PII: 0315-0860(90)90089-V HISTORIA MATHEMATICA 17 (1990), 81-96 ABSTRACTS Editedby DAVID E. ZITARELLI 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 Prof. David E. Zitarelli, Department of Mathematics, Temple University, Philadelphia, PA 19122, U.S.A. Readers are invited to send reprints, autoabstracts, corrections, additions, and notices of publications that have been overlooked. Be sure to include complete bibliographic informa- tion, as well as transliteration and translation for non-European languages. We need volun- teers willing to cover one or more journals for this department. Readers interested in receiving a computer-readable version of the abstracts, beginning with #11.3.1, are invited to write to the Abstracts Editor. 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 12, Number 1, are num- bered: 12.1.1, 12.1.2, 12.1.3, etc. For reviews and abstracts published in Volumes 1 through 13 there is 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 Victor Albis (Bogota), Joe Albree (Montgomery, AL), Thomas Bartlow (Villanova, PA), Gary Brown (Collegeville, MN), Louise Grinstein (Brooklyn, NY), Susanne Hensel (Jena), James J. Kaput (North Dartmouth, MA), Robert E. Kennedy (Warrensburg, MO), Albert C. Lewis (Hamilton), Peter Ross (Santa Clara, CA), and David E. Zitarelli. ADELE, GAIL H. 1989. When did Euclid live? An answer plus a short history of geometry. The Mathematics Teacher 82(6), 460-463. A classroom module based on a chronological table of the history of GEOMETRY. It omits the projective geometry of Desargues and Poncelet. (DEZ) #17.1.1 ALCOLEA BANEGAS, JESUS. 1988. Arend Heyting. Mathesis (M&co) 4, 189-220. Succinct presen- tation of AREND HEYTING’S work on INTUITIONISM. BROUWER. Heyting’s BIBLIOGRAPHY. WA) #17.1.2 ANDERSON, J. M. 1988. ELISHA NETANYAHU (1912-1986). Bulletin of the London Mathematical Society 20,613-618. Netanyahu was a native of Warsaw, and his family emigrated to Palestine in 1920. He was influenced by MICHAEL FEKTE at the Hebrew University in Jerusalem in the 1930s and his early mathematical career was concerned with COMPLEX ANALYSIS, in particular, Dirichlet series. This was interrupted by his service during World War II and in the early years of the state of Israel. “In a very real sense he was the creator of the Mathematics Department at the TECHNION” [in Haifa]. The “second flowering” of Netanyahu’s mathematical career involved his work on UNIVALENT FUNC- TIONS. The list of Netanyahu’s 24 published papers omits his three papers in Hebrew; there is also a photo. (JA) #17.1.3 ANON. 1987. Academician Leonid Vitalevich Kantorovich (on the 75th anniversary of his birth). [In Russian] Optimizatsiya 40(57), 5-6. Brief biography Of LEONID VITALEVICH KANTOROVICH. Other 81 0316~0860/90 $3.00 Copyright 0 1990 by Academic Press, Inc. All rights of reproduction in any form reserved. 82 ABSTRACTS HM 17 articles in this volume of the journal dealing with his work are: D. A. Vladimirov, “The works of V. I. Kantorovich in the descriptive theory of sets and functions” (pp. 7-l 1. 159); L. T. Petrova. “Com- mentary on the works of L. V. Kantorovich on large-block programming” (pp. 12-16, 159); Ya. 1. Fet. “The investigations of L. V. Kantorovich in the area of computer architecture” (pp. 17-25, 159); and A. G. Kusaraev and S. S. Kutateladze, “The contribution of L. V. Kantorovich to the theory of ordered vector spaces” (pp. 26-39, 159). PHOTOGRAPH. (DEZ) #17.1.4 ANON. 1988. Jan Mikusinski: 3 April 1913-27 July 1987. Studiu Muthemafica 89(l), ii-xi. Brief obituary of JAN MIKUSINSKI. Bibliography of 26 books and 149 papers. PHOTOGRAPH. (DEZ) #17.1.5 ANON. 1988. Professor Raj Chandra Bose. Journal of Geometry 33(1-2) l-2. Brief obituary of RAJ CHANDRA BOSE. PHOTOGRAPH. (DEZ) #17.1.6 ANON. 1988. Recipients of the Korean Mathematical Society PRIZES for 1987. [In Korean] Bulletin of the Korean Mathematical Society 25(l), 162-163. Brief biographies of two of the winners, CHIN MYUNG CH~NG and JONGSIK KIM. PHOTOGRAPHS. (DEZ) #17.1.7 ARNOLD, V. I. 1989. A topological proof for the transcendence of the ABELIAN INTEGRAL of I. NEWTON’S Principia mathematics. Istoriko-matematicheskie Zssledovaniya 31, 7-17. [In Russian] In this paper, which was presented at the 1987 Moscow Conference on the 300th Anniversary of Principia mathematico, a modern proof is given of an integral which appeared in Principia Lemma 18. Newton’s proof is translated into Russian by A. N. Krylov and analyzed from a modern viewpoint. The author also generalizes the Newtonian theorem to the multidimensional case of smooth hypersurfaces in R”. W-U #17.1.8 BELLER, WALTER. 1988. Sicologia y matem8ticas: Convergencias y divergencias (PSYCHOLOGY and mathematics: Convergences and divergences). Muthesis (M&ico) 4, 393-412. (VA) #17.1.9 BINDER, CHRISTA. 1989. II. Gsterreichisches Symposium zur Geschichte der Mathematik. Hisro- ria Mathematics 16(2), 166. Announcement of a week-long symposium in October 1989 on the history of mathematics. (DEZ) #17.1.10 BOROWCZYK, JACQUES. 1989. Universite d’ete d’histoire des mathematiques, 28 aotit au 2 septem- bre 1988. Hisroria Mathematics 16(2), 167-168. A list of the speakers and the titles of their talks from five conferences, six presentations, and numerous workshops at the Third Interdisciplinary History of Mathematics Meeting, held at La Rochelle from August 28 to September 2, 1988. (DEZ) #17.1.11 BOWEN, K. C. 1988. A mathematician’s journey through operational research. Mathematical Pro- gramming 42(l) (Ser. B), 33-40. The author reminisces on how, as a pure mathematician in 1940, he gradually became involved in OPERATIONS RESEARCH. He also discusses his relationship with MARTIN BERLE. (DEZ) #17.1.12 BROWDER, FELIX E. 1989. Stone age of mathematics at the midway. The Mathematical Zntelli- gencer 11(3), 22-24. A tribute to MARSHALL STONE’S chairmanship at the University of Chicago. See also #17.1.125. (DEZ) #17.1.13 BROWN, MORTON. 1987. The mathematical work of R. H. Bing. Topology Proceedings 12(l), l-25. A discussion of the work of R. H. BING on the Kline sphere characterization problem, the pseudoarc, homogeneity, metrization, convex metrics, 3-manifolds, and decomposition spaces. TOPOLOGY. (DEZ) #17.1.14 BULICHEVA, S. See #17.1.102. CERUZZI, PAUL. 1989. Electronics technology and computer science 1940-1975: A coevolution. Annals of the History of Computing U(4), 257-275. An analysis of the continuous interplay between ELECTRONIC ENGINEERING and COMPUTER SCIENCE since 1940. Electronic engineering dominated the HM 17 ABSTRACTS 83 activities from 1940 to 1955 but computer science dominated from 1955 to 1975. More recently both electronic engineers and computer scientists see their work as “the management of complexity.” (LW #17.1.15 COLEMAN, A. JOHN. 1989. The greatest mathematical paper of all time. The Mafhemarical Intelli- gencer 11(3), 29-38. Coleman exceeds even Thomas Hawkins in his praise of the work of WILHELM KILLING. He chooses a paper by Killing as the greatest paper of all time, explains the main ideas and results in it, and describes its subsequent effects on E. CARTAN, COXETER, KAC, and MOODY. PHOTO- GRAPHS. (DEZ) #17.1.16 DALE, A. I. 1989. THOMAS BAYES: A memorial. The Mathematical Intelligencer 11(3), 18-19. The family vault in Bunhill Fields, where Thomas Bayes is buried, was restored in 1969 but “is once again in a sorry state.” (DEZ) #17.1.17 D’AMBROSIO, UBIRATAN. 1989. A research program and a course in the history of mathematics: ETHNOMATHEMATICS. Historia Marhematica 16(3), 285-287. The term ethnomathematics is defined, and a program for teaching a non-Eurocentric, ethnomathematical history of mathematics course is described. (DEZ) #17.1.18 DEBARNOT, MARIE-TH~%sE. See #17.1.69. DEBNATH, LOKENATH. 1987. Srinivasa Ramanujan (1887-1920). A centennial tribute. Znrerna- tional Journal of Mathematical Education in Science and Technology 18(6), 821-861. A tribute to SRINIVASA RAMANUJAN on his 100th birthday. The first part gives an account of Ramanujan’s life. The remainder is a synopsis of his contributions and their importance. See Mathematical Reviews 89g:O1048 for a review by Bruce Berndt, who states that “much of this material is incorrect or misleading.” (PR) #17.1.19 DEL PINO ARABOLAZA, PILAR, AND VALERA, MANUEL. 1988. Analisis estadistico y sociometrico de la production matematica espariola a travts de la Revista Matemritica Hispanoamericana (Statisti- cal and sociometric analysis of the Spanish mathematical production through the Reuista Maremdtica Hispanoamericana). LLULL l&263-284. Evolution of Spanish mathematical production from 1919 to 1936 through the study of papers that appeared in Rev&a Matemdtica Hispanoamericana, from a bibliometrical viewpoint. SPANISH MATH. (VA) #17.1.20 DEMIDOV, S. S. 1988. Der philosophische Kontext der Herausbildung der Moskauer funktionen- theoretischen Schule. NTM-Schrijtenreihe fiir Geschichte der Naturwissenschafren, Technik und Medizin 25, 25-3 1. The philosophical context of the development of the MOSCOW SCHOOL OF FUNC- TION THEORY. D. F. EGOROV; N. N. LUZIN; N. G. BUGAEV. (ACL) #17.1.21 DEMIDOV, S. S., PARSHIN A. N., AND POLOVINKIN, S. M. 1989. On the correspondence of N. N. LUZIN with P. A. FLORENSKI. Isroriko-matematicheskie Issledovaniya 31, 116-190. [In Russian] This continues the account, started in Vol. 30, of the source materials for the history of the Moscow SCHOOL in function theory found in the Florenski archives. An overview of the history of the Moscow school is followed by an analysis of the historical relevance and the content of the correspondence from 1904 to 1922. The correspondence for these years is published on pages 125-190. (SH) #17.1.22 DUTT, SUKOMAL. 1988. Bibhuti Bhusan Datta (1888-1958) or Swami Vidyaranya. Pp. 3-15 in #17.1.45. Biography of the Indian historian of mathematics, BIBHUTI BHUSAN DATTA, who is known for his work on ancient HINDU contributions, especially the decimal number system. At age 45 Datta left his professorship at Calcutta University for the ascetic life of Sannyas, where he was known as VIDYARANYA. There is a bibliography of Datta’s publications in the history of mathematics. INDIAN MATHEMATICS. PHOTOGRAPH. (DEZ) #17.1.23 EMERSON, ROGER. 1988. SIR ROBERT SIBBALD, Kt, the Royal Society of Scotland and the origins of the Scottish enlightenment. Annals qfScience 45(l), 41-72. The author claims that there existed in 84 ABSTRACTS HM 17 fate 17th century SCOTLAND a sizeabfe virtuoso community whose leaders were abreast of European developments in philosophy, history, and science. There is little mention of this community’s knowf- edge of mathematical developments. (GB) #17.1.24 ERMOLAEVA, N. S. 1989. New biographical material on N. N. LUZIN. Isforiko-matematicheskie Issledovaniya 31, 191-272. [In Russian] An introduction to newly revealed correspondence between Luzin and A. N. KRYLOV between 1928 and 1942. The fetters are preserved in the archives of the USSR Academy of Sciences in Moscow and in its Leningrad division. The author provides not only biographical information but also a history of the mathematics concerned, especially of the Moscow SCHOOL in the theory of functions of real variables. The author also reconstructs the beginning of the relationship between Luzin and Kryfov. Following the article, on pages 203-272, the correspondence is reproduced along with additional documents: (1) Luzin’s travel report for the 1928 International Congress in Bologna which he presented to the USSR Academy of Sciences in 1930; (2) Luzin’s notes on a 1931 paper by A. Kaz; (3) a 1942 letter from Luzin to the Remembrance Jubilee Commission for Newton’s 300th anniversary. (SH) #17.1.25 ERMOLAEVA, N. S. 1989. The dissertation of G. W. KOLOSOV and its evaluation by V. A. STEKLOV. Istoriko-matematicheskie Issledovaniya 31,52-74. [In Russian] Kofosov’s “On the appfica- tion of the theory of complex variables to the plane cases of the mathematical theory of elasticity,” is considered for its theory of functions and the fact that not all of Kofosov’s ideas have been further developed later by other researchers. Further, several circumstances relating to Kofosov’s disserta- tion defense in 1911 at Petersburg University are clarified on the basis of manuscripts of the two referees (Stekfov and Bobylev) and of two fetters from Kolosov to Stekfov. These concern the differ- ences of opinion during the defense which, though they have been known, have not hitherto been explained in the historical literature. (SH) #f7.1.26 EVANS, JAMES. 1987. On the origin of the Ptofemaic star catafogue. I. Journal ofrhe History of Astronomy 18(3), 155-172. Provides evidence to dispute earlier accounts that claim that PTOLEMY borrowed HIPPARCHUS’S star catafogue instead of establishing the catafogue himself in Almagesr 7-8. GREEK ASTRONOMY. Mathematical Reviews 89h:01003. (DEZ) #17.1.27 EVANS, JAMES. 1987. On the origin of the Ptofemaic star catafogue. II. Journal of the History of Asfronomy 18(4), 233-278. A continuation of #17.1.27. Suggests various solutions to account for a shift of 40’ in PTOLEMY'S star longitudes, thus providing further evidence of Ptolemy’s paternity of the star catafogue in the Almagest. Mathematical Reviews 89h:01004. (DEZ) #17.1.28 FAUVEL, JOHN. 1989. Platonic rhetoric in distance learning: How Robert Record taught the home learner. For the Learning of Mathematics 9(l), 2-6. This article analyzes the pedagogic style of ROBERT RECORD, who was one of the best and most successful textbook writers of all time. His geometry was the reverse of Euclid, and his arithmetic provided the foundation for the practical mathematics of navigation and science of Elizabethan times. (JJK) #17.1.29 FENTON, P. C. 1989. An extremaf problem in Harriet’s mathematics. Historia Marhematica 16(2), 154-163. This note provides an elementary geometrical proof to refute the suggestion that THOMAS HARRIOT needed to use INFINITESIMALS to solve an optimization problem. (DEZ) #17.1.30 FLEMING, WENDELL, AND KLEE, VICTOR. 1989. EDWARD JAMES MCSHANE 1904-1989. Notices of the American Marhematical Society 36(7), 828-830. Brief biography with an indication of Mc- Shane’s contributions to the cafcufus of variations, integration theory, control theory, and stochastic calculus. (DEZ) #17.1.31 FLETCHER, COLIN R. 1989. Fermat’s theorem. Hisroria Mathemarica 16(2), 149-153. Arguments are given to support the claim that the usual interpretation regarding FRENICLE'S challenge to FERMAT to find a perfect number with at feast 20 digits is flawed. (DEZ) #17.1.32 FOLKERTS, MENSO, AND KNOBLOCH, EBERHARD. 1989. Christoph J. Scriba-60 Jahre. Historia HM 17 ABSTRACTS 85 Muthematica 16(3), 207-212. Biographical comments on the historian of mathematics, CHRISTOPH J. SCRIBA, with a bibliography of his works. (DEZ) #17.1.33 FOLTA, JAROSLAV. 1988. Some remarks on the history of numerical analysis especially in the area of Prague. LLULL 11, 217-233. The concept of NUMERICAL ANALYSIS in Goldstine’s History of numerical analysis from the 16th century through the 19th cenfury is contrasted with that of computa- tional mathematics of the Babylonians, the Egyptians, BRAHE, WITTICH, BORGI, and KEPLER as related to ASTRONOMY. (VA) #17.1.34 FREGUGLIA, PAOLO. 1989. Study centre for scientific thought between 1500 and 1600. Historia Mathematics 16(2), 170. Report of a seminar held at Perugia University on “Moments of the mathe- matical culture between the 16th and 17th centuries, ” including a list of speakers and the titles of their lectures. (DEZ) #17.1.35 GOLDSTEIN, BERNARD R. 1986. Levi ben Gerson’s theory of planetary distances. Centaurus 29(4), 272-313. Presents LEVI’S theory as found in Chapters 130 and 131 in his Astronomy. A translation of the two chapters is included. ASTRONOMY. (TB) #17.1.36 GORDAN, PAUL. 1987. Vorlesungen iiber Invariantenrheorie. Erster Band: Determinanten. Zweiter Band: Bin&e Formen. New York: Chelsea. Vol. I: xii + 201 pp.; Vol. II: xii + 360 pp. $49.95. A new printing in one book of the second edition of two classic volumes that were first issued in 188.5 and 1887, Lectures on invariant theory. Vol. I: Determinants. Vol. II: Binary forms, edited by Georg Kerschensteiner. The book contains an elaboration of two series of lectures by PAUL GORDAN, the first of which dealt with the theory of DETERMINANTS and the second with INVARIANTS OF BINARY FORMS. See the review by Jean Dieudonne in Mathematical Reviews 89g:O1034. (DEZ) #17.1.37 GOWER, B. 1987. Planets and PROBABILITY: Daniel Bernoulli on the inclinations of the planetary orbits. Studies in History and Philosophy of Science B(4), 441-454. A review Of DANIEL BERNOULLI’S different approaches to the problem of the inclination of planes of the planetary orbits with the plane of the solar equator. Also looks at criticisms by JEAN D’ALEMBERT and ISAAC TODHUNTER of these approaches. ASTRONOMY. (GB) #17.1.38 GRAEF [FERNANDEZ], CARLOS. 1988. Espacio matemfitico y espacio ffsico (Mathematical space and physical space). Mathesis (ML;xico) 4,327-353. In Cuadernos de1 seminario de problemas cient@ cos yfilos$icos. Cuadernos y Suplementos. Primera Serie, Mtxico: Universidad National AutBnoma de Mtxico. 1956, l-25. (VA) #17.1.39 GRAEF [FERNANDEZ], CARLOS. 1988. Mi justa con ALBERT EINSTEIN (My tilt with Albert Ein- stein). Mathesis (MPxico) 4, 413-422. Spanish version from The American Scientist 44 (1956), 204- 211. (VA) #17.1.40 GRIGORYAN, A. T. 1988. Lev Davidovich Landau (on the 80th anniversary of his birth). [In Russian] Voprosy Istorii Estestvoznaniya i Tekhniki 1988(l), 116-119. A brief biography of LEV DAVIDOVICH LANDAU. (DEZ) #17.1.41 GRUENBERG, K. W. 1988. KURT AUGUST HIRSCH (1906-1986). Bulletin of the London Mathemati- cal Society 20, 350-358. Hirsch was first influenced by I. SCHUR at the University of Berlin, 1925- 1930, but began his career as a journalist. He fled the Nazis in 1934 and settled in Cambridge where he came under the influence of PHILIP HALL and earned a second PhD. His mathematical interests were in GROUP THEORY. “His most impressive achievement” was his leadership in the 1950s in transform- ing the department of pure mathematics of the UNIVERSITY OF LONDON into “an active, internation- ally respected centre for research in ALGEBRA, without being in overall charge of the department. . . ” Furthermore, “internationally, the mathematical community owes him a debt of gratitude for the immense amount of work he devoted to the translation of Russian mathematics” over the 40 years from the end of World War II until his death. Unfortunately, a complete list of these translations is not included. There is a list of Hirsch’s 20 papers and there are two photos. (JA) #17.1.42 86 ABSTRACTS HM 17 GUPTA, R. C. 1988. Kurt Vogel (1888-1985). the veteran German historian of mathematics. Pp. 16- 20 in #17.1.45. Brief biography of KURT VOGEL, who, among other things, was responsible for founding the Institute for the History of Science in Munich. Also included is some of Vogel’s corre- spondence with the INDIAN mathematicians B. B. DATTA (see also #17.1.23) and A. N. SINGH. PHOTOGRAPH. (DEZ) #17.1.43 GUPTA, R. C. 1988. On values of a from the Bible. Pp. 51-58 in #17.1.45. An examination of several explanations of the biblical quotation “a molten sea, ten cubits from the one brim to the other; it was round all about; . . and a line of thirty cubits did compass it round about.” PI. (DEZ) #17.1.44 GUPTA, R. C. (Ed.) 1988. Tenth anniversary volume. Gn#a-Bhrirati lO(l-4). The Datta-Vogel centenary issue celebrating 10 years as the official Bulletin of the Indian Society for History of Mathematics. Articles by Sukomal Dutt, R. C. Gupta, Parmeshwar Jha, J. N. Kapur, Kripanath Sinha, and B. L. van der Waerden are abstracted separately. (DEZ) #17.1.45 GUPTA, R. C. 1988. Tombstone mathematics. Pp. 69-74 in #17.1.45. Brief discussions of 12 mathe- matical EPITAPHS ranging from Archimedes to Sierpinski. (DEZ) #17.1.46 HALD, A. 1986. Galileo’s statistical analysis of astronomical observations. Internafional Statisti- cal Review 54(2), 21 I-220. A statistical analysis carried out by GALILEO in 1632 contains the rudiments of a theory for comparing hypotheses by means of the sums of the absolute deviations of the observa- tions from the hypothetical values. STATISTICS. (DEZ) #17.1.47 HANSEN, VAGN LUNDSGAARD. 1988. From geometry to topology. Normat 36(2), 48-60, 90. [In Danish with a summary in English] A discussion of the development of TOPOLOGY from its origins up to the Brouwer fixed point theorem and the Borsuk-Ulam theorem. Mathematical Reviews 89h:OlO42. (DEZ) #17.1.48 HEINZMANN, GERHARD. 1988. Poincare et la philosophie des mathematiques. Cahiers du SPmi- naire d’tlistoire des MathPmafiques, Univ. Paris VI 9, 99-121. A discussion of POINCARR and his PHILOSOPHY of mathematics, which he called “pragmatism,” a synthesis of his intuitionistic require- ments followed by a descriptive analysis of the mathematical constructions. See Mathematical Re- views 89h:OlO43 for a list of corrections to the references in the paper. (DEZ) #17.1.49 HENTSCHEL, KLAUS. 1988. Die Korrespondenz Duhem-Mach: Zur Modellbeladenheit von Wis- senschaftsgeschichte. Annals of Science 45(l), 73-91. The preserved part of the hitherto unpublished correspondence between PIERRE DUHEM and ERNST MACH, kept in the Archives de I’Acadtmie des Sciences, Paris, and in the Ernst Mach institute of the Fraunhofer Society, Freiburg im Breisgau, is documented and commented upon. (GB) #17.1.50 HEWITT, EDWIN. 1986. What Pave1 Sergeevich Aleksandrov meant to me. [In Russian] Uspekhi Matematicheskikh Nauk 41(6)(252), 205-208. Hewitt’s remembrances of his personal contact with PAVEL SERGEEVICH ALEKSANDROV, and the influence exerted on him by Aleksandrov’s books. Trans- lated into English in Russian Marhematical Surveys 41(6), 247-250. Zentralblatr 621:O1010. (DEZ) #17.1.51 HEYDE, C. C.. AND SENETA, E. (Eds.) 1988. Bicentennial history issue. The Australian Journal of Statistics 30 (Special Vol. B), l-130. Contents: E. Seneta, “Silhouettes in early Australian STATIS- TICS” (pp. 2-22); C. C. Heyde, “Official statistics in the late colonial period leading on to the work of the first Commonwealth Statistician, G. KNIBBS” (pp. 23-43); John D. Kerr, “Introductionof statisti- cal design and analysis by the Queensland Bureau of Sugar Experiment Stations” (pp. 44-53); J. B. F. Field, F. E. Speed, and J. M. Williams, “Biometrics in the CSIR: 1930-1940” (pp. 54-76); David B. Duncan, “Australian BIOMETRY and multiple comparisons” (pp. 77-98); H. 0. Lancaster, “Statistical Society of New South Wales” (pp. 99-109); E. J. Williams, “A survey of experimental design in AUSTRALIA” (pp. 110-130). (DEZ) #17.1.52 HM 17 ABSTRACTS 87 HOGENDIJK, JAN P. 1984. al-Ktihi’s construction of an equilateral pentagon in a given square. Zeitschrift fiir Geschichte der Arab&h-Zslamischen Wissenschaften 1,9-54. AL-KOtii was a mathe- matician and astronomer working in Iran in the 10th century. He was a leading figure in a revival and continuation of Greek GEOMETRY in the MEDIEVAL ISLAMIC world. His method for constructing an equilateral pentagon in a square involves the intersection of hyperbolas and the solution of a quartic equation. CONIC SECTIONS. ALGEBRA. Mathematical Reviews 89g:O1011. (DEZ) #17.1.53 HORMIG~N, MARIANO. See #17.1.91. HOUZEL, CHRISTIAN. 1989. Colloque d’histoire des mathtmatiques sous le patronage de la SociCte MathCmatique de France. Hisforia Mathematics 16(2), 169. A list of the speakers and the titles of their talks at the Conference on the History of ALGEBRAIC EQUATIONS held June 17-22, 1985, in Marseille. (DEZ) #17.1.54 HOYNINGEN-HUENE, P. 1987. Context of discovery and context ofjustification. Studies in History and Philosophy of Science l&4), 501-515. The author argues that the traditional argument between “positivist” philosophers and “historicist” philosophers can be clarified by focusing on the distinction between the “context of discovery” versus the “context of justification.” PHILOSOPHY OF MATHE- MATICS. (GB) #17.1.55 HUGHES, BARNABAS. 1989. The arithmetical triangle of Jordanus de Nemore. Historia Mathe- matica 16(3), 213-223. An analysis of Book IX, Proposition 70, of De arithmetica by JORDANUS DE NEMORE. Three illustrations suggest a knowledge of PASCAL’S TRIANGLE. Appendices include an English translation and a critical edition of the material. (DEZ) #17.1.56 HUNTER, M. 1988. Promoting the new science: HENRY OLDENBURG and the early Royal Society. History of Science X(2), 165-181. Analyzes why Oldenburg came to be so dominant in his correspon- dences with early members of the ROYAL SOCIETY. (GB) #17.1.57 ILLY, J. 1989. Einstein teaches Lorentz, Lorentz teaches Einstein: Their collaboration in general relativity, 1912-1920. Archive for History of Exact Sciences 39(3), 247-289. This paper discusses the cooperative work of EINSTEIN and LORENTZ in developing the theory of general RELATIVITY between 1913 and 1920. (GB) #17.1.58 INDORATO, LUIGI, AND NASTASI, PIETRO. 1989. The 1740 resolution of the Fermat-Descartes controversy. Historia Mathematics 16(2), 137-148. An examination of a booklet from 1740 by PIETRO Dr MARTINO disputing the prevailing view that FERMAT’S law of refraction was obtained by DES- CARTES from an opposite hypothesis. There is also an explanation of the reason why Di Martin0 stated his minimum principle only for OPTICS, unlike the similar principle discovered by MAUPERTUIS and extending to DYNAMICS. ISAAC NEWTON. ITALY. (DEZ) #17.1.59 IOSIFESCU, MARIUS. 1986. Obituary notice: Octav Oniciscu, 1892-1983. International Sratistical Review 54(l), 97-108. Brief biography of OCTAV ONICISCU, a description of his major contributions, and lists of his 222 papers and 32 books. STATISTICS. (DEZ) #17.1.60 JANUSZ, GERALD J. 1988. Irving Reiner 1924-1986. Illinois Journal of Mathematics 32(3), 315-328. A biography of IRVING REINER, a discussion of his work, a list of his students, and a bibliography. (DEZ) #17.1.61 JHA, PARMESHWAR. 1987. Mm. Hemtirigada Thtikura and his work “RBhiipar%gapaiiji.” The Math- ematics Education 21(Z), 38-43. HEM.&&GADA TH.%KURA was the grandson of a king whose family ruled MithilH for four centuries. The work, whose title means “table of eclipses,” gives a list of predicted lunar and solar eclipses from 1620 to 2708. ASTRONOMY. Mathematical Reviews 89g:OlOl4. (DW #17.1.62 88 ABSTRACTS HM 17 JHA, PARMESHWAR. 1988. Study of history of mathematics in Bihar. Pp. 59-63 in #17.1.45. A description of research activity in the history of mathematics that has taken place in Bihar, INDIA. It includes biographical comments about several of the present researchers. (DEZ) #17.1.63 JONES, F. BURTON. 1987. R. H. Bing. Topology Proceedings 12(l), 181-186. Some personal remi- niscences of R. H. BING. TOPOLOGY. (DEZ) #17.1.64 KAPUR, J. N. 1988. A brief history of mathematics education in India. Pp. 31-39 in #17.1.45. Eight periods in the MATHEMATICS EDUCATION in INDIA are discussed: ancient India (up to the 15th century), medieval India (16th and 17th centuries), the transition period (18th century), early British period (1780-1834), pre-university period (1835-1857), post-university 19th century (1857-1900), pre- independence 20th century (1900-1947), and post-independence 20th century (1947- ). CD=) #17.1.65 KAUFMANN-B~HLER, WALTER. 1987. Gaufl: Eine biogruphische Studie. Berlin/Heidelberg: Springer Verlag. viii + 191 pp. DM 56. A German translation of Gauss: A biographical study. This edition of a biography of GAUSS contains some corrections and “alters some historical explanations that can be omitted for an edition intended for a German-speaking reader.” Reviewed by Karin Reich in Historic Mathematics 16(1989), 178-179. See Muthematica/ Reviews 82j:O1066 for a review of the English original. (DEZ) #17.1.66 KAUNZNER, WOLFGANG. 1987. ijber Charakteristika in der mittelalterlichen abendllndischen Mathematik. Mathematische Semesterberichte 34(2), 143-186. The characteristics of MEDIEVAL Oc- CIDENTAL mathematics are described in three periods. In the 13th and 14th centuries the primary concern was practical problems, even though the material appeared to be strongly theoreticized; between 1450 and 1550 the theoretical direction dominated in symbolic ALGEBRA; the 1600s again witnessed the dominance of the practical side. Zentralblart 638:01004. (DEZ) #17.1.67 KEIDING, NIELS. 1987. The method of expected number of deaths, 1796-1886-1986. international Statistical Review 55(l), I-20. The expected number of deaths was calculated in 18th century ACTU- ARIAL MATHEMATICS but the method seems to have been forgotten, and was reinvented in connection with 19th century studies of geographical and occupational variations of mortality. STATISTICS. (DEZ) #17.1.68 KENNEDY, EDWARD S., AND DEBARNOT, MARIE-TH~R~SE. 1984. Two mappings proposed by Biruni. Zeitschriftfir Geschichte der Arabisch-lslamischen Wissenschaften 1, 145-147. Two ways of mapping a hemisphere upon a plane by AL-BIRLJNI. (DEZ) #17.1.69 KERSCHENSTEINER, GEORG. See #17.1.37. KILMISTER, C. W. 1988. J. T. COMBRIDGE (1897?-1986). Bulletin of the London Mathematical Society 20, 156-158. Combridge was a student of MATHEMATICAL PHYSICS. The major intellectual influence in his life was Sir ARTHUR EDDINGTON, with whom he carried on an important scientific correspondence from the end of World War I until 1936. His major scientific contributions were two: “Notes on RELATIVITY ,” a survey of the most important literature of the 1920s and 1930s in three volumes, now in the archives of King’s College, London; and, a bibliography of general relativity covering the same time period and published in a limited edition in 1965. In 1937, he moved into the administration of King’s College, LONDON. He was president of the MATHEMATICAL ASSOCIATION in l%l-62 and wrote a history of the Association in 1971, apparently never published. There is a photo. (JAI #17.1.70 KLEE, VICTOR. See #17.1.31. KLEINER, ISRAEL. 1989. Evolution of the function concept: A brief survey. The Cokge Mat&mat- its Journal 20(4), 282-300. After a glimpse of precalculus notions, the paper considers the 18th and early 19th century view of a FUNCTION as a formula or a geometric curve, DIRICHLET’S definition in terms of an arbitrary correspondence, the study of various pathological examples, BAIRE class&a- HM 17 ABSTRACTS 89 tion, the controversy relating to the use of the axiom of choice, L2 functions in functional analysis, distributions, and category theory. (DEZ) #17.1.71 KNOBLOCH, EBEIUIARD. 1989. Analogie und mathematisches Denken. Berichte zur Wissen- schafisgeschichte 12, 35-47. ANALOGICAL THINKING in mathematics, especially in the works of KEPLER, WALLIS, LEIBNIZ, EULER, and LAPLACE. (ACL) #17.1.72 KNOBLOCH, EBERHARD. See #17.1.33. KNORR, WILBUR. 1985. Archimedes and the pseudo-Euclidean Catoptrics: Early stages in the ancient geometric theory of mirrors. Archives Znternationales d’Histoire des Sciences 35(114-l IS), 28-105. Part 1 supports the viewpoint that the work Catoptrics on the reflections of light was written by THEON of Alexandria and not by EUCLID. The connection with ARCHIMEDES is explained. Part 2 discusses the correspondences between Catoptrics and other works on OPTICS by DAMIANUS, PTOLEMY, HERO, and DIOCLES in relation to the dating question. Appendix I excludes Damianus. Appendix II discusses Ptolemy’s authorship of the Optics ascribed to him. ANCIENT GREECE. Mathematical Reviews 89g:OlOOS. (DEZ) #17.1.73 KOBLITZ, ANN HIBNER. 1988. Science, women and the Russian intelligentsia: The generation of the 1860s. Isis 79(297), 208-227. Discusses how the 1860s in Russian history offered greater opportuni- ties for WOMEN in science and medicine. RUSSIA. (GB) #17.1.74 LAM, LAY-Y• NG, AND SHEN, KANGSHEN. 1989. Methods of solving linear equations in traditional CHINA. Historia Mathematics 16(2), 107-122. A survey of the methods used by ancient Chinese mathematicians to solve problems that today can be solved by the modem methods of linear equations. The ROD NUMERAL notation encapsulates the complexity of the underlying concept. ALGEBRA. SI- MULTANEOUS EQUATIONS. (DEZ) #17.1.75 LANCASTER, H. 0. 1986. A bibliography of statistical bibliographies: An eighteenth list. Interna- tional Statistical Review 54(l), 109-l 14. Another list of bibliographies in STATISTICS. The 13th list contained national bibliographies [49(2), 177-1831 while the 14th listed biographies [50(2), 195-2171. (DEZ) #17.1.76 LARROYO, FRANCISCO. 1988. Filosofia de las matemdticas (Philosophy of mathematics). Mexico: Editorial Pomia. MATH PHILOSOPHY. (VA) #17.1.77 LAUGWITZ, D. 1987. Hidden lemmas in the early history of INFINITE SERIES. Aequatianes Mathe- maticae 34(2-3), 264-276. Certain results are put into the language of infinitesimals (as in NONSTAN- DARD ANALYSIS) and then claimed to be implicit in the work of EULER, POISSON, and CAUCHY. Mathematical Reviews 89g:O1031. (DEZ) #17.1.78 LAUGWITZ, D. 1989. Definite values of infinite sums: Aspects of the foundations of infinitesimal analysis around 1820. Archive for History of Exact Sciences 39(3), 197-245. Usually the reorganization of ANALYSIS during the 19th century is attributed to the textbooks of CAUCHY. The foundational changes, the author claims, are not just a result of teaching obligations but also a result of the study of convergent and divergent SERIES. The convergent series studied by EULER are first reviewed, followed by a discussion of Cauchy’s banning of divergent series, and finally a discussion of the need for divergent series in FOURIER ANALYSIS and its applications to partial differential equations of mathe- matical physics. (GB) #17.1.79 Ldvu, TOI~Y. 1987. Figures de l’infini: Les mattmatiques au miroir des cultures. Paris: Edition du Seuil. 279 pp. Paperbound. F 99. Reviewed by Karen Hunger Parshall in Isis 79(1988), 325-326. The author wishes to unify the various “faces of the infinite.” According to Parshall, Levy has produced an eminently readable and engaging book on an ever-tantalizing subject. INFINITY. (GB) #17.1.80 LINTON, MATTHEW. 1988. BABYLONIAN TRIPLES. Bulletin: The Institute of Mathematics and Its Applications 24(3-4), 37-41. Brief discussion of Plimpton 322. See also Historia Mathematics 8(1981), 90 ABSTRACTS HM 17 277-318, in which .I. Friberg came to the same conclusions. Mathematical Reviews 89h:01002. (DEZ) #17.1.81 LIU, DUN. 1989. International symposium for the commemoration of MEI WENDING and the CHI- NESE third annual meeting on the history of mathematics. Historia Mathematics 16(3), 281-282. A list of the 21 speakers, and the titles of their talks, from a symposium held November 1-5, 1988, in Mei’s hometown of Xuanzhou. (DEZ) #17.1.82 LLOMBART PALET, Jose. 1987. Ciencia y libertad: El papel de1 cient@co ante la independencia americana (Science andfreedom: The role of the scientist in the presence of American Independence). Cuadernos Galileo de Historia de la Ciencia, 7. Centro de Estudios Hismricos. Consejo Superior de Investigaciones Cientificas. Madrid. 350 pp. (VA) #17.1.83 LOZANO, JUAN MANUEL. 1988. Carlos Graef Fernandez. Mathesis (Mexico) 4,309-3 10. Biograph- ical sketch of the Mexican physicist and mathematician C. GRAEF. MEXICO. (VA) #17.1.84 MAEYAMA, Y. 1988. The Keplerian and mean motions: A geometric study. Archivefor History of Exact Sciences 38(4), 365-383. Mathematical derivation of the point from which Keplerian motion of a planet appears most regular to an observer. The author seeks to keep “historical statements to a necessary minimum” and has attained a minimum of one, in the penultimate sentence of the paper. ASTRONOMY. (TB) #17.1.85 MAINZER, KLAUS. 1988. Symmetrien der Natur: Ein Handbuch zur Natur- und Wissenschaftsphi- losophie. Berlin/New York: de Gruyter. xi + 739 pp. Illustrated. Bibliography. Index. Hardbound DM 365 (SYMMETRY in nature: A handbook for natural philosophy and philosophy of science). A compre- hensive historical account of symmetry in science, philosophy, and art. The mathematical topics include Galois theory, Lie groups, representation theory, and Hilbert spaces. (ACL) #17.1.86 MANCOSLJ, PAOLO. 1989. The metaphysics of the CALCULUS: A foundational debate in the Paris Academy of Sciences, 1700-1706. Historia Murhematica 16(3), 224-248. A sketch of L’H~PITAL’S Analyse des infinimentpetifs. A description of the debate on the logical admissibility of the differential calculus in the Parisian Academy of Sciences from 1700 to 1706. The most outspoken adversary for the finitist faction was MICHEL ROLLE. FOUNDATIONS. INFINITESIMALS. (DEZ) #17.1.87 MARCHISOTTO, ELENA ANNE. 1989. Mario Pieri: His contributions to the foundations and teaching of GEOMETRY. Historia Mathematics 16(3), 287-288. A discussion of the work and influence of MARIO PIERI, a member of PEANO’S school of Italian geometers. An appeal is made for additional information on Pieri’s influence. (DEZ) #17.1.88 MEDVEDEV, F. A. 1989. The HORN ANGLE in the works of NEWTON. Zstoriko-matematicheskie Issledovaniya 31, 18-37. [In Russian] Applications are looked at in Methodus differentialis and in Principia mathematics. On the basis of two extracts from these texts the author analyzes Newton’s treatment of the infinitely small from the standpoint of NON-STANDARD ANALYSIS. (SH) #17.1.89 MEHRTENS, HERBERT. 1989. The Gleichschaltung of mathematical societies in Nazi Germany. The Mathematical Zntelligencer 11(3), 48-60. A translation by Victoria M. Kingsbury of the article “Die ‘Gleichschaltung’ der mathematischen Gesellschaften im nationalsoziahstischen Deutschland,” which appeared in 1985. It is a report on how three MATHEMATICAL SOCIETIES were brought into line with Nazi ideology. The roles played by some pivotal people are discussed: LUDWIG BIEBERBACH, WILHELMBLASCHKE, WILHELM S~SS,GEORGHAMEL, andLunw~~PnA~~~~.Theconclusioncon- tams an analysis of the histories of the three organizations. GERMAN MATHEMATICS. PHOTOGRAPHS. (DEZ) #17.1.90 MILLAN GASCA, ANA. 1987. El matemtitico Julio Rey Pastor (The mathematician Julio Rey Pas- tor). LogroAo: Instituto de Estudios Riojanos. 105 pp. Foreword by Mariano Hormigon. The life and works ofthe SPANISH MATHEMATICIAN JULIO REY PASTOR. (VA) #17.1.91 HM 17 ABSTRACTS 91 MILLS, A. A. 1988. The mercury clock of the Libros del Saber. Annals of Science 45(4), 329-344. Translation of the section of the Libros de1 Saber de Asrronomia dealing with a mercury clock, preceded by an introduction and followed by a description of a model constructed by the author. ASTRONOMY. (TB) #17.1.92 MILTON, J. R. 1987. INDUCTION before Hume. The British Journal for the Philosophy of Science 38(l), 49-74. This paper demonstrates that in the centuries before DAVID HUME virtually everyone was affected by doubts about the reliability of inductive inferences. The last two sections of the paper criticize both Ian Hacking’s and the author’s own explanations of the emergence of the modem problem of induction. Mathematical Reviews 89g:OlO32. (DEZ) #17.1.93 MITCHELL, CHARLES E. 1989. HENRY WADSWORTH LONGFELLOW, poet extraordinaire. The Mathematics Teacher 82(5), 378-379. Five problems written by this American poet attest to his interest in mathematics. (DEZ) #17.1.94 MONASTIRSKI, M. I. 1989. The FIELDS MEDALLISTS. Istoriko-matematicheskie Issledovaniya 31, 88-115. [In Russian] After a short account of its history, the author takes up the conditions under which the medal is awarded, the method of selection and the conferral. The members of the Fields committee from 1950 to 1986 and the medallists from 1936 to 1986 are introduced. In the second part of the article the author gives summary descriptions of the medallists’ work. (SH) #17.1.95 MONNA, A. F. 1988. Marcel Brelot (1903-1987) hommage posthume. [In French] Nieuw Archief voor Wiskunde (4) 6(1-2) 63-68. A homage to MARCEL BRELOT and his contributions to POTENTIAL THEORY. The author recalls his relationship with Brelot beginning in the 1930s. (DEZ) #17.1.96 MOLLER, CLAUS. 1986. Zum 100. Geburtstag von Hermann Weyl. Jahresbericht der Deutschen Mathematiker-Vereinigung @J(4), 159-189. On the 100th anniversary of the birth of HERMANN WEYL. Describes the historical background, mathematical content, physical motivation, and applications of Weyl’s work. Also includes the philosophical context and implications. Mathematical Reviews 89h:OlO77. (DEZ) #17.1.97 NASTASI, PIETRO. See #17.1.59. NEWING, ANGELA. 1988/1989. The life and work of H. E. Dudeney. Mathematical Spectrum 21(2), 37-44. A popular account of H. E. DUDENEY’S contributions to mathematics, particularly recreational mathematics. In his day Dudeney was known as “The Puzzle King.” Includes some biographical information. (PR) #17.1.98 ORTIZ, EDUARDO L. 1988. Una alianza para la ciencia: Las relaciones cientificas entre Argentina y Espana a principios de este siglo (An alliance for science: Scientific relations between SPAIN and ARGENTINA at the beginning of this century). LLULL 11, 263-284. (VA) #17.1.99 PALTER, R. 1987. Saving Newton’s text: Documents, readers and the ways of the world. Studies in History and Philosophy of Science U(4), 385-439. A discussion of ISAAC NEWTON’S De Gravitatione. In this work, Newton criticizes DESCARTES’ formulation of physics and definition of motion. Palter raises the following questions about this criticism: (i) why is Descartes the sole target of Newton’s criticism; (ii) who if anyone influenced this criticism; (iii) how closely does the natural philosophy of De Gravitatione resemble that of Newton’s later writings; and (iv) how closely does Newton’s physics compare with modem physics? (GB) #17.1.100 PARSHALL, KAREN. 1988. The art of ALGEBRA from AL-K~XOWARIZMI to VIBTE: A study in the natural selection of ideas. History of Science 26(2), 129-164. The “natural selection of ideas” is an approach to the study of the historical and evolutionary development of mathematical ideas that may include a mathematician’s false starts, ill conceived techniques, and imperfectly formed theories. The author argues that the development of algebra from Al-Khowarizmi to Vi&e provides a good “test case” for this model of the natural selection of ideas. (GB) #17.1.101 92 ABSTRACTS HM 17 PARSHIN, A. N. See #17.1.22. PETROVA, S. S., AND BULICHEVA, M. G. 1989. On the history of NEWTON’S POLYGONAL METHOD. Istoriko-matematicheskie Issledouaniya 31, 38-51. [In Russian] Three matters are taken up. First is the view, represented by Yushkevich, that Newton did not consider the question of the number of developments of an implicit function in the neighborhood of the point x = 0. Second is Chebotarev’s objection that the term “Newton’s diagram” would not be appropriate for the method since Newton himself did not use a polygon but rather only drew a straight line in the diagram. And the third is the position that the analytical representation of the polygonal method is almost exclusiveIy tied to the name of LAGRANGE, although D. M. Sinzov has already indicated an analytical approach to the question in Newton. The authors base their review on Newton’s manuscripts published by D. T. Whiteside in 1971 and in particular on the incomplete work of 1684 on series. (SH) #17.1.102 Prcurrr, ETTORE. 1989. Pour l’histoire des sept premiers nombres parfaits. Historia Mathematics 16(2), 123-136. The history of the first seven PERFECT NUMBERS. Two manuscripts from 1458 and 1460 by ALLIEVO DEL VAIAIO contain the fifth and sixth perfect numbers, respectively. The criteria fol- lowed by PIETRO CATALDI are also explained. NUMBER THEORY. See also #17.1.32. (DEZ) #17.1.103 PLACKETT, R. L. 1988. Data analysis before 17.50. International Staristical Review 56(2), 181-195. The focus is on nonstatistical DATA ANALYSIS in pneumatics, sound, and physiology during the period 1650-1750. STATISTICS. (DEZ) #17.1.104 POLOVINKIN, S. M. See #17.1.22. REY PASTOR, JULIO. 1988. Julio Rey Pastor. Selecta. Madrid: Edition of the Real Acad. Cie. Exact. Fis. Nat. Fundacion Banco Exterior. 724 pp. Comments by Sixto Rios, Luis A. Santalo, and Ernest0 Garcia Camarero. A selection of REY PASTOR’S publications on Analysis, Algebra, Geometry, and Topology. SPANISH MATH. (VA) #17.1.105 RoDRfGuEz CONSUEGRA, FRANCISCO. 1988. Bertrand Russell, 1900-1913: Los principios de /a matemdtica (parte 1) (Bertrand Russell, 1900-1913: The principles of mathemafics (Part 1). Mathesis (M&co) 4, 355-392. The last of three papers dealing with the genesis of BERTRAND RUSSELL’S “Principles.” PEANO. CANTOR. (VA) #17.1.106 RODRIGUEZ CONSUEGRA, FRANCISCO. 1988. Elementos logicistas en la obra de Peano y su escuela (Logicist elements in Peano’s work and his school). Mathesis (Mexico) 4, 221-299. MATH LOGIC. FOUNDATIONS. PEANO. (VA) #17.1.107 ROERO, C. S. 1989. Giomate di storia della matematica. Historia Mathematics 16(2), 171-172. Report from an international symposium held September 8-12, 1988, in Cetraro (Cosenza), Italy, dealing with the birth and first developments of CALCULUS, and the achievements of modem mathe- matics beginning with the last decades of the 19th century. A list of speakers and the titles of their lectures is included. (DEZ) #17.1.108 ROSE, H. E. 1988. R. L. GOODSTEIN (1912-1985). Bulletin of the London Mathematical Society 20, 159-166. Goodstein was “greatly influenced by LUDWIG WITTGENSTEIN,” and he “was the first person whose main interests were in mathematical LOGIC to hold a chair in a British university.” To be more specific, his interests included RECURSIVE FUNCTIONS, FOUNDATIONS, and the PHILOSOPHY OF MATHEMATICS. In addition to being a member of the faculty, Goodstein held several administrative positions at the University of LEICESTER, 1948-1977. Also, he was quite active in the MATHEMATICAL ASSOCIATION, serving as editor of the Mathematical Gazette, 1956-1962, and as president of the Association, 1975-1976. Included is a list of 12 of Goodstein’s research students, a list of his 11 books and 132 papers and notes, and a photo. (JA) #17.1.109 HM 17 ABSTRACTS 93 Ross, GEORGE. 1989. Lagrange conference. Historia Mathematics X(2), 174-175. Report of a one- day conference held at King’s College, London, to mark the 200th anniversary of LAGRANGE’S Mb- chanique analitique. (DEZ) #17.1.110 Rowe, David E. 1989. Symposium on the history of modern mathematics. Historia Mathematics 16(3), 271-280. Abstracts of 29 papers, about half of which deal with the interface between pure and applied mathematics, from a symposium held June 20-24, 1988, at Vassar College. (DEZ) #17.1.111 SALIBA, GEORGE. 1986. The determination of new planetary parameters at the Maragha Observa- tory. Centaurus 29(4), 249-271. Analysis of the determination of Jupiter’s eccentricity according to the Ptolemaic model, using observations of Yahya b. Abi al-Shukr al-MAormmt in his 13th~century text halkhis al-majisti. There is also a brief comment on Maghribi’s use of a clock. ASTRONOMY. (TB) #17.1.112 SCANLAN, MICHAEL J. 1988. Beltrami’s model and the independence of the parallel postulate. History and Philosophy of Logic 9(l), 13-34. A treatment of NON-EUCLIDEAN GEOMETRY in which BELTRAMI’S original model is contrasted with its later presentation that occurred after the shift in attitude toward the axiomatic method in the 1890s. LOGIC. Mathematical Reviews 89h:01037. (DEZ) #17.1.113 SENETA, E. See #17.1.52. SHEN, KANGSHEN. 1988. Historical development of the Chinese remainder theorem. Archive for History of Exact Sciences 38(4), 285-305. Discusses the appearance of problems on simultaneous congruences, and their solution methods, in China, Japan, India and Europe, from ancient Chinese calendrical reckoning to Gauss’ Disquisitiones Arithmeticae. ALGEBRA. (TB) #17.1.114 SHEN, KANGSHEN. See #17.1.75. SHERRY, D. 1987. The wake of Berkeley’s Analyst: Rigor Mathematicae? Studies in History and Philosophy of Science W(4), 455-480. Questions the traditional view that BERKELEY’S Analyst im- pugned the foundations of the newborn CALCULUS and spurred mathematicians to situate their edifice more securely. Instead, the author reexamines the Analyst’s criticisms both in the context of Berke- ley’s philosophy and the development of the calculus. The author argues that there is some of Berke- ley’s “idealism” that is more congenial to Newton’s approach to the calculus. (GB) #17.1.115 SHEYNIN, 0. B. 1989. Letters from A. M. LYAPUNOV to K. A. ANDREEV. Zstoriko-matemati- cheskie Zssledouaniya 31,306-313. [In Russian] Six letters from the archives at Lomonossov Univer- sity in Moscow are published and commented upon. (SH) #17.1.116 SHIELDS, ALLEN. 1989. BANACH ALGEBRAS, 1939-1989. The Mathematical Zntelligencer 11(3), 15-17. A discussion of some contributions of I. M. GELFAND to FUNCTIONAL ANALYSIS, including his collaboration with D. A. RAIKOV and G. E. SHILOV. (DEZ) #17.1.117 SHIMURA, GORO. 1989. YUTAKA TANIYAMA and his time: Very personal reflections. Bulletin ofthe London Mathematical Society 21, 186-196. In his tragically short life, Yutaka Taniyama (1927-1958) was “one of the most brilliant and pioneering minds of the time” (the middle 1950s) and “the moral support of many of those who came into mathematical contact with him” at the UNIVERSITY OF TOKYO. This affectionate and intimate memoir also recounts the start of Taniyama’s promising career (ALGEBRAIC NUMBERS). There are two photos and a list of Taniyama’s five papers and two books (with G. Shimura). (JA) #17.1.118 SIKIC, ZVONIMIR. 1986. Joseph Louis Lagrange (on the 250th anniversary of his birth). Matematika (Zagreb) #(4), 47-50. A brief treatment of the influence of JOSEPH LOUIS LAGRANGE on French mathematics. FRANCE. (DEZ) #17.1.119 94 ABSTRACTS HM 17 SIMSON, DANIEL. 1988. In memoriam. Journal of Pure and Applied Algebra 52(1-2), 76. Obituary of ROMAN KIELPIASKI (1939-1987). ALGEBRA. (DEZ) #17.1.120 SINGH, PARMANAND. 1987. “Ratna Matijusa,” a Jain work on Sanskrit prosody and binomial coefficients. The Mathematics Education 21(2), 44-50. Written about 800 A.D., this work of an un- known author contains two rules for the formation of BINOMIAL COEFFICIENTS. PERMUTATIONS. Mathematical Reviews 89gOlOl5. (DEZ) #17.1.121 SINGH, SUKHJIT. 1987. Publications of R. H. BING classified by the year. Topology Proceedings 12(l), 27-37. A list of 115 publications and one preprint from 1943 to 1986. TOPOLOGY. (DEZ) #17.1.122 SINHA, KRIPANATH. 1988. Vyaktaganitadhyaya of SrIpati’s SiddhrintaSekhara. Pp. 40-50 in #17.1.45. An English translation of, with an introduction to, SRIPATI’S SIDDHxNTA$EKHARA, a major work on ASTRONOMY written during the period 1039-1056 A.D. The 13th chapter, titled vyakta- ganitadhyaya, contains 55 verses, some of which deal with SERIES and MENSURATION. INDIAN MATH- EMATICS. (DEZ) #17.1.123 STIGLER, STEPHEN M. 1988. A look backward on the occasion of the centenary of the JASA. Journal of the American Statistical Association 83(403), 583-587. A discussion of the history of this PROFESSIONAL ORGANIZATION, including extracts from the first two volumes of JASA. (DEZ) #17.1.124 STONE, MARSHALL H. 1989. Reminiscences of mathematics at Chicago. The Mathematical Zntelli- gencer 11(3), 20-25. MARSHALL STONE served as the Chairman of the Mathematics Department at the University of Chicago for 7 years. Here he discusses his drastic revision of the curriculum. See also #17.1.13 for an accompanying commentary. AMERICAN MATHEMATICS. (DEZ) #17.1.125 STRUIK, D. J. 1988. Dirk Jan Struik. NTM-Schriftenreihe fir Geschichte der Naturwissenschaften, Technik und Medizin 25, 5-23. Interview with David E. Rowe covering aspects of Struik’s life and work. (ACL) #17.1.126 SWETZ, FRANK J. 1989. Using problems from the history of mathematics in classroom instruction. The Muthematics Teacher 82(5), 370-377. There are several sets of problems for students to solve that interested early mathematicians. The problems are drawn from different time periods of China, Egypt, Babylonia, India, Europe, and America. EDUCATION. (DEZ) #17.1.127 TYRRELL, J. A. 1989. PATRICK Du VAL (1903-1987). Bulletin of the London Mathematical Society 21,93-99. Du Val was a student of H. F. BAKER in ALGEBRAIC GEOMETRY, and he also was influenced by FEDERIGO ENRIQUES and other Italian geometers of the 1930s. His most important mathematical contributions were concerned with ALGEBRAIC SURFACES. His book (1973) “is the best source, in English, for the geometric applications of ELLIPTIC FUNCTIONS.” He made many geometric models, some of which are still to be seen at University College, London. There are two photos and a list of 60 of Du Val’s publications, but omitted are his works published in Turkish while he was on the faculty of the University of Istanbul. (JA) #17.1.128 VALERA, MANUEL. See #17.1.20. VAN DEN DRIES, Lou. 1988. Alfred Tarski’s elimination theory for real closed fields. The Journal of Symbolic Logic 53(l), 7-19. A description of the history of some of ALFRED TARSKI’S contributions to LOGIC. Mathematical Reviews 89h:OlO40. (DEZ) #17.1.129 VAN DER WAERDEN, B. L. 1987. The astronomical system of the Persian tables, II. Centaurus M(3), 197-211. A continuation of the paper entitled “Das Astronomische System der Persischen Tafeln I” that appeared in Centaurus W(l%S), l-28. In that first part, 16 horoscopes recorded by the HM 17 ABSTRACTS 95 Arabian astrologer IBU HIBINTA were analyzed. The aim was to reconstruct the astronomical theory underlying the tables which were used to compute the horoscopes. In the present continuation, the author wishes to compare the lunar longitudes presented in the horoscopes with those computed by means of the Midnight System. PERSIA. ASTRONOMY. (GB) #17.1.130 VAN DER WAERDEN, B. L. 1988. A summary of Roger Billard’s L’Astronomie indienne. Pp. 21-30 in #17.1.45. ROGER BILLARD’S book Indian astronomy [In French] sheds light on INDIAN ASTRONOMY by its method of dating astronomical theorems. (DEZ) #17.1.131 VAN DER WAERDEN, B. L. 1988. Die Astronomie der Griechen. Eine Einfiihrung. Dannstadt: Wissenschaftliche Buchgesellschaft. xi + 315 pp. Illustrated. Paperback. The author intends this to be a less mathematical treatment than 0. Neugebauer’s A history of ancient mathematical astronomy (1975). He emphasizes, for example, the observations upon which the mathematics is based. The work includes an argument that the heliocentric theory of Aristarchos of Samos played a much greater role in scientific GREEK ASTRONOMY than has been hitherto assumed. (ACL) #17.1.132 VIZGIN, V. P. 1988. Die Rolle der Mathematik bei der Aufnahme der Relativitltstheorie und der Quantenmechanik in Russland und in der U.d.S.S.R. NTM-Schriftenreihe fiir Geschichte der Naturwissenschaften, Technik und Medizin 25, 33-42 (The role of mathematics in the acceptance of RELATIVITY THEORY and QUANTUM MECHANICS in RUSSIA and the U.S.S.R.) (ACL) #17.1.133 VIZGIN, V. P. 1989. The role of mathematics in the acceptance of fundamental physical theories (in the case of relativity theory and quantum mechanics in Russia and in the U.S.S.R.). Istoriko-mate- maticheskie Zssfedouaniya 31,75-87. [In Russian] This study points out the greatly increased ROLE OF MATHEMATICS IN PHYSICS, with its new structures, which moved into prominence in the first third of the 20th century. This new mathematics essentially played no role in the classical theories which were tied to national mathematical traditions. The author’s goal is to show that, in the case being consid- ered, the “mathematical canal” for the acceptance of the scientific revolution was of substantial, if not decisive, significance. (SH) #17.1.134 WANG, YUAN. 1985. Obituary. Graphs and Combinatorics l(3), 205-206. LUO-GENG HUA (1910- 1984). GRAPH THEORY. (DEZ) #17.1.135 WHITE, MICHAEL J. 1988. On continuity: Aristotle versus TOPOLOGY. History and Philosophy of Logic 9(l), l-12. An analogy between ARISTOTLE’S idea of “continuity” and topological notions of continuum. Mathematical Reviews 89g:O1007. (DEZ) #17.1.136 WHYBURN, LUCILLE. 1987. R. H. Bing 1949-50. Topology Proceedings 12(l), 177-180. Some reminiscences and comments about R. H. BING at the University of Virginia in 1949-1950. TOPOLOGY. (DEZ) #17.1.137 WILLIAMS, GURNEY, III. 1989. The master of math. Omni 11(S), 58-64. Was RAMANUJAN reli- gious? This article, otherwise a standard biographical sketch, answers “No.” (REK) #17.1.138 WILSON, ROBIN. 1989. Mathematics in the Low Countries. The Mathematical Zntelligencer 11(3), 80. Stamps honoring SIMON STEVIN, JOHANN DE WITT, and CHRISTIAAN HUYGENS. (DEZ) #17.1.139 Wu, WEN-TSUN. 1987. Recent studies of the history of Chinese mathematics. In Proceedings of the International Congress of Mathematicians, Vol. 2, pp. 1657-1667. Providence, RI: American Mathematical Society. A panoramic view of various results of recent historical research on ancient CHINESE MATHEMATICS. The major topics include problems concerning integers, GEOMETRY, and ALGEBRA. Mathematical Reviews 89h:OlOO8. (DEZ) #17.1.140 YUSHKEVICH, A. P. 1989. On the history of the scientific relationships between mathematicians in the USSR and France (on the election of S. N. BERNSTEIN, I. M. VINOGRADOV, and M. A. LAVREN- 96 ABSTRACTS HM 17 TIEV to the Paris Academy of Sciences). fstoriko-matematicheskie Issledouaniya 31, 273-305. (In Russian] The evaluative reports held at the archives of the Paris Academy on these three mathemati- cians are transcribed with a commentary. (SH) #17.1.141 ZHMUD, LEONID. 1989. Pythagoras as a mathematician. Historia Mathematics 16(3), 249-268. An examination of the reliability of the evidence concerning PYTHAGORAS’S mathematical studies, and the IogicaI establishment of his contributions. DEDUCTIVE PROOF. (DEZ) #17.1.142