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Historia Mathematica 38 (2011) 429–452www.elsevier.com/locate/yhmat

Abstracts

Duncan J. Melville, Editor

Laura Martini and Kim Plofker, Assistant Editors

0315-08

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General

Clark, Kathleen M. Connecting local history, ancient history, and mathematics: TheEustis Elementary School pilot project. British Society for the History of MathematicsBulletin 25 (3) (2010), 132–143. Author describes the development of an instructional unitfor grades 4 and 5 (US) based on two cuneiform tablets held at Florida State University.The unit was introduced to two classroom teachers who then used it in their classrooms.

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430 Abstracts / Historia Mathematica 38 (2011) 429–452

Article includes an assessment of the students’ engagement and a discussion of the teachers’reactions to the unit. (PWH) #38.3.1

Djebbar, Ahmed. See #38.3.2.

Gerdes, Paulus; and Djebbar, Ahmed. Mathematics in African History and Cultures. AnAnnotated Bibliography, second ed. Maputo: African Mathematical Union, Commission onthe History of Mathematics in Africa; London: Lulu, 2007, 430 pp. This volume consists ofan updated version of the bibliography published by the African Mathematical Union in2004. (LM) #38.3.2

Grünbaum, Branko. The Bilinski Dodecahedron and assorted Parallelohedra, Zonohe-dra, Monohedra, Isozonohedra, and Otherhedra. The Mathematical Intelligencer 32 (4)(2010), 5–15. An account of corrections to E.S. Fedorov’s 1885 enumeration of convexpolyhedra having congruent rhombi as faces, a publication that was considered a milestonein mathematical crystallography for seventy-five years. Grünbaum adds his own observa-tions about non-convex polyhedra resulting in a conjecture that gives the requirementsfor a sphere-like polyhedron to be a parallelohedron. (FA) #38.3.3

Kaplan, Ellen. See #38.3.4.

Kaplan, Robert; and Kaplan, Ellen. Hidden Harmonies: The Lives and Times of thePythagorean Theorem. New York: Bloomsbury Press, 2011, xii+290 pp. A tour throughthe history of the Pythagorean theorem, using the many different proofs of the theoremto illuminate mathematics in different cultures. The authors also look at generalizationsand connected ideas such as irrational numbers. (DJM) #38.3.4

Kourkoulos, Michael; and Tzanakis, Constantinos. History, and students’ understand-ing of variance in statistics. British Society for the History of Mathematics Bulletin 25 (3)(2010), 168–178. Authors describe the confusion about variance among prospective primaryschool teachers, and their efforts to lead students to a deeper conceptual understanding ofthe measurement through the study of some of the models from physics in which the ideafirst emerged in the 19th century. (PWH) #38.3.5

Krantz, Steven G., Coordinating ed. Memories of Martin Gardner. Notices of the Amer-ican Matheamtical Society 58 (3) (2011), 418–422. Brief appreciations of prolific popularizerof mathematics Martin Gardner (1914–2010). Contributions by Steven G. Krantz, Persi W.Diaconis, Ronald L. Graham, Donald E. Knuth, James Randi, Peter Renz, and RaymondM. Smullyan. (DJM) #38.3.6

Krantz, Steven G. An Episodic History of Mathematics. Mathematical Culture ThroughProblem Solving (MAA Textbooks). Washington, DC: Mathematical Association of Amer-ica, 2010 xiv+381 pp. A survey of many of the topics treated in undergraduate mathematicsviewed through an historical lens. See the lengthy and critical review by Victor J. Katz inMathematical Reviews 2604456 (2011d:00001). Katz’s concluding remarks are, “I cannotrecommend it to anyone, either for personal reading or for use in a classroom setting.”(DJM) #38.3.7

Luo, Jianjin. Tangent numbers: Its meaning and research history in China and West.Journal of Inner Mongolia Normal University. Natural Science Edition 37 (1) (2008), 120–123, 131. This paper analyzes tangent numbers and its meaning in mathematics through

Abstracts / Historia Mathematica 38 (2011) 429–452 431

the studies of some Western mathematicians and the work of Chinese mathematicians inthe Qing Dynasty. (LM) #38.3.8

Medvedeva, N.N. Survey of the development of additive partition theory [in Russian].Istoriko-Matematicheskie Issledovaniya (2) 13 (48) (2009), 295–307. The paper is dividedinto 4 historical periods outlining the history of partition calculus. See the review by Rado-slav M. Dimitric in Zentralblatt MATH 1202.01056. (TBC) #38.3.9

Meskens, Ad. Travelling Mathematics. The Fate of Diophantos’ Arithmetic (Science Net-works. Historical Studies 41). Basel: Birkhäuser, 2010, ix+208 pp. Surveys the ancientsources and later reception of Diophantos’ seminal third-century CE treatise on algebraand methods of solving equations, as well as interpreting the various algebra methods geo-metrically. See the review by Franz Lemmermeyer in Zentralblatt MATH 1204.01006.(KP) #38.3.10

Morini, Simona. Francis Galton ou comment photographier une moyenne [Francis Gal-ton’s composite portraits: The picture of a number]. Mathématiques et Sciences Humaines,Mathematics and Social Sciences 189 (2010), 5–17. The author discusses Galton’s attemptsto capture the image of an abstract entity by realizing “generic images” or “composite por-traits”. (LM) #38.3.11

Musto, Garrod. Mathematical timelines. British Society for the History of MathematicsBulletin 25 (3) (2010), 162–167. Author describes a joint project with art department col-league to display students’ portraits of mathematicians in the school hallways.(PWH) #38.3.12

Qu, Anjing. See #38.3.16.

Rozhanskaya, M.M. From the history of the theory of balances and weighting [in Rus-sian]. Istoriko-Matematicheskie Issledovaniya (2) 13 (48) (2009), 259–269. The paper reviewsthe history of the well known “weight problem” which, in the simplest formulation, reads asfollows. “Given balance scales, determine the minimal number and denomination ofweights required for weighting all loads whose weight does not exceed certain value.”See the review by Svitlana P. Rogovchenko in Zentralblatt MATH 1202.01002.(TBC) #38.3.13

Schubring, Gert. 120 Jahre Deutsche Mathematiker-Vereinigung: Neue Ergebnisse zuihrer Geschichte [120 years of the Deutsche Mathematiker-Vereinigung: New results fromtheir history]. Mitteilungen der Deutschen Mathematiker-Vereinigung 18 (2) (2010), 103–108.The author surveys recent research into the DMV since the pioneering centennial volume of1990, with emphasis on the early period of the society and the Nazi and post-war years.(DJM) #38.3.14

Tang, Quan. A study on Shicha algorithm of parallax theory in Almagest and Surya Sid-dhanta [in Chinese]. Journal of Northwest University. Natural Sciences Edition 38 (3) (2008),508–512. Methods of parallax computation for eclipses, under the name Shicha by whichthe subject was known in Chinese astronomy, are compared in two key texts of Hellenisticand medieval Indian astronomy. (KP) #38.3.15

Tang, Quan; and Qu, Anjing. Research on the parallax theory in ancient Greece, India,Arabia and China [in Chinese]. Studies in the History of Natural Sciences 27 (2) (2008), 131–


150. Compares techniques of parallax computation for solar eclipses in Hellenistic, Indian,Islamic, and Chinese mathematical astronomy. (KP) #38.3.16

Toma, Marina. A history of zero. Journal of Science and Arts 8 (1) (2008), 117–122. Anoverview of the historical origins of the number zero in Babylonian, Greek, and Indianmathematics. See the review by Neeraj Anant Pande in Zentralblatt MATH 1200.01003.(CH) #38.3.17

Tzanakis, Constantinos. See #38.3.5.

Wanner, G. Kepler, Newton and numerical analysis. Acta Numerica 19 (2010), 561–598.Drawing on sources from Ptolemy to Feynman, the author shows how inverse numericalmethods were important in the development of the differential equations describing plan-etary motion. See the review by Rémi Vaillancourt in Mathematical Reviews 2652786(2011d:65002). (DJM) #38.3.18

Wußing, Hans. EAGLE-Guide. Von Leonardo da Vinci bis Galileo Galilei. Mathematikund Renaissance [EAGLE-Guide. From Leonardo da Vinci to Galileo Galilei. Mathematicsand Renaissance] (EAGLE 41). Leipzig: Edition am Gutenbergplatz Leipzig (EAGLE),2010, 70 pp. A short review of the development of mathematics, physics and astronomyin Europe from roughly 1200 to 1600. Includes many pictures of stamps. See the reviewby Hans Fischer in Zentralblatt MATH 1204.01011. (DJM) #38.3.19

Mesopotamia

Britton, John P. Studies in Babylonian lunar theory. III: The introduction of the uni-form zodiac. Archive for History of Exact Sciences 64 (6) (2010), 617–663. “This paper con-tinues the examination of the Babylonian mathematical lunar theories called Systems Aand B, given by the author in [Archive for History of Exact Sciences. 61 (2) (2007), 83–145. (Zbl 1128.01003) and 63 (4) (2009), 357–431. (Zbl 1181.01004)], respectively.” See thereview by Hermann Hunger in Zentralblatt MATH 1203.01003. (TBC) #38.3.20

Duke, Dennis. Greek angles from Babylonian numbers. Archive for History of Exact Sci-ences 64 (3) (2010), 375–394. The author outlines the basic assumptions of Babylonianastronomical “System A” and then shows how the parameters needed for a geometricalmodel of the outer planets could be derived from them. It is possible “that a Greek astron-omer could have used those models to estimate the zodiacal variation of the equation ofcenter for each planet.” See the review by Hermann Hunger in Zentralblatt MATH1202.01018. (TBC) #38.3.21

Gray, J.M.K.; and Steele, J.M. Studies on Babylonian goal-year astronomy II: The Bab-ylonian calendar and goal-year methods of prediction. Archive for History of Exact Sci-ences 63 (6) (2009), 611–633. A continuation of an earlier study of Babylonianastronomical texts, focusing on how astronomical predictions in the Almanacs and NormalStar Almanacs may have been derived from the Goal-Year Texts. See the review by JensHøyrup in Zentralblatt MATH 1200.01004. (CH) #38.3.22

Steele, J.M. See #38.3.22.

See also #38.3.17.


India

Hua, Guodong. See #38.3.27.

Khmurkin, G.G. Zero and the Buddhistic doctrine of emptiness [in Russian]. Istoriko-Matematicheskie Issledovaniya (2) 13 (48) (2009), 246–258. “The paper has a three-fold pur-pose: (1) to present main ideas of s�unyá-v�ada, . . . (2) to draw several historical, semanticand logical parallels between the ideas of s�unyá-v�ada and the concept of zero . . . (3) to dis-cuss popularity of this parallelism in science.” See the review by Svitlana P. Rogovchenko inZentralblatt MATH 1202.01006. (TBC) #38.3.23

Mallayya, V. Madhukar. Analysis of M�adhava’s series method for determination ofdesired Rsines. Gan: ita-Bh�arat�ı 30 (2) (2008), 195–209. Discusses the methods used by thefamous fourteenth-century South Indian mathematician M�adhava to compute the termsof his version of the power series for the sine. See the review by Girish Ramaiah in Zen-tralblatt MATH 1200.01008. (KP) #38.3.24

Mallayya, V. Madhukar. Kerala mathematical tradition—some landmarks. Gan: ita-Bh�arat�ı 28 (1–2) (2006), 51–65. Summarizes some outstanding achievements of the SouthIndian mathematicians and astronomers known as the “Kerala school”, active in the four-teenth through eighteenth centuries. See the review by T. Thrivikraman in ZentralblattMATH 1200.01007. (KP) #38.3.25

Shah, R.S. Mathematical ideas in Bhagavat�ı S�utra (BS). Gan: ita-Bh�arat�ı 30 (1) (2008), 1–25. Describes mathematical concepts involved in Jain religious, philosophical and cosmo-logical thought, such as ways of expressing very small and very large numbers, and combi-natorial principles. The Jain canonical text in question, the Bhagavat�ı S�utra, was composedperhaps over several centuries around the beginning of the common era. See the review byT. Thrivikraman in Zentralblatt MATH 1200.01009. (KP) #38.3.26

Yan, Xuemin; and Hua, Guodong. Restoring Bhaskara’s formula of the area of thesphere [in Chinese]. Journal of Zhengzhou University. Natural Science Edition 40 (1)(2008), 27–30, 35. The twelfth-century mathematician Bhaskara’s rationales for the formulafor the sphere’s surface area are investigated in relation to notions of limit and trigonomet-ric quantities. (KP) #38.3.27

See also #38.3.15; #38.3.16; #38.3.17; and #38.3.32.

China

Bo, Shuren. See #38.3.39.

Chen, Meidong. See #38.3.39.

Dong, Jie; and Wang, Weidong. Chinese mathematicians’ researches on the golden sec-tion in the early Qing Dynasty [in Chinese]. Journal of Inner Mongolia Normal University.Natural Science Edition 37 (4) (2008), 573–578. This paper analyzes Chinese mathemati-cians’ research on the Golden Section in the early Qing Dynasty, focusing in particularon the work of Li Zijin, Mei Wending, and Yang Zuomei. (LM) #38.3.28

Guan, Yuzhen. A new interpretation of Shen Kuo’s Ying Biao Yi. Archive for History ofExact Sciences 64 (6) (2010), 707–719. A critical analysis of Shen Kuo’s use of gnomon


shadows in astronomy from around 1072. See the review by Jean-Claude Martzloff in Zen-tralblatt MATH 1204.01008. (DJM) #38.3.29

Guo, Shuchun. Several issues on history of mathematics in China. Journal of GuangxiUniversity for Nationalities. Natural Science Edition 14 (4) (2008), 9–13. This paper analyzesthe development of mathematics in China before the middle of Yuan Dynasty and discussesthe existence of pure mathematical research. (LM) #38.3.30

Guo, Shuchun. On the relation between the Suanshu Shu and the Nine Chapters onMathematical Procedures [in Chinese]. Qufu Shifan Daxue Xuebao. Ziran Kexue Ban. Jour-nal of Qufu Normal University. Natural Science 34 (3) (2008), 1–7. Statistically compares thecontent of these two ancient Chinese mathematical works to assess their textual relation-ship; the small percentage of shared content indicates a common origin in Pre-Qin mathe-matical knowledge. (KP) #38.3.31

Hu, Tiezhu. See #38.3.39.

Li, Wenlin. On the algorithmic spirit of the ancient Chinese and Indian mathematics.Gan: ita-Bh�arat�ı 28 (1–2) (2006), 39–49. A discussion of Chinese and Indian algorithms forsolving linear systems in three unknowns and extraction of roots, and Brahmagupta’s cyclicmethod. See the review by Jean-Claude Martzloff in Zentralblatt MATH 1204.01003.(DJM) #38.3.32

Martzloff, Jean-Claude. The history of the Chinese written zeroes revisited. Gan: ita-Bh�arat�ı 28 (1–2) (2006), 67–83. A re-examination of the history of the written zero in Chi-nese mathematics and astronomy. The author considers evidence relating to three differentrepresentations for zero: a dot, a blank space, and a circle. See the review by Pao-Sheng Hsuin Zentralblatt MATH 1200.01006. (CH) #38.3.33

Ôhashi, Yukio. Formulation of Chinese classical mathematical astronomy. Gan: ita-Bh�arat�ı 29 (1–2) (2007), 101–115. A study of the development of Chinese astronomy fromthe Shang-Yin to the Han Dynasty. The author also discusses connections between Chineseand Indian astronomy. See the review by J.-C. Martzloff in Zentralblatt MATH 1201.01006.(CH) #38.3.34

Ôhashi, Yukio. Chinese mathematical astronomy from ca. 4th century to ca. 6th century.Gan: ita-Bh�arat�ı 30 (1) (2008), 27–39. A discussion of important topics relating to Chineseastronomy during this period, including reforms to the calendar and techniques for deter-mining the exact moment of the winter solstice. See the review by J.-C. Martzloff in Zen-tralblatt MATH 1201.01007. (CH) #38.3.35

Pan, Yining. Source and influence of the numerical solution for high degree equation inTongwen Suanzhi [in Chinese]. Studies in the History of Natural Sciences 27 (1) (2008), 71–82. The paper argues that the methods for numerical solution of equations of higher degreein the seventeenth-century Chinese Tongwen Suanzhi, which is largely a redaction ofRenaissance mathematical works, were due to the algebra of Michael Stifel, and were stud-ied and modified by later Chinese scholars. (KP) #38.3.36

Teng, Yanhui; and Wang, Pengyun. The algorithm model of the real new moon in Jiy-uan Li and its analysis [in Chinese]. Journal of Northwest University. Natural Sciences Edi-tion 38 (5) (2008), 855–858. Analyzes an astronomical model for true new moon in medieval


Chinese calendrics and lays out an algorithm reproduce its computations electronically.(KP) #38.3.37

Wang, Pengyun. See #38.3.37.

Wang, Weidong. See #38.3.28.

Xu, Zelin. Research on Wu’s method and Japanese geometry [in Chinese]. Studies in theHistory of Natural Sciences 27 (4) (2008), 471–484. Examines second-millennium Chinese“algebraical geometry” and its connections to Japanese wasan geometry and Wu’s methodfor solving polynomial equations. (KP) #38.3.38

Zhang, Peiyu; Chen, Meidong; Bo, Shuren; and Hu, Tiezhu. Ancient Chinese Astronom-ical Canons (Zhongguo gu dai li fa) [in Chinese]. 10 vols. Beijing: Zhongguo Kexue JishuChubanshe (Scientific and Technical Editions), 2008, viii+viii+726 pp. This series of mono-graphs describes with unprecedented detail and comprehensiveness each of the major can-ons of Chinese astronomy and calendrics, as well as discussing the general mathematicalmethods they used. See the review by J.-C. Martzloff in Zentralblatt MATH 1205.01003.(KP) #38.3.39

Zhu, Yiwen. Reviewing the process of Liu Hui’s deducing the circular constant through“modifying by ratio” [in Chinese]. Studies in the History of Natural Sciences 27 (1) (2008),59–70. Compares and analyzes various reconstructions of the third-century mathematicianLiu Hui’s derivation of the value 3927/1250 for p. (KP) #38.3.40

See also #38.3.8; #38.3.15; #38.3.16; and #38.3.45.

Islamic/Islamicate

Azarian, Mohammad K. al-Ris�ala al-Muh�ıt�ıyya: A summary. Missouri Journal ofMathematical Sciences 22 (2) (2010), 64–85. Summarizes, with an annotated table of con-tents, al-K�ash�ı’s fifteenth-century Treatise on the Circumference in which he calculates pto sixteen decimal places. See the review by Benno van Dalen in Zentralblatt MATH1204.01009. (KP) #38.3.41

Berggren, J. Lennart. Mathematik im mittelalterlichen Islam [Mathematics in MedievalIslam]. Petra G. Schmidl with Heinz Klaus Strick, trans., Berlin: Springer, 2011, xvi+219pp. A German translation (with minor revisions) of the 1986 Episodes in the Mathematicsof Medieval Islam, an introduction to Islamic mathematics accessible to students as well asspecialists. See the review by Benno van Dalen in Zentralblatt MATH 1204.01010.(KP) #38.3.42

See also #38.3.16

Other Non-Western

Gerdes, Paul. African Basketry. A Gallery of Twill-plaited Designs and Patterns. Maputo:Center for Mozambican Studies and Ethnoscience, Universidade Pedagógica; Lulu Press,2007, 220 pp. This book is a gallery of twill-plaited African designs. (LM) #38.3.43

Halliru, Aisha. See #38.3.44.


Mohammed, Waziri Yusuf; Saidu, Ibrahim; and Halliru, Aisha. Ethnomathematics: Amathematical game in Hausa culture. Sutra: International Journal of Mathematical ScienceEducation 3 (1) (2010), 36–42. This paper describes mathematical games in Hausa culture(Nigeria) that involve calculations and highlights the existence of algebra, set theory, coor-dinate geometry, arithmetic progression, and geometric progression in such culture.(LM) #38.3.44

Saidu, Ibrahim. See #38.3.44.

Ying, Jia-Ming. The Kujang sulhae: Nam Py�ong-Gil’s reinterpretation of the mathemat-ical methods of the Jiuzhang suanshu. Historia Mathematica 38 (1) (2011), 1–27. NamPy�ong-Gil (1820–1869) was a Korean mathematician who wrote a commentary on the Jiuz-hang suanshu. He retained the text of the original, but substituted his own commentary forthose of Liu Hui and Li Chunfeng. In this paper, the author gives a detailed analysis ofNam’s commentary and comparison with the earlier Chinese commentaries.(DJM) #38.3.45

Zhou, Chang. The trailblazer of analysis in Wasan: Takebe Katahiro [in Chinese]. Jour-nal of Inner Mongolia Normal University. Natural Science Edition 37 (1) (2008), 124–131.The author presents a textual research on Takebe Katahiro’s life and mathematicalachievements during the Edo period, when the Wasan mathematician lived.(LM) #38.3.46

See also #38.3.2; and #38.3.38.

Antiquity

Chondros, Thomas G. Archimedes life works and machines. Mechanism and MachineTheory 45 (11) (2010), 1766–1775. This article analyzes Archimedes’ life, as well as his the-ory and practice of machines. (LM) #38.3.47

Duke, Dennis. Mean motions in Ptolemy’s Planetary Hypotheses. Archive for History ofExact Sciences 63 (6) (2009), 635–654 (2009). A technical analysis of the numerical param-eters of the planetary models in the Planetary Hypotheses in comparison to those of theAlmagest, and suggestions for their origins. See the review by Jens Høyrup in ZentralblattMATH 1204.01005. (DJM) #38.3.48

Gautschi, Walter. The spiral of Theodorus, numerical analysis, and special functions.Journal of Computational and Applied Mathematics 235 (4) (2010), 1042–1052. The classicalmathematician Theodorus of Cyrene is mentioned in connection with a numerical-analysisapproach to interpolating the discrete spiral ascribed to him with a smooth spiral.(KP) #38.3.49

Sefrin-Weis, Heike, ed. Pappus of Alexandria: Book 4 of the Collection. Berlin: Springer,2010, xxxi+328 pp. A new edition with English translation and commentary of the fourthbook of Pappus’s fourth-century mathematical Collection, including a general introductionand biographical survey. See the review by Eberhard Knobloch in Zentralblatt MATH1204.01047. (KP) #38.3.50

Theodosius. Theodosius Sphaerica. Arabic and medieval Latin translations (Boethius.Texte und Abhandlungen zur Geschichte der Mathematik und der Naturwissenschaften 62).


Paul Kunitzsch and Richard Lorch, eds., Stuttgart: Franz Steiner Verlag, 2010, 431 pp. Pre-sents critical editions of the Arabic and Latin versions of the second-century BCE treatiseon spherics by the Hellenistic mathematician Theodosius of Bithynia, along with variousnotes and a mathematical summary. See the review by Eberhard Knobloch in ZentralblattMATH 1203.01035. (KP) #38.3.51

Thomaidis, Yannis. Some remarks on the meaning of equality in Diophantos’s Arithme-tica. Historia Mathematica 38 (1) (2011), 28–41. The author studies Diophantos’s tech-niques in the creation and simplification of equalities to elucidate the meaning of“equation” in the Arithmetica. (DJM) #38.3.52

See also #38.3.10; #38.3.15; #38.3.16; and #38.3.17.

Renaissance

Aubel, Matthias. Michael Stifel. Ein Mathematiker im Zeitalter des Humanismus und derReformation [Michael Stifel. A Mathematician in the Age of Humanism and Reformation](Algorismus 72). Augsburg: ERV Dr. Erwin Rauner Verlag, 2008, 531 pp. Explores the lifeand work of the sixteenth-century monk and mathematician Michael Stifel, including hisgroundbreaking ideas in symbolic notation. See the review (in German) by W. Kaunznerin Zentralblatt MATH 1205.01026. (KP) #38.3.53

Gessner, Samuel. Savoir manier les instruments: la géométrie dans les écrits italiensd’architecture (1545–1570) [Knowing how to handle instruments: Geometry in Italian writ-ings on architecture (1545–1570)]. Revue d’Histoire des Mathématiques 16 (1) (2010), 1–62.This article explores the mathematical content of Italian architectural writings of the sec-ond half of the 16th century and analyzes the role mathematical instruments played ingeometry. See the review by Maria Rosa Massa Esteve in Zentralblatt MATH1200.01010. (LM) #38.3.54

James, Kathryn. Reading numbers in early modern England. British Society for the His-tory of Mathematics Bulletin 26 (1) (2011), 1–16. Examines instructional texts, copybooks,and popular series in order to characterize the popular (as over against scholarly) mathe-matical writing of early modern Britain. The author argues that over the course of the 16thcentury, mathematics made its way into the broader English popular culture.(PWH) #38.3.55

Ulivi, Elisabetta. Documenti inediti su Luca Pacioli, Piero della Francesca e Leonardoda Vinci, con alcuni autografi [Unpublished documents concerning Luca Pacioli, Pierodella Francesca and Leonardo da Vinci, with some autographs]. Bollettino di Storia delleScienze Matematiche 29 (1) (2009), 15–160. This article gathers unpublished documentson Luca Pacioli, Leonardo da Vinci, Piero della Francesca, and their families.(LM) #38.3.56

Zhao, Jiwei. Cardano’s constructive geometric demonstration [in Chinese]. Journal ofShaanxi Normal University. Natural Science Edition 36 (6) (2008), 14–18. The authorexplains Cardano’s constructive geometric demonstration and generalizes his demonstra-tion in the case of the cubic equation to the general case by his own method.(LM) #38.3.57


Zhao, Jiwei. Reconstruction of Cardano’s four special rules of quartic equation: A dis-cussion on the paradigms of research on the history of mathematics [in Chinese]. Studies inthe History of Natural Sciences 27 (3) (2008), 325–336. Investigates Cardano’s method ofsolving a quartic equation in light of the historiographic paradigms “what mathematicswas done”, “how mathematics was done”, and “why mathematics was done”.(KP) #38.3.58

See also #38.3.36.

17th century

Adhikari, Swapan Kumar. Descartes’ concept on pineal gland: Recent views and mathe-matical appreciation. News Bulletin of Calcutta Mathematical Society 31 (1–3) (2008), 9–18.Comments on both the mathematical and philosophical remarks of Descartes on the pinealgland. See the review by Teodora-Liliana R�adulescu in Zentralblatt MATH 1200.01011.(DJM) #38.3.59

Cheng, Xiaohong. See #38.3.72.

Coumet, Ernest. Le probléme des partis avant Pascal [The problem of points before Pas-cal]. Journal Électronique d’Histoire des Probabilités et de la Statistique/Electronic Journalfor History of Probability and Statistics 3 (1) (2007), 15 pp., electronic only. On the historyof division of stakes before Pascal, including work by Luca Pacioli, Niccolò Tartaglia,Girolamo Cardano, and Lorenzo Forestani. See the review by Anatoliy Milka in Zentralbl-att MATH 1203.01008. (DJM) #38.3.60

Deschauer, Stefan. Die Rigischen Rechenbücher. Spiegel einer lokalen mathematischenTradition im Ostseeraum [The Arithmetic Books of Riga. Reflection of a Local MathematicalTradition in the Baltic Sea Area] (Algorismus 73). Augsburg: ERV Dr. Erwin Rauner Ver-lag, 2010, ix+230 pp. The author presents a central aspect of Riga’s culture, the mathemat-ical tradition carried by textbooks of commercial arithmetic from the mid-17th to the early19th century. He analyzes the mathematical tradition per se and the commercial arithmeticlinked to actual commercial practice. See the review by Jens Høyrup in Zentralblatt MATH1205.01008. (LM) #38.3.61

Friendly, Michael; Valero-Mora, Pedro; and Ulargui, Joaquín Ibáñez. The first (known)statistical graph: Michael Florent van Langren and the “secret” of longitude. The AmericanStatistician 64 (2) (2010), 174–184. An examination of the historical background of a dia-gram composed by van Langren in 1644, often considered the first graphical representationof statistical data. The authors discuss the origin of this diagram in reference to a letterwritten by van Langren in 1628. See the review by Teodora-Liliana R�adulescu in Zentralbl-att MATH 1200.01013. (CH) #38.3.62

Graney, Christopher M. But still, it moves: Tides, stellar parallax, and Galileo’s commit-ment to the Copernican theory. Physics in Perspective 10 (3) (2008), 258–268. The authordiscusses Galileo’s commitment to the Copernican heliocentric theory of the universe.See the review by Alan S. McRae in Mathematical Reviews 2438725 (2011b:85001).(LM) #38.3.63

Khruschev, Sergey. Two great theorems of Lord Brouncker and his formula. The Mathe-matical Intelligencer 32 (4) (2010), 19–31. A tortuous discussion of the two formulas for


continued fractions discovered by the British mathematician W. Brouncker in 1655, includ-ing the background for them which involves work by Wallis, Huygens, Euler and Fermat,among others. The author also gives relevant excursions into politics, astrology, and musi-cal harmony. (FA) #38.3.64

Krüger, Jenneke. Lessons from the early seventeenth century for mathematics curricu-lum design. British Society for the History of Mathematics Bulletin 25 (3) (2010), 144–161.Examines developments in mathematics education in the Dutch Republic in the first half ofthe 17th century, focusing particularly on the creation of the Duytsche Mathematique, aschool for military engineers at the University of Leiden. Briefly considers what lessonsfrom this episode might apply to present day discussions of mathematics curricula in theNetherlands. (PWH) #38.3.65

Kudryashova, L.V. From the history of the origin of the concept of “moment inertia” [inRussian]. Istoriko-Matematicheskie Issledovaniya (2) 13 (48) (2009), 284–295. On the devel-opment of the concept of moment of inertia from a problem stated by Mersenne and solvedby Huygens, to the fundamental contribution by Euler and later development in mechanics.See the review by Roman Duda in Zentralblatt MATH 1204.01013. (DJM) #38.3.66

Liu, Shuyong. See #38.3.70.

Nauenberg, Michael. Periodic orbits of the three-body problem: Early history, contribu-tions of Hill and Poincaré, and some recent developments, in #38.3.119, pp. 113–142. Theauthor argues that the first approximation to existence of periodic orbits in the restrictedthree-body problem is to be found in Newton’s work on lunar motion. He then considersHill’s lunar orbits and Poincaré’s periodic orbits in the three-body problem. See the reviewby Jesús F. Palacián in Mathematical Reviews 2647622. (DJM) #38.3.67

Panza, Marco. Rethinking geometrical exactness. Historia Mathematica 38 (1) (2011),42–95. The exactness concern is the question of which techniques and constructions shouldbe permitted into geometry. Here, the author argues that Descartes evolved a conservativeextension of Euclidean plane geometry as a response to this issue. (DJM) #38.3.68

Ren, Ruifang. Newton’s study on differential equations in his creation of the differential[in Chinese]. Journal of Northwest University. Natural Sciences Edition 38 (2) (2008), 334–338. Concludes that the concept of differential equations was crucial in Newton’s develop-ment of the methods of differential calculus. (KP) #38.3.69

Song, Guangli; Zhang, Wei; and Liu, Shuyong. The analysis of prosperity of Bernoullifamily in mathematics [in Chinese]. Journal of Capital Normal University. Natural ScienceEdition 29 (4) (2008), 18–21, 31. This paper analyzes the reasons for the Bernoulli family’schequered history in science and especially in mathematics. (LM) #38.3.70

Thorvaldsen, Steinar. Early numerical analysis in Kepler’s new astronomy. Science inContext 23 (1) (2010), 39–63. “The central interest of the article is Kepler’s use of numericalanalysis to solve the problems generated by his elliptical model for planetary movement”.See the review by Jens Høyrup in Zentralblatt MATH 1203.01009. (TBC) #38.3.71

Ulargui, Joaquín Ibáñez. See #38.3.62.

Valero-Mora, Pedro. See #38.3.62.


Yang, Jing; and Cheng, Xiaohong. The algorithmic tendency of mathematical develop-ment in the 17th century [in Chinese]. Journal of Northwest University. Natural SciencesEdition 38 (5) (2008), 851–854. Examines analytic geometry, calculus, algebra and syntheticgeometry in seventeenth-century mathematics and concludes that computational oralgorithmic methods rather than rigorous proof formed the chief focus of the period.(KP) #38.3.72

Zhang, Wei. See #38.3.70.

18th century

Grabiner, Judith V. A Historian Looks Back. The Calculus as Algebra and Selected Writ-ings (MAA Spectrum). Washington, DC: The Mathematical Association of America, 2010,xv+287 pp. The author republishes her 1966 dissertation, first published in 1990 [The Cal-culus as Algebra. J.-L. Lagrange, 1736–1813. New York etc.: Garland Publishing, Inc., 1990]with an updated bibliography and adds ten articles on the history of calculus from journalspublished by the Mathematical Association of America. See the review by Reinhard Sieg-mund-Schultze and Albert C. Lewis in Zentralblatt MATH 1205.01009. (LM) #38.3.73

Jia, Suijun; and Ren, Ruifang. The development of Euler’s contribution to the conceptof function [in Chinese]. Journal of Northwest University. Natural Sciences Edition 38 (3)(2008), 513–516. The authors conclude that Euler’s perception of a function as an analyticalexpression was crucial to the transformation of the idea of function from a geometrical toan algebraic concept. (KP) #38.3.74

Kwasniewski, A.K. Ivan Bernoulli series universalissima. Gan: ita-Bh�arat�ı 28 (1–2) (2006),93–101. A discussion of the mathematical work of Ivan (Johann) Bernoulli and Brook Tay-lor, including the dispute between the two men that began in 1715 over credit for certainresults relating to series. See the review by Fiacre O’Cairbre in Zentralblatt MATH1201.01011. (CH) #38.3.75

Ren, Ruifang. See #38.3.74.

Zubkov, A.M. Euler and combinatorial analysis [in Russian]. Istoriko-MatematicheskieIssledovaniya (2) 13 (48) (2009), 38–48. The author surveys Euler’s work in Graph Theory,Latin Squares and Pentagonal Numbers. See the review by Radoslav M. Dimitric in Zen-tralblatt MATH 1202.01059. (TBC) #38.3.76

See also #38.3.61; #38.3.66; and #38.3.70.

19th century

Ackerberg-Hastings, Amy. John Farrar and curricular transitions in mathematics edu-cation. International Journal for the History of Mathematics Education 5 (2) (2010), 17–30.The Harvard career of John Farrar (1779–1853), especially his introduction of the Cam-bridge Course of Mathematics, based on recent texts by Lacroix, Legendre, and Bézout,as textbooks for Harvard courses. (CB) #38.3.77

Batterson, Steve. The contribution of John Parker Jr. to American mathematics Noticesof the American Mathematical Society 58 (2) (2011), 262–273. Parker (1783–1844), a wealthy


Boston merchant, left a bequest to Harvard University that was used to fund Harvard trav-eling fellowships, allowing numerous mathematicians to further their studies in Europe.Several of them went on to build significant mathematical departments in the United Stateson their return. (DJM) #38.3.78

Boissonnade, Auguste. See #38.3.92.

Bradley, Robert E.; and Petrilli, Salvatore J., Jr. Servois’ 1814 Essay on a New Method ofExposition of the Principles of Differential Calculus, with an English translation. Loci: Con-vergence (November 2010), 19 pp., electronic only. A study and English translation of Ser-vois’ attempt to place calculus on a foundation of algebraic analysis without recourse toinfinitesimals, continuing the work of Lagrange. (JLB) #38.3.79

Brigaglia, Aldo; and Di Sieno, Simonetta. The Luigi Cremona archive of the MazziniInstitute of Genoa. Historia Mathematica 38 (1) (2011), 96–110. This paper describes theproject of editing Cremona’s correspondence and other documents held in the Luigi Cre-mona archive of the Mazzini Institute of Genoa (Italy). See the review by Luigi Borzacchiniin Zentralblatt MATH 1205.01011. (LM) #38.3.80

Capecchi, Danilo; Ruta, Giuseppe; and Trovalusci, Patrizia. From classical to Voigt’smolecular models in elasticity. Archive for History of Exact Sciences 64 (5) (2010), 525–559. The paper discusses the development of Voigt’s corpuscular theory modeling an elasticmaterial. See the review by Teun Koetsier in Zentralblatt MATH 1203.01010.(TBC) #38.3.81

Craik, Alex D.D.; and O’Conner, John J. Some unknown documents associated withWilliam Wallace (1768–1843). British Society for the History of Mathematics Bulletin 26(1) (2011), 17–28. Describes the contents of a folder of Wallace papers (manuscript andprinted) that has recently come to light and been made accessible online. (PWH) #38.3.82

Dénes, Tamás. Real face of János Bolyai. Notices of the American Mathematical Society58 (1) (2011), 41–51. The widely-circulated portrait of János Bolyai (1802–1860) is, in fact,not of him. However, the relief on the Culture Palace in Marosvásárhely, although commis-sioned long after his death, is argued to be a close likeness. The author also summarizessome of Bolyai’s work in number theory. (DJM) #38.3.83

Di Sieno, Simonetta. See #38.3.80.

Gabriel, Gottfried; Hülser, Karlheinz; and Schlotter, Sven. Zur Miete bei Frege – RudolfHirzel und die Rezeption der stoischen Logik und Semantik in Jena [For rent at Frege’s –Rudolf Hirzel and the reception of stoic logic and semantics in Jena]. History and Philos-ophy of Logic 30 (4) (2009), 369–388. An examination of the influence of Stoic logic onthe work of Gottlob Frege, focusing on the communication between Frege and the classicalphilologist Rudolf Hirzel. See the review by Karl-Heinz Schlote in Zentralblatt MATH1200.01017. (CH) #38.3.84

Ghys, Étienne. Variations on Poincaré’s recurrence theorem, in #38.3.119, pp. 193–206.A modern analysis of Poincaré’s recurrence theorem of 1890 showing that a three-body sys-tem can return arbitrarily close to its initial configuration infinitely often. See the review byThomas Ward in Mathematical Reviews 2647625 (2011e:37016). (DJM) #38.3.85

Gispert, Hélène. Les traités d’analyze et la rigueur en France dans la deuxième moitié duXIXe siècle, des questions, des choix et des contextes [The contributions in analysis and


rigor in France in the second half of the nineteenth century, questions, selections, contexts],in Brizzi, G.P.; and Tavoni, M.G., eds., Dalla pecia all’e-book. Libri per l’università: Stampa,editoria, circolazione e lettura. Atti del convegno internazionale di studi. Bologna, 21-25 otto-bre 2008 (Bologna: CLUEB, 2009), pp. 415–430. The development of rigor in French anal-ysis from Duhamel, through Jordan, to J. Houel and G. Darboux. Included is theinstitutional development and increasing importance of universities and the increase inresearch along with pedagogy. See the review by Albert C. Lewis in Zentralblatt MATH1200.01018. (DJM) #38.3.86

Gray, Jeremy. Worlds Out of Nothing. A Course in the History of Geometry in the 19thCentury. 2nd corrected ed. (Springer Undergraduate Mathematics Series). London: Springer,2011, xxv+384 pp. This book provides a course on the history of geometry in the 19th cen-tury based on the author’s lectures given at the University of Warwick between 2001 and2004. See the review by Roman Murawski in Zentralblatt MATH 1205.01013.(LM) #38.3.87

Grivel, Pierre-Paul. Poincaré, and Lie’s third theorem, in #38.3.119, pp. 307–328. Ananalysis of Poincaré’s 1899 paper on the construction of the universal enveloping algebraof a Lie algebra and his use of the exponential map to prove Lie’s Third Theorem. Seethe review by Leon Harkleroad in Zentralblatt MATH 1194.01022. (DJM) #38.3.88

Hamilton, William Rowan. Elements of Quaternions. 2 Part set. Edited by WilliamEdwin Hamilton. Reprint of the 1866 original (Cambridge Library Collection – Mathemat-ics). Cambridge: Cambridge University Press, 2009, lix+762 pp. This book is a reprint ofHamilton’s book on quaternions published posthumously in 1866 by the mathematician’sson William Edwin Hamilton. See the review by Roman Murawski in Zentralblatt MATH1204.01046. (LM) #38.3.89

Hamilton, William Edwin. See #38.3.89.

Hülser, Karlheinz. See #38.3.84.

Jacobi, C.G.J. Jacobi’s Lectures on Dynamics. Delivered at the University of Königsberg inthe winter semester 1842–1843 and according to the notes prepared by C.W. Borchardt (Textsand Readings in Mathematics 51). A. Clebsch, ed.; K. Balagangadharan, trans.; BiswarupBanerjee, ed. trans. (2nd revised edition). New Delhi: Hindustan Book Agency, 2009.x+339 pp. Provides an English translation of the German text (originally edited by Clebsch)of Jacobi’s Königsberg lectures on key concepts in mechanics such as partial differentialequations and fundamental physical principles. See the review by Reinhard Siegmund-Schultze in Zentralblatt MATH 1200.01019. (KP) #38.3.90

Jin, Yingji. See #38.3.93.

Kidwell, Peggy Aldrich. Benjamin Peirce and technologies of mathematics education.International Journal for the History of Mathematics Education, 5 (2) (2010), 31–40. Peirce(1809–1880) and his Harvard colleagues “embraced the three basic tools of Americanteaching that became common in his day — the blackboard, the student-owned textbookand the written exam.” Also, text writing by Peirce and calculating machines by his stu-dents. (CB) #38.3.91

Lagrange, J.L. Analytical Mechanics. Translated from the 1811 French original. Editedby Auguste Boissonnade and Victor N. Vagliente (Boston Studies in the Philosophy of Sci-


ence 191). Dordrecht: Kluwer Academic Publishers, 1997, xlvi+592 pp. This book is the firstEnglish translation of the Méchanique analitique based upon the second edition ofLagrange’s work on analytical mechanics. See the review by A. Kleinert in ZentralblattMATH 0999.01032. (LM) #38.3.92

Li, Yuewu; and Jin, Yingji. Principle of the permanence of equivalent forms: GeorgePeacock’s symbolical algebra [in Chinese]. Journal of Northwest University. Natural Sci-ences Edition 38 (1) (2008), 157–160. Describes how the Cambridge mathematician GeorgePeacock’s principle generalized arithmetical algebra to symbolical algebra by consideringalgebraic operations valid for general algebraic symbols as well as symbols denoting onlynumerical values. (KP) #38.3.93

McCartney, Mark. The poetic life of James Clerk Maxwell. British Society for the His-tory of Mathematics Bulletin 26 (1) (2011), 29–43. Discusses examples of Maxwell’s poetry,arguing that it sheds light on his life and his scientific work. (PWH) #38.3.94

O’Conner, John J. See #38.3.82.

Petrilli, Salvatore J., Jr. See #38.3.79.

Rice, Adrian. “To a factor près”: Cayley’s partial anticipation of the Weierstrass }-func-tion. American Mathematical Monthly 117 (4) (2010), 291–302. In addition to biographicalmaterial on Cayley and Weierstrass, the article presents Cayley’s transformation of an inte-gral equaling a quartic polynomial into an integral of Weierstrass equaling a cubic polyno-mial. See the review by Franz Lemmermeyer in Zentralblatt MATH 1202.01070.(TBC) #38.3.95

Roberts, David Lindsay. Simon Newcomb and the institutional hierarchy of mathemat-ics education. International Journal for the History of Mathematics Education 5 (2) (2010),41–51. The “improbable” career of Simon Newcomb (1835–1909). From rural Nova Scotia,to the Nautical Almanac Office and the Lawrence Scientific School, at Harvard (degree1858), to work at the Naval Observatory in Washington, DC, his articles and lecturesbrought him the respect that landed him on the Committee of Ten, 1892, for reform of sec-ondary education, and fourth president of the AMS. (CB) #38.3.96

Ruta, Giuseppe. See #38.3.81.

Schlotter, Sven. See #38.3.84.

Schubring, Gert. Hermann Graßmann – zwei sich unterscheidende Lebensläufe [Her-mann Grassmann – two distinctive curricula vitae]. Internationale Zeitschrift für Geschichteund Ethik der Naturwissen- schaften, Technik und Medizin (N.S.) 18 (2) (2010), 197–230.Together these two vitae (one for a gymnasium teacher, the other for a pastor) give insightinto Grassmann’s personality and the motivations of his mathematical ideas. See the reviewby Roman Duda in Zentralblatt MATH 1203.01031. (TBC) #38.3.97

Shaposhnikov, V.A. The philosophical methodological interests of N.D. Brashman [inRussian]. Istoriko-Matematicheskie Issledovaniya (2) 13 (48) (2009), 68–89. A study ofthe philosophical positions of Nikolaus Braschman, including his views on the place ofmathematics within a liberal arts education and the role of geometry in understandingthe nature of space. See the review by Siegfried J. Gottwald in Zentralblatt MATH1200.01020. (CH) #38.3.98


Somerville, Mary. Personal Recollections, from Early Life to Old Age. With Selectionsfrom Her Correspondence. Edited by Martha Somerville. Reprint of the 1873 original (Cam-bridge Library Collection – Astronomy). Cambridge: Cambridge University Press, 2010, 392pp. This book is a reprint of the 1873 original edition. It contains memoirs and a selectionof the correspondence of the nineteenth-century polymath Mary Somerville (1780–1872).(LM) #38.3.99

Somerville, Martha. See #38.3.99.

Strutt, John William, Lord Rayleigh. Scientific Papers. 1869–1919, 6 volume set, paper-back ed. (Cambridge Library Collection – Mathematics). Cambridge: Cambridge UniversityPress, 2010, 3944 pp. These six volumes collect the scientific papers Lord Rayleigh wrotefrom 1869 to 1919. It includes 446 publications except The Theory of Sound [See thereviews of the original editions (1899–1920) in JFM 47.0868.04; JFM 43.0052.05; JFM34.0037.01; JFM 33.0046.01; JFM 31.0031.04; JFM 30.0027.01]. (LM) #38.3.100

Trovalusci, Patrizia. See #38.3.81.

Vagliente, Victor N. See #38.3.92.

Wang, Chang. The origin of the concept of residue. Journal of Guangxi University forNationalities. Natural Science Edition 14 (4) (2008), 14–16. The author analyzes Cauchy’sresidue concept by using the method of historic analysis and literature review.(LM) #38.3.101

Wang, Quanlai. The research on Emile Borel’s work relative to function singularities [inChinese]. Studies in the History of Natural Sciences 27 (2) (2008), 236–248. “Discusses thebackground [and] the development of his idea and the influence of his theory on othermathematicians at that time.” (KP) #38.3.102

Wilson, Curtis. The Hill–Brown Theory of the Moon’s Motion. Its Coming-to-be andShort-lived Ascendancy (1877–1984). With an appendix of undated pages from a file ofGeorge William Hill (Sources and Studies in the History of Mathematics and Physical Sci-ences). Springer: New York, 2010, xiv+323 pp. The author documents the rise and fall ofthe Hill–Brown lunar theory by sketching the history of the lunar theory up to 1870 andby describing Hill’s investigations on perturbation theory. He also describes Brown’s devel-opment of the theory and the analytical solutions to the lunar problem. See the review byChris M. Linton in Mathematical Reviews 2662365 (2011d:70005). (LM) #38.3.103

Zhai, Shaodan. See #38.3.104.

Zhao, Chenyang; and Zhai, Shaodan. Galton and the invention of correlation [in Chi-nese]. Journal of Northwest University. Natural Sciences Edition 38 (4) (2008), 680–684.Describes the role of the polymath Francis Galton (1822–1911) in establishing key statisti-cal concepts such as correlation. (KP) #38.3.104

See also #38.3.61; and #38.3.73.

20th century

Abramson, Michael. See #38.3.126.


Amdeberhan,T.; Espinosa, O.R.; Moll, V.H.; and Straub, A. Wallis–Ramanujan–Schur–Feynman. American Mathematical Monthly 117 (7) (2010), 618–632. “The authors presentseveral formulas with integrals, binomial coefficients, Schur functions, Matsubara sums andmake connections with Feynman diagrams.” This is the review by Florin Nicolae in Zen-tralblatt MATH 1202.01061. (TBC) #38.3.105

Anantharaman, Nalini. On the existence of closed geodesics, in #38.3.119, pp. 143–160. #38.3.106

Babbitt, Donald; and Goodstein, Judith. Federigo Enriques’s quest to prove the “Com-pleteness Theorem”. Notices of the American Mathematical Society 58 (2) (2011), 240–249.In 1905, Enriques (1871–1946) gave a flawed proof of the Completeness Theorem, whichbecame a key ingredient in the proof of the Fundamental Theorem of Irregular Surfaces.Enriques spent the rest of his life trying to find a proof using only algebro-geometric tech-niques and although he had insightful ideas, he lacked the tools to develop them with fullrigor. The article includes a previously unpublished 1945 letter from Enriques to BeniaminoSegre. (DJM) #38.3.107

Béguin, Franc�ois. Poincaré’s memoir for the prize of King Oscar II: Celestial harmonyentangled in homoclinic intersections, in #38.3.119, pp. 161–191. #38.3.108

Bergeron, Nicolas. Differential equations with algebraic coefficients over arithmeticmanifolds, in #38.3.119, pp. 47–71. On the contributions of Poincaré to the developmentof hyperbolic geometry. See the review by Lee-Peng Tao in Mathematical ReviewsMR2647618. (DJM) #38.3.109

Bessières, Laurent; Besson, Gérard; and Boileau, Michel. The proof of the Poincaré con-jecture, according to Perelman, in #38.3.119, pp. 243–255. #38.3.110

Besson, Gérard. See #38.3.110.

Boffetta, Guido; Lacorata, Guglielmo; and Vulpiani, Angelo. Low-dimensional chaosand asymptotic time behavior in the mechanics of fluids, in #38.3.119, pp. 207–223. #38.3.111

Boileau, Michel. See #38.3.110.

Borga, Marco; Fenaroli, Giuseppina; and Garibaldi, Antonio C. Un inedito di Alessan-dro Padoa [An unpublished paper by Alessandro Padoa]. Epistemologia 32 (2) (2009), 233–254. This paper explores the work of a member of Peano’s mathematical school, AlessandroPadoa, including the text of an unpublished paper of his. See the review by Luigi Borzac-chini in Zentralblatt MATH 1203.01012. (LM) #38.3.112

Borowitz, Sidney. The Norwegian and the Englishman. Physics in Perspective 10 (3)(2008), 287–294. The author sketches the lives and work of the Norwegian physicist Kris-tian Birkeland (1867–1917) and the English mathematician Sydney Chapman (1888–1970)focusing on Chapman’s controversy with Birkeland over the origin and development ofauroras. (LM) #38.3.113

Boskoff, Wladimir G.; Dao, Vyvy; and Suceava, Bogdan D. From Felix Klein’s Erlan-gen program to Secondary Game: Dan Barbilian’s poetry and its connection with founda-tions of geometry. Memoriile Sect�iilor S�tiint�ifice (IV) 31 (2008), 17–33. Dan Barbilian(1895–1961) was both a geometer and a poet. This paper is the first attempt to understand


both his geometry and poetry and explore the connections between them. See the review byVictor V. Pambuccian in Mathematical Reviews 2582942 (2011b:01003). (DJM) #38.3.114

Bowman, Joshua. See #38.3.119.

Busev, V.M. Reforms of the mathematical education in school in the USSR [in Russian].Istoriko-Matematicheskie Issledovaniya (2) 13 (48) (2009), 154–184. A discussion of Sovietreform of school mathematics education in the period 1920–1938. See the review by GrozioStanilov in Zentralblatt MATH 1200.01016. (DJM) #38.3.115

Cartier, Pierre. Poincaré’s Calculus of probabilities, in #38.3.119, pp. 279–291. #38.3.116

Cerroni, Cinzia. Some models of geometries after Hilbert’s Grundlagen. Rendiconti diMatematica e delle Sue Applicazioni (VII) 30 (1) (2010) 47–66. The paper discusses the con-tributions of Max Dehn and his student Ruth Moufang to the foundations of geometry inthe research tradition opened up by Hilbert’s “Grundlagen der Geometrie”. See review byVolker Peckhaus in Zentralblatt MATH 1203.01013. (TBC) #38.3.117

Cerveau, Dominique. Singular points of differential equations: On a theorem of Poin-caré, in #38.3.119, pp. 99–112. #38.3.118

Charpentier, Éric; Ghys, Étienne; and Lesne, Annick, eds. The Scientific Legacy of Poin-caré. Translated from the 2006 French original by Joshua Bowman. (History of Mathemat-ics 36). Providence, RI: American Mathematical Society, 2010, xiv+392 pp. A collection ofindividual chapters, each on a different aspect of Poincaré’s work. The articles are listed orabstracted separately as: #38.3.67; #38.3.85; #38.3.88; #38.3.106; #38.3.108; #38.3.109;#38.3.110; #38.3.111; #38.3.116; #38.3.118; #38.3.123; #38.3.125; #38.3.127; #38.3.132;#38.3.135; #38.3.137; #38.3.139; #38.3.148; and #38.3.159. (DJM) #38.3.119

Dao, Vyvy. See #38.3.114.

Elstrodt, Júrgen. Alte Briefe – aktuelle Fragen. Aus Hausdorffs Briefwechsel [Old letters,current questions. From Felix Hausdorff’s correspondence]. Mitteilungen der DeutschenMathematiker-Vereinigung 18 (3) (2010), 183–187. A letter from Pavel Alexandrov to FelixHausdorff in 1932 relayed a question on measurable sets posed by Kolmogorov. The prob-lem is still not solved in full generality, but there has been some recent progress by M. Lacz-kovich. See the review by Reinhard Siegmund-Schultze in Zentralblatt MATH 1205.01014.(DJM) #38.3.120

Erickson, Paul. Mathematical models, rational choice, and the search for Cold War cul-ture. Isis 101 (2) (2010), 386–392. This article explores episodes in the history of game the-ory from its early development to its subsequent spread across disciplines ranging frompolitical science to evolutionary biology as a result of debates about the nature of “ratio-nality” and “choice” that marked the Cold War era. (LM) #38.3.121

Espinosa, O.R. See #38.3.105.

Fenaroli, Giuseppina. See #38.3.112.

Fick, Dieter; and Kant, Horst. Walther Bothe’s contributions to the understanding ofthe wave-particle duality of light. Studies in History and Philosophy of Science. Part B. Stud-ies in History and Philosophy of Modern Physics 40 (4) (2009), 395–405. An analysis of Wal-ther Bothe’s (1891–1957) contributions to the understanding of the wave-particle duality of


light in the 1920s, from his 20 theoretical and experimental papers, many of them jointwork with Hans Geiger (1882–1945). (DJM) #38.3.122

Franc�oise, Jean-Pierre. The theory of limit cycles, in #38.3.119, pp. 87–97. On Poincaré’swork on limit cycles and Hilbert’s 16th Problem. See the review by Michèle Pelletier inMathematical Reviews 2647620. (DJM) #38.3.123

Garibaldi, Antonio C. See #38.3.112.

Getoor, Ronald. J.L. Doob: Foundations of stochastic processes and probabilisticpotential theory. Annals of Probability 37 (5) (2009), 1647–1663. An appreciation of thework of probabilist J.L. Doob (1910–2004). See the review by René L. Schilling in Mathe-matical Reviews 2561428 (2011b:01008). (DJM) #38.3.124

Ghys, Étienne. See #38.3.119.

Ghys, Étienne. Poincaré and his disk, in #38.3.119, pp. 17–46. #38.3.125

Goodstein, Judith. See #38.3.107.

Gotel, Orlena. See #38.3.141.

Gröbner, Wolfgang. On the algebraic properties of integrals of linear differential equa-tions with constant coefficients. Translated from the German by Michael Abramson. ACMCommunications in Computer Algebra 43 (1–2) (2009), 24–46. An English translation ofGröbner’s classic 1939 paper introducing what is now known as the Gröbner basis method.See the review by Alexander B. Levin in Mathematical Reviews 2571830 (2011b:13001).(DJM) #38.3.126

Heinzmann, Gerhard. Henri Poincaré and his thoughts on the philosophy of science, in#38.3.119, pp. 373–391. A critical assessment of Poincaré’s depth as a philosopher of sci-ence. See the review by Øystein Linnebo in Zentralblatt MATH 1195.00015.(DJM) #38.3.127

Helgason, Sigurdur. The Selected Works of Sigurdur Helgason. Edited by Gestur Ólafs-son and Henrik Schlichtkrull. Providence, RI: American Mathematical Society, 2009,xlii+715 pp. A selection of 32 articles by Helgason on geometric analysis from 1956 to2007. (DJM) #38.3.128

Hilbert, David. David Hilbert’s Lectures on the Foundations of Physics 1915–1927. Rel-ativity, Quantum Theory and Epistemology. Edited by Tilman Sauer and Ulrich Majer incollaboration with Arne Schirrmacher and Heinz-Jürgen Schmidt. (David Hilbert’s Founda-tional Lectures 5). Berlin: Springer-Verlag, 2009, xii+795 pp. The second published volumeof Hilbert’s unpublished lecture notes from his courses on the foundations of mathematicsand physics in Göttingen. This volume contains notes spanning the period from 1915 to1927 on foundations of physics, epistemology and quantum theory. See the review by Vol-ker Peckhaus in Mathematical Reviews 2569313. (DJM) #38.3.129

Hinch, John. A perspective of Batchelor’s research in micro-hydrodynamics. Journal ofFluid Mechanics 663 (2010), 8–17. The author describes George Keith Batchelor’s keyresults on turbulence and on low-Reynolds-number suspensions of particles ten years afterhis death. (LM) #38.3.130

Kant, Horst. See #38.3.122.


Knuth, Donald E. Selected Papers on Design of Algorithms. (CSLI Lecture Notes 191).Stanford, CA: CSLI Publications, 2010, xvi+453 pp. Donald Knuth has put together a col-lection of his papers on the design of algorithms, unifying the formatting and correctingerrors in the originals. (DJM) #38.3.131

Kowalski, Emmanuel. Poincaré and analytic number theory, in #38.3.119, pp. 73–85. Asurvey of the work of Poincaré on Poincaré series. See the review by Robert Juricevic inMathematical Reviews 2647619. (DJM) #38.3.132

Kunita, Hiroshi. Itô’s stochastic calculus: Its surprising power for applications. Stochas-tic Processes and their Applications 120 (5) (2010), 622–652. A survey of the work of KiyosiItô (1915–2008) in stochastic integrals and stochastic differential equations, including appli-cations in mathematical finance. See the review by A.I. Dale in Mathematical Reviews2603057 (2011b:60215). (DJM) #38.3.133

Lacki, Jan; Ruegg, Henri; and Wanders, Gérard, eds. E.C.G. Stueckelberg, An Uncon-ventional Figure of Twentieth Century Physics. Selected Scientific Papers with Commentaries.Basel: Birkhäuser Verlag, 2009, xvi+422 pp. A brief biography, extensive bibliography, andselection of papers of Swiss mathematician and physicist Ernst C.G. Stueckelberg (1905–1984). Several introductory chapters provide context for Stueckelberg’s papers.(DJM) #38.3.134

Lacorata, Guglielmo. See #38.3.111.

Le Bellac, Michel. The Poincaré group, in #38.3.119, pp. 329–350. #38.3.135

Lesne, Annick. See #38.3.119.

Lorenz, Falko; and Roquette, Peter. On the Arf invariant in historical perspective.Mathematische Semesterberichte 57 (1) (2010), 73–102. An examination of the career andwork of Cahit Arf (1910–1997), focusing on the interaction between Arf and his advisorHelmut Hasse. See the review by Albert C. Lewis in Zentralblatt MATH 1201.01015.(CH) #38.3.136

Majer, Ulrich. See #38.3.129.

Mawhin, Jean. Henri Poincaré and the partial differential equations of mathematicalphysics, in #38.3.119, pp. 257–277. #38.3.137

Mazliak, Laurent; and Tazzioli, Rossana. Mathematicians at War. Volterra andhis French Colleagues in World War I (Archimedes 22). Dordrecht: Springer, 2009,ix+194 pp. This book presents the ideas, concerns and hesitation of the Italian mathemati-cian, Vito Volterra (1860–1940), and his French colleagues Émile Borel (1871–1956),Jacques Hadamard (1865–1963) and Émile Picard (1855–1941) about World War I througha collection of 115 letters exchanged between Volterra and his French friends from Septem-ber 1914 to August 1920. See the review by Ubiratan D’Ambrosio in Zentralblatt MATH1201.01016. (LM) #38.3.138

Mendès France, Michel. Poincaré and geometric probability, in #38.3.119, pp. 293–305. #38.3.139

Moffatt, H.K. George Batchelor: A personal tribute, ten years on. Journal of FluidMechanics 663 (2010), 2–7. This paper remembers George Keith Batchelor, formerly Pro-fessor of Fluid Dynamics at the University of Cambridge and Founder Editor of the Jour-


nal of Fluid Mechanics, ten years after his death as scientist and mentor of generations ofresearchers. (LM) #38.3.140

Moll, V.H. See #38.3.105.

Morris, Stephen; and Gotel, Orlena. The role of flow charts in the early automation ofapplied mathematics. British Society for the History of Mathematics Bulletin 26 (1) (2011),44–52. Drawing on archival material in the US and UK, the authors examine one aspect ofmathematicians’ early efforts to use computers in their work. (PWH) #38.3.141

Mumford, David. Intuition and rigor and Enriques’s quest. Notices of the AmericanMathematical Society 58 (2) (2011), 250–260. Mumford translates key parts of Enriques’1936 paper “Curve infinitamente vicine sopra una superficie algebrica” to illustrate his“visionary” ideas on resolving his proof of the Completeness Theorem and shows howto complete the argument using modern tools. (DJM) #38.3.142

Ólafsson, Gestur. See #38.3.128.

Panchev, S. Edward N. Lorenz – founder of the modern chaos theory. Journal of the Cal-cutta Mathematical Society 4 (1–2) (2008), 15–30. A review of the work of Lorenz (1917–2008) on chaotic systems of differential equations and some later systems derived fromhis work. See the review by Antonín Slavík in Zentralblatt MATH 1203.01029.(DJM) #38.3.143

Parshin, Aleksej N. Mathematik in Moskau – es war eine große Epoche [Mathematics inMoscow: It has been a great era]. Mitteilungen der Deutschen Mathematiker-Vereinigung 18(1) (2010), 43–48. A look back to the seminar culture of mathematics in the Soviet Unionand discussion of its decline with the emigration of many mathematicians in the post-Sovietperiod. See the review by Victor V. Pambuccian in Zentralblatt MATH 1204.01042.(DJM) #38.3.144

Pérez, Enric; and Sauer, Tilman. Einstein’s quantum theory of the monatomic ideal gas:Non-statistical arguments for a new statistics. Archive for History of Exact Sciences 64 (5)(2010), 561–612. The authors analyse the third of the three papers in which Einstein pre-sented his quantum theory of ideal gas (1924–1925). See the review by Girish Ramaiahin Zentralblatt MATH 1202.01077. (TBC) #38.3.145

Pillai, S. Sivasankaranarayana. Collected Works of S. Sivasankaranarayana Pillai. Vols. Iand II: Published/Unpublished Papers and Letters. R. Balasubramanian and R. Thangadu-rai, eds., Mysore: Ramanujan Mathematical Society, 2010, lxxix+1–345/vol. 1; xxiii+347–724/vol. 2. Contains articles by the editors on various aspects of Pillai’s work on numbertheory, in addition to some of Pillai’s own writings and correspondence. The book includesbibliographies of his output in various periods and a classification of his papers. See thereview by Grozio Stanilov in Zentralblatt MATH 1200.01048. (KP) #38.3.146

Pollard, Stephen. ‘As if’ reasoning in Vaihinger and Pasch. Erkenntnis 73 (1) (2010), 83–95. A study of the intellectual interaction between the mathematician Moritz Pasch (1843–1930) and the philosopher Hans Vaihinger (1852–1933). See the review by Elliott Mendel-son in Zentralblatt MATH 1200.01023. (CH) #38.3.147

Pomeau, Yves. Henri Poincaré as an applied mathematician, in #38.3.119, pp. 351–371.On Poincaré’s contributions to applied mathematics. (DJM) #38.3.148


Raussen, Martin; and Skau, Christian. Interview with Abel laureate John Tate. Noticesof the American Mathematical Society 58 (3) (2011), 444–452. A wide-ranging interviewwith John Tate before his award of the Abel Prize on teaching and research mathematicsand roles of mathematics in the future. (DJM) #38.3.149

Roquette, Peter. See #38.3.136.

Roquette, Peter. Numbers and models, standard and nonstandard. MathematischeSemesterberichte 57 (2) (2010), 185–199. The author relates his personal recollections ofAbraham Robinson and his non-standard analysis. See review by Jean-Paul Pier in Zen-tralblatt MATH 1203.01030. (TBC) #38.3.150

Ruegg, Henri. See #38.3.134.

Sakhri, Mohsen. See #38.3.152.

Sarason, Donald, Coordinating ed. A tribute to Henry Helson. Notices of the AmericanMathematical Society 58 (2) (2011), 274–288. Reminiscences and appreciation of harmonicanalyst Henry Helson (1927–2010). Along with the article by Sarason, there are contribu-tions by Y. Katznelson, John Wermer, William A. Veech, William Arveson, Kathy Merrill,Jun-ichi Tanaka, John E. McCarthy, Herbert Medina, and Farhad Zabihi.(DJM) #38.3.151

Sauer, Tilman. See #38.3.129; and #38.3.145.

Schirrmacher, Arne. See #38.3.129.

Schlaudt, Oliver; and Sakhri, Mohsen, eds. Louis Couturat – Traité de Logique algorith-mique [Louis Couturat – Treatise on Algorithmic logic]. Basel: Birkhäuser, 2010, viii+317 pp.A previously unpublished treatise by Louis Couturat, dating from around 1901, that wasdiscovered by the second-named editor in 2003 at the municipal library of La Chaux-de-Fonds in Switzerland. The content of the book relates to symbolic logic and set theory(and not, it should be noted, to the modern theory of algorithms). In addition to Couturat’stext, the book contains an extensive introduction by the editors and a variety of supplemen-tary materials. See the review by Elliott Mendelson in Zentralblatt MATH 1200.01051.(CH) #38.3.152

Schlichtkrull, Henrik. See #38.3.128.

Schlomiuk, Norbert. The great mathematical research centres of the 20th century andthe “miracle” of Lwow I. Gan: ita-Bh�arat�ı 28 (1–2) (2006), 103–109. An overview of themathematical culture in Europe from 1900 to 1940, focusing on the great mathematiciansand the important research centers of the day (particularly the Lwów School of Mathemat-ics). See the review by Girish Ramaiah in Zentralblatt MATH 1200.01025. (CH) #38.3.153

Schmidt, Heinz-Jürgen. See #38.3.129.

Skau, Christian. See #38.3.149.

Smith, James T. Definitions and nondefinability in geometry. American MathematicalMonthly 117 (6) (2010), 475–489. The paper is concerned with early 20th century attemptsto reformulate geometry on a more rigorous basis, with emphasis on the work of MarioPieri (1860–1913) and Alfred Tarski (1901–1983). (DJM) #38.3.154


Soifer, Alexander. Issai Schur, the first giant of Ramsey theory: An essay in seven parts.Congressus Numerantium 195 (2009), 205–220. A study of the role played by Issai Schur inthe development of Ramsey theory, emphasizing Schur’s continuing contributions after thepublication of his most famous result in this area (in 1916). See the review by AntonínSlavík in Zentralblatt MATH 1201.01027. (CH) #38.3.155

Straub, A. See #38.3.105.

Suceava, Bogdan D. See #38.3.114.

Szabó, Péter Gábor. On the roots of the trinomial equation. Central European Journal ofOperations Research 18 (1) (2010), 97–104. On the work of Hungarian mathematician Jen}oEgervary (1891–1958) on locating the roots of trinomial equations. See the review by JanM. Verschelde in Mathematical Reviews 2593126 (2011d:65110). (DJM) #38.3.156

Tazzioli, Rossana. See #38.3.138.

Vulpiani, Angelo. See #38.3.111.

Wanders, Gérard. See #38.3.134.

Wang, Chaowang. See #38.3.158.

Wang, Xian Fen. Contributions of Hassler Whitney to graph theory [in Chinese]. Studiesin the History of Natural Sciences 29 (1) (2010), 87–103. A study of the early contributionsof Hassler Whitney (1907–1989) to graph theory, in particular planar graphs, chromaticpolynomials and matroid theory, before he moved over to topology. (DJM) #38.3.157

Xu, Chuansheng. See #38.158.

Yang, Jing; Xu, Chuansheng; and Wang, Chaowang. A study on the influence of L.Bachelier’s Theory of Speculation on mathematics [in Chinese]. Studies in the History ofNatural Sciences 27 (1) (2008), 94–104. Examines the effect of Bachelier’s seminal financialmathematics work on the development of mathematics and economics. (KP) #38.3.158

Yger, Alain. The concept of “residue” after Poincaré: Cutting across all of mathematics,in #38.3.119, pp. 225–241. #38.3.159

Zambelli, Stefano. Chemical kinetics and diffusion approach: The history of the Klein–Kramers equation. Archive for History of Exact Sciences 64 (4) (2010), 395–428. The articlefocusses on the development of the stochastic diffusion approach to chemical reactions,and, in particular, why it was neglected for so long. See the review by Thorsten Dickhausin Zentralblatt MATH 1204.01020. (DJM) #38.3.160

See also #38.3.102.

Reviewers

Index of authors of reviews in Mathematical Reviews, Zentralblatt MATH, and otherpublications that are referenced in these abstracts.

Dale, A.I. — #38.3.133.van Dalen, Benno — #38.3.41; and #38.3.42.Borzacchini, Luigi — #38.3.80; and #38.3.112.

D’Ambrosio, Ubiratan — #38.3.138.Dickhaus, Thorsten — #38.3.160.Borzacchini, Luigi — #38.3.80; and #38.3.112.

Dimitric, Radoslav M. — #38.3.9; and#38.3.76.

Duda, Roman — #38.3.66; and #38.3.97.Fischer, Hans — #38.3.19.Gottwald, Siegfried J. — #38.3.98.Harkleroad, Leon — #38.3.88.Høyrup — #38.3.22; #38.3.48; #38.3.61; and

#38.3.71.Hsu, Pao-Sheng — #38.3.33.Hunger, Hermann — #38.3.20; and #38.3.21.Juricevic, Robert — #38.3.132.Katz, Victor J. — #38.3.7.Kaunzner, W. — #38.3.53.Kleinert, A. — #38.3.92.Knobloch, Eberhard — #38.3.50; and

#38.3.51.Koetsier, Teun — #38.3.81.Lemmermeyer, Franz — #38.3.10; and

#38.3.95.Levin, Alexander B. — #38.3.126.Lewis, Albert C. — #38.3.73; #38.3.86; and

#38.3.136.Linnebo, Øystein — #38.3.127.Linton, Chris M. — #38.3.103.Martzloff, Jean-Claude — #38.3.29; #38.3.32;

#38.3.34; #38.3.35; and #38.3.39.Massa Esteve, Maria Rosa — #38.3.54.McRae, Alan S. — #38.3.63.Mendelson, Elliott — #38.3.147; and

#38.3.152.Borzacchini, Luigi — #38.3.80; and #38.3.112.

Milka, Anatoliy — #38.3.60.Murawski, Roman — #38.3.87; and #38.3.89.Nicolae, Florin — #38.3.105.O’Cairbre, Fiacre — #38.3.75.Palacián, Jesús F. — #38.3.67.Pambuccian, Victor V. — #38.3.114; and

#38.3.144.Pande, Neeraj Anant — #38.3.17.Peckhaus, Volker — #38.3.117; and #38.3.129.Pelletier, Michèle — #38.3.123.Pier, Jean-Paul — #38.3.150.Ra�dulescu, Teodora-Liliana — #38.3.59; and

#38.3.62.Ramaiah, Girish — #38.3.24; #38.3.145; and

#38.3.153.Rogovchenko, Svitlana P. — #38.3.13; and

#38.3.23.Schilling, René L. — #38.3.124.Schlote, Karl-Heinz — #38.3.84.Siegmund-Schultze, Reinhard — #38.3.73;

#38.3.90; and #38.3.120.Slavík, Antonín — #38.3.143; and #38.3.155.Stanilov, Grozio — #38.3.115; and #38.3.146.Teo, Lee-Peng Teo — #38.3.109.Thrivikraman, T. — #38.3.25; and #38.3.26.Vaillancourt, Rémi — #38.3.18.Verschelde, M. — #38.3.156.Ward, Thomas — #38.3.85.


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