict with Gaston Darboux). (DA) #29.3.159

Rusnock, Paul. Philosophy of Mathematics: Bolzano’s Responses to Kant and Lagrange, Revue d’Histoire desSciences 52(3–4) (1999), 399–427. A discussion of Bolzano’s position on the nature of mathematical proof incontrast to those of Kant and Lagrange. The reviewer in Mathematical Reviews 2002a:01019, Michael Otte,complains that it “is very well informed with respect to Bolzano’s mathematical and logical accomplishments


but transforms his adversaries into mere dummies and does not do justice to the epistemology of mathematics.”(HEK) #29.3.160

Sanchez Valenzuela, Adolfo. A Partial Description of the Development of Differential Geometry in the XXthCentury, and a Biased Look at Its Future [in Spanish], Miscelanea Matematica 32 (2000), 69–102. This is anontechnical overview of the development of differential geometry in the previous century. See the review byClaudio Bartocci in Mathematical Reviews 2002c:01041. (TBC) #29.3.161

Sandl, Marcus. Raumvorstellungen und Erkenntnismodelle im 18. Jahrhundert [Concepts of Space and Modelsof Cognition in the 18th Century], Berichte zue Wissenschaftsgeschichte 23(4) (2000), 419–431. Compares andcontrasts Newton’s and Leibniz’s physical concepts of space, illustrating Leibniz’s less-well-known theory withexamples of 18th century natural history, demography, and economic theory. (GVB) #29.3.162

Sargolini, Federica. Vincenzo Galilei’s Critique of Gioseffo Zarlino’s Numerical Mysticism [in Italian] Nuncius15(2) (2000), 519–550. Explores important issues concerning the methodological approach to musical phenomenaraised in the dispute between the foremost musical theorist of the 16th century and Galileo’s father, a practicalmusician. (EAM) #29.3.163

Sarma, Sreeramula Rajeswara. Sul.tan, Suri and the Astrolabe, Indian Journal of History of Science 35(2) (2000),129–147. The 14th-century chronicle S ırat-i F ıruz Shahı, written during a period of considerable interest in theastrolabe, is analyzed to glean coherent information concerning this astronomical instrument. (GVB) #29.3.164

Sayward, Charles. See #29.3.81.

Schalley, Andrea C. Das Mathematische Weltbild der Maya [The Mathematical Worldview of the Maya],Frankfurt am Main: Peter Lang, 2000, 296 pp. This book is a rich review of current research concerning Mayancalendars and numerical systems, with the necessary references to Maya religion, cosmology and mythology. Thebibliography of 534 titles adds to this attractive book an introduction to a variety of research topics. See the reviewby Ubiratan D’Ambrosio in Mathematical Reviews 2002c:01004. (TBC) #29.3.165

Scharlig, Alain. Compter avec des Cailloux: Le Calcul Elementaire sur l’Abaque chez les Anciens Grecs [Count-ing with Pebbles: Elementary Calculation on the Abacus among the Ancient Greeks], Lausanne: Presses Poly-techniques et Universitaires Romandes, 2001, ii+340 pp. The author presents the results of research by himselfand others into the use of the abacus by the Greeks from 500 to 1 BC. Contains a useful set of references. See thereview by Albert C. Lewis in Mathematical Reviews 2002c:01011. (TBC) #29.3.166

Schlote, Karl-Heinz. See #29.3.22 and #29.3.82.

Schneider, Ivo. See #29.3.188.

Schotch, Peter K. See #29.3.115.

Schubring, Gert. Recent Research on Institutional History of Science and Its Application to Islamic Civilization,in Ekmeleddin Ihsanoglu and Feza Gunergun, eds., Science in Islamic Civilization, Istanbul: Research Centre forIslamic History, Art & Culture, IRCICA, 2000, pp. 19–36. A study of institutions in the history of Islamic scienceand comparison with Western counterparts. The author has himself released this paper restored to its originalversion from the published version due to his disagreement with how the paper was edited. (GVB) #29.3.167

Schubring, Gert. Argand and the Early Work on Graphical Representation: New Sources and Interpretations, inJesper Lutzen, ed., Around Caspar Wessel and the Geometric Representation of Complex Numbers, Copenhagen:Royal Danish Academy of Sciences and Letters, 2001, pp. 125–145. An investigation of some of the works ongraphical representation of complex numbers of mathematicians who worked independently of Wessel, especiallyArgand, Buee, Daviet de Foncenex, Wallis, and Karsten. (GVB) #29.3.168

Schulmann, Robert. See #29.3.50.

Schupp, Franz. See #29.3.104.

Scriba, Christoph. See #29.3.18 and #29.3.19.


Sela, Schlomo. Abraham ibn Ezra’s Scientific Corpus Basic Constituents and General Characterization, ArabicSciences and Philosophy 11(1) (2001), 91–149. Attempts to analyze the texts relevant to judging the importanceof the work of 10th-century mathematician Abu Sahl al-Quhı on centers of gravity. (GVB) #29.3.169

Selin, Helaine; and Sun, Xiaochun, eds. Astronomy across Cultures: The History of Non-Western Astronomy,Dordrecht: Kluwer, 2000, xxiv+655 pp. This book is a series of extended survey articles on specific topics compiledby the editor of the recent Encyclopedia of the History of Science, Technology, and Medicine in Non-WesternCultures. This book has the potential to make the serious study of non-Western astronomy accessible to a wideraudience. The 21 articles are arranged roughly geographically. A theme throughout the book is the link betweenthe sky, nature, and humanity. See the review by Glen R. Van Brummelen in Mathematical Reviews 2002c:01001.(TBC) #29.3.170

Selin, Helaine. See also #29.3.41.

Serre, Jean-Pierre. Exposes de Seminaires (1950–1999), Paris: Societe Mathematique de France, 2001, viii+259pp., 39 . A collection of talks given by Serre; themes include algebraic topology, number theory, Lie groups,algebraic geometry, and modular forms. (GVB) #29.3.171

Serre, Jean-Pierre. See also #29.3.39.

Sesiano, Jacques. Algebra of Leonard of Pisa and Its Influence in Medieval Europe, Proceedings of the In-ternational Conference “Bejaıa and Its Region Through the Ages: History, Society, Sciences, Culture,” Bejaıa:Gehimab Edition, 1997, pp. 282–287. In this article the author presents Leonardo of Pisa’s work, which influencedmathematical research for three centuries. In algebra, Fibonacci considered systems of linear equations and wasthe first to consider the possibility of problems of negative numbers. (DA) #29.3.172

Sesiano, Jacques. Islamic Mathematics, in #29.3.41, pp. 137–165. (GVB) #29.3.173

Shafarevich, I. R. Reminiscences about V. A. Rokhlin [in Russian], in N. N. Ural’tseva, ed., Proceedings ofthe St. Petersburg Mathematical Society, vol. 7 [in Russian], Novosibirsk: Nauchnaya Kniga, 1999, pp. 269–273. Personal accounts of several episodes in the life of V. A. Rokhlin, who was a major contributor to topology,ergodic theory, and real algebraic geometry. See the review by N. V. Ivanov in Mathematical Reviews 2002b:01043.(EAM) #29.3.174

Shank, Michael H., ed. The Scientific Enterprise in Antiquity and the Middle Ages, Chicago: Univ. of ChicagoPress, 2001, 450 pp., hardbound $50, softbound $27. A collection of papers taken from Isis on a wide variety ofscientific topics, many of which are relevant to early history of mathematical astronomy. (GVB) #29.3.175

Shea, William R. See #29.3.207.

Shigeru, Jochi. The Dawn of Wasan (Japanese Mathematics), in #29.3.41, pp. 423–454. (GVB) #29.3.176

Sieg, Wilfried. A New Perspective on Hilbert’s Program [in Italian], Lettera Matematica Pristem 38 (2000),38–45. Despite the failure of Hilbert’s foundational program caused by Godel’s Theorem, some reformulationsallowed the derivation of results concerning the problem of consistency in analysis. (GVB) #29.3.177

Simonson, Shai. See #29.3.99.

Sinaceur, Hourya. See #29.3.142 and #29.3.209.

Siu, Man-Keung. The Pythagorean Theorem Again? Anything New? Cubo 3(2) (2001), 1–9. Various proofs andgeneralizations due to, or adopted by, Pappus, Legendre, the Zhou Bi Suan Jing, Liu Hui, and Thabit ibn Qurra.The emphasis is on “the teaching aspect.” (HG) #29.3.178

Sizer, Walter S. Traditional Mathematics in Pacific Cultures, in #29.3.41, pp. 253–287. (GVB) #29.3.179

Smithies, F. See #29.3.131.

Sonar, Thomas H. See #29.3.132.


Spraggon, Donna I. M. Felix Klein’s Erlanger Programm and Its Influence, in #29.3.91, pp. 64–76. Theauthor examines the possible influence of the “EP” on the “Italian school” of geometry, on Riemannian geometryand the theory of relativity and on the teaching of geometry before about 1920 and concludes that much ofthe credit traditionally given to the EP “has more to do with the reputation of Klein than with the EP itself.”(HG) #29.3.180

Steele, John M. A 3405: An Unusual Astronomical Text from Uruk, Archive for History of Exact Sciences55(2) (2000), 103–135. Demonstrates that the astronomical data on planetary phenomena and lunar eclipses inthis text are consistent with calculation by schemes given in the astronomical cuneiform texts published by OttoNeugebauer. See the review by George Abraham in Mathematical Reviews 2002a:01003. (HEK) #29.3.181

Steele, John M. Eclipse Prediction in Mesopotamia, Archive for History of Exact Sciences 54(5) (2000), 421–454. An account of the various methods apparently used by Mesopotamian astronomers to predict both solar andlunar eclipses. (GVB) #29.3.182

Stefanescu, Doru. See #29.3.33 and #29.3.81.

Stigler, Stephen M. Ancillary History, in Mathista de Gunst, Chris Klaassen, and Aad van der Vaart, eds., Stateof the Art in Probability and Statistics (Leiden, 1999), Beachwood, OH: Institute of Mathematical Statistics, 2001,pp. 555–567. Three examples from ancillary statistics (Laplace and the location parameter problem; Edgeworth,Pearson, and the correlation coefficient; and Galton and contingency tables) are presented and discussed. See thereview by Kun He in Mathematical Reviews 2002c:62001. (TBC) #29.3.183

Stillwell, John. The Continuum Problem, American Mathematical Monthly 109 (2002), 286–297. Describesvarious themes that have developed in the study of the continuum problem in the 20th century and notes that theproblem continues to generate new ideas in set theory. (GVB) #29.3.184

Straume, Eldar. From Kepler’s Problem to the Three-Body Problem and the Trojan Asteroids, Normat 48(3)(2000), 97–114. Describes Lagrange’s assertion of the existence of the Trojan asteroids and a well-known butunsolved problem arising from it. (GVB) #29.3.185

Strikwerda, John C. See #29.3.194.

Sudakov, V. N. The Unrealized Project of V. A. Rokhlin [in Russian], in N. N. Ural’tseva, ed., Proceedings ofthe St. Petersburg Mathematical Society, vol. 7 [in Russian], Novosibirsk: Nauchnaya Kniga, 1999, pp. 274–289.Gives a detailed outline of a planned book (which was never produced) to discuss the evolution of geometricalideas from ancient to modern times. See the review by N. V. Ivanov in Mathematical Reviews 2002b:01044.(EAM) #29.3.186

Sun, Xiaochun. See #29.3.170.

Suppes, Patrick. Finitism in Geometry, Erkenntnis 54(1) (2001), 133–144. In this Festschrift in honour of WilhelmK. Essler on his 60th birthday, the author presents a quantifier-free axiom system for affine geometry. See thereview by Victor V. Pambuccian in Mathematical Reviews 2002b:03024. (EAM) #29.3.187

Sylla, Edith Dudley. Jacob Bernoulli on Analysis, Synthesis, and the Law of Large Numbers, in Michael Otteand Marco Panza, eds., Analysis and Synthesis in Mathematics, Dordrecht: Kluwer, 1997, pp. 79–101. The paperconcerns the cultural history of science. The mathematics in the paper is restricted to a short quotation fromTodhunter’s account of Jakob Bernoulli’s proof of the law of large numbers. See the review by Ivo Schneider inMathematical Reviews 2002c:01027. (TBC) #29.3.188

Tait, W. W. Cantor’s Grundlagen and the Paradoxes of Set Theory, in Gila Sher and Richard Tieszen, eds.,Between Logic and Intuition, Cambridge, UK: Cambridge Univ. Press, 2000, pp. 269–290. An argument for abetter understanding of Cantor’s Grundlagen, one of the principal purposes of which was to explain and justifyhis theory of transfinite numbers. Cantor’s distinction between sets and proper classes did not arise from the set-theoretic paradoxes. See the review by E. Mendelson in Mathematical Reviews 2002a:01020. (HEK) #29.3.189

Tattersall, James; and McMurran, Shawnee. An Interview with Dame Mary L. Cartwright, D.B.E., F.R.S., TheCollege Mathematics Journal 32(4) (2001), 242–254. Interview conducted in person and through correspondence.


Cartwright (1900–1998), a student of G. H. Hardy and E. C. Titchmarsh, made important contributions to thetheory of functions and differential equations. (PWH) #29.3.190

Tazzioli, Rossana. Green’s Function in Some Contributions of 19th Century Mathematicians, Historia Mathe-matica 28 (2001), 232–252. Green’s function, one of a number of direct methods to solve Dirichlet’s problem,appears in the work of Helmholtz, Riemann, Lipschitz, Carl and Franz Neumann, and Betti as a way to solvevarious problems in physics. (GVB) #29.3.191

Thiele, Rudiger. Hilbert and His 24 Problems, in #29.3.91, pp. 1–22. This paper discusses Hilbert’s careerbefore 1900, the background of his famous Paris lecture, the 23 problems there set out, Hilbert’s philosophy ofmathematics, and the (hitherto unpublished) “24th problem,” on simplicity of proofs. (HG) #29.3.192

Thomas, Robert S. D. Mathematics and Fiction: A Pedagogical Comparison, in #29.3.91, pp. 204–208. The authorundertakes an exploration, “which might be useful pedagogically,” of analogies between a (simple) story and atheorem-with-proof in mathematics. Thus each begins with entities (in a story, characters) and their relationships;and narrative consequence in a story corresponds to logical consequence in a proof. (HG) #29.3.193

Thomee, Vidar. From Finite Differences to Finite Elements. A Short History of Numerical Analysis of PartialDifferential Equations, Journal of Computational and Applied Mathematics 128(1–2) (2001), 1–54. Discussesimportant developments in the theory of the ideas of stability and convergence, beginning with the 1928 paperof Courant, Friedrichs, and Lewy. See the review by John C. Strikwerda in Mathematical Reviews 2002b:65003.(EAM) #29.3.194

Torres Alcaraz, Carlos. Mathematical Logic in the XXth Century [in Spanish], Miscelanea Matematica 31(2000), 61–105. An expository paper giving an overview of the development of mathematical logic in the 20thcentury. See the review by Ignacio Angelelli in Mathematical Reviews 2002c:01042. (TBC) #29.3.195

Treder, H. See #29.3.50.

Troitskii, Evgenii V. See #29.3.118.

Tsarev, Serguei P. Integrability of Equations of Hydrodynamic Type from the End of the 19th to the End ofthe 20th Century, in H. W. Braden and I. M. Krichever, eds., Integrability: The Seiberg–Witten and WhithamEquations, Amsterdam: Gordon & Breach, 2000, pp. 251–265. This is a review paper on the modern theory ofintegrable systems of hydrodynamic type with the form u j

t = ∑nj=1 vi

j (u)u jx , i = 1, . . . , n. See the review by

Youjin Zhang in Mathematical Reviews 2002c:37001. (TBC) #29.3.196

Tuckey, Curtis. See #29.3.114.

Turnbull, David. Rationality and the Disunity of the Sciences, in #29.3.41, pp. 37–54. (GVB) #29.3.197

Van Brummelen, Glen R. Sin (1◦): From Ptolemy to al-Kashı, in #29.3.91, pp. 209–215. Ptolemy found, bya geometric argument, upper and lower bounds for sin (1◦). Al-Kashı improved this estimate tremendously byworking with sines of differences of angles rather than the angles themselves before turning to his more famousiterative method. (HG) #29.3.198

Van Brummelen, Glen R. See also #29.3.170.

Van Kley, Edwin J. East and West, in #29.3.41, pp. 23–35. (GVB) #29.3.199

Verelst, Karin. See #29.3.44.

Verran, Helen. Logics and Mathematics: Challenges Arising in Working across Cultures, in #29.3.41, pp. 55–78.(GVB) #29.3.200

Verran, Helen. Aboriginal Australian Mathematics: Disparate Mathematics of Land Ownership, in #29.3.41,pp. 289–311. (GVB) #29.3.201

Verran, Helen. Accounting Mathematics in West Africa: Some Stories of Yoruba Number, in #29.3.41,pp. 345–371. (GVB) #29.3.202


Vilain, Christiane. La Question du “Centre d’Oscillation” de 1660 a 1690, Physis 37(1) (2000), 21–51. Discussesthe contributions of Huygens, Mariotte, Mersenne, de Catelan, Deschasles, Jacob Bernoulli, de l’Hospital, andothers in the latter half of the 17th century to the development of ideas associated with the compound pendulum.See the review by Llewelyn G. Chambers in Mathematical Reviews 2002b:01025. (EAM) #29.3.203

Villemoes, Lars F. See #29.3.85.

Vogt, Annette. Von Petersburg nach Moskau: Zur Geschichte der Russisch-Sowjetischen Mathematik zwischen1850 und 1975, in Aloys Henning and Jutta Petersdorf, eds., Wissenschaftsgeschichte in Osteuropa, Wiesbaden:Harrassowitz, 1998, pp. 165–183. This survey of the development of Russian mathematics divides naturally intothe periods before and after V. A. Steklov, thanks to whose influence Russian mathematicians enjoyed a degree offreedom. (HEK) #29.3.204

Volodarskiı, A. I. See #29.3.72.

Von Neumann, John. Invariant Measures, Providence, RI: American Mathematical Society, 1999, xvi+134pp., $39. A written version of von Neumann’s 1940–1941 lectures beginning with general measure theory andproceeding to Haar measure and some of its generalizations. See the review by R. B. Burckel in MathematicalReviews 2002b:28012. (EAM) #29.3.205

Vucinich, Alexander. Soviet Mathematics and Dialectics in the Post-Stalin Era: New Horizons, Historia Mathe-matica 29 (2002), 13–39. The weakening of ideological interference in Soviet scientific work during the post-Stalinperiod allowed several branches of mathematics to participate in the struggle against Stalinist dogma. However,dialectical materialism remained the only officially recognized philosophy in the USSR. (GVB) #29.3.206

Weber, Stephanie. See #29.3.104.

Weinrich, Klaus. Die Lichtbrechung in den Theorien von Descartes und Fermat [The Refraction of Light in theTheories of Descartes and Fermat], Sudhoffs Archiv 1998, suppl. 40, 1–171. An examination of the discussionbetween Descartes and Fermat after the law of refraction was published by Descartes in 1637. Although they hadstarted from different postulates, both discovered the same law. See the review by William R. Shea in MathematicalReviews 2002b:01026. (EAM) #29.3.207

White, Alvin M. See #29.3.6.

Wood, Leigh N. Communicating Mathematics across Culture and Time, in #29.3.41, pp. 1–12.(GVB) #29.3.208

Zach, Richard. Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic, Bul-letin of Symbolic Logic 5(3) (1999), 331–366. The paper focuses on unpublished lecture notes and other manuscriptsby Hilbert and Bernays dating back to the period 1917–1923 aiming at showing that these manuscripts containvaluable results on propositional logic. See the review by Hourya Sinaceur in Mathematical Reviews 2002c:03003.(TBC) #29.3.209

Zerrouki, Mokhtadir. Some Mathematical Algorithms Used in Sciences of the Heritages [in Arabic], Proceed-ings of the International Conference “Bejaıa and Its Region Through the Ages: History, Society, Sciences, Cul-ture,” Bejaıa: Gehimab Edition, 1997, pp. 237–251. The author presents two specialists in science in medievalBougie: al-Qurashi (d. 1184) and al-Uqbani (d. 1408). He introduces mathematical algorithms used by al-Qurashiwhich reach us through the commentary of al-Uqbani, who lived in Bougie at the end of the 14th century.(DA) #29.3.210

Zhang, Youjin. See #29.3.196.

Zitarelli, David E. Towering Figures in American Mathematics, 1890–1950, American Mathematical Monthly108 (2001), 606–635. The remarkable growth of American mathematics in this time period is interspersed withdiscussions of E. H. Moore, Oswald Veblen, George David Birkhoff, R. L. Moore, Norbert Weiner, and MarshallStone. (GVB) #29.3.211

ABSTRACTS - COnnecting REpositoriesHMAT 29 ABSTRACTS 341 Agazzi, Evandro. The Relation of...

Documents

Transcript of ABSTRACTS - COnnecting REpositoriesHMAT 29 ABSTRACTS 341 Agazzi, Evandro. The Relation of...