BULLETIN

May/Mai 2009 Number/le numero 44

WHAT’S INSIDE

President’s Message [Duncan Melville] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 2

ArticlesAnnouncements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 3Annals of Science Prize [Katharine Brown]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 8Cauchy in Quebec City [David Orenstein] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 10HPM Americas Section in Washington, DC [Amy Ackerberg-Hastings] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 11Web Review: Twitter [Amy Ackerberg-Hastings] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 13

Erwin Kreyszig (1922-2008) [Martin Muldoon] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 15Inequalities as Political Argument [David Orenstein] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 14CMS Winter Meeting [Tom Archibald] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 14Quotations in Context [Dan Sonnenschein] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 16Mathematical Ephemera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 18Book Reviews [Yvon Gauthier, Mike Molinsky] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pages 6 & 10ReportsCSHPM/SCHPM & CMS Meeting Information [Tom Drucker & Tom Archibald]. . . . . . . . . . . . . . . . . . . . .page 72008 Financial Statements [Nathan Sidoli] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 9From the Webmaster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 12Annual General Meeting CFHSS [Ed Cohen] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 17New Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 19From the Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 19

Canadian Society for Historyand Philosophy of Mathematics

Societe canadienne d’histoire etde philosophie des mathematiques

ISSN 0835-5924

ABOUT THE SOCIETY

Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Societe canadi-enne d’histoire et de philosophie des mathematiques(CSHPM/SCHPM) promotes research and teachingin the history and philosophy of mathematics. Offi-cers of the Society are:

President : Duncan J. Melville, St. LawrenceUniv., Canton, NY 13617, USA, dmelville@stlawu.eduVice-President : Jean-Pierre Marquis, Universitede Montreal, Montreal, QC H3C 3J7, CA, jean-pierre.marquis@umontreal.caSecretary : Pat Allaire, 148-18 60 Ave., Flushing,NY 11355, USA, PatAllaire@gmail.comTreasurer : Nathan Sidoli, Waseda University, Tokyo,169-8050, Japan, sidoli@aoni.waseda.jpPast President : Alexander Jones, Institute for theStudy of the Ancient World, New York University,New York, NY 10028, USA, alexander.jones@nyu.edu

Members of Council

Francine Abeles, Kean University, Union, NJ07083, USA, fabeles@kean.eduGregory Lavers, Concordia University, Montreal,QC H3G 1M8, CA, laverscourses@gmail.comAdrian Rice, Randolph-Macon College, Ashland,VA 23005, USA, arice4@rmc.eduSylvia Svitak, Queensborough Comm. Coll., CUNY,Bayside, NY 11364, USA, Ssvitak@qcc.cuny.edu

The Society’s Web Page (www.cshpm.org) is main-tained by Michael Molinsky, University of Maine atFarmington, Farmington, ME 04938, USA, michael.-molinsky@maine.edu. The Proceedings of the AnnualMeeting are edited by Antonella Cupillari, PennState Erie, The Behrend College, Erie, PA 16563,USA, axc5@psu.edu. The Society’s Archives are man-aged by Michael Molinsky (see above).

New Members are most cordially welcome; please con-tact the Secretary.

From the President

Since my last column, many members of our societyhave been actively promoting history and philosophyof mathematics by reporting their research, organiz-ing meetings and workshops, increasing our visibil-ity, and strengthening our ties, especially with theCMS in Canada and the AMS and MAA south ofthe border. Both history and philosophy were wellrepresented at the Joint Mathematics Meetings inWashington, DC, this past January. There was anMAA minicourse on ‘Teaching a course in the his-tory of mathematics’, organized by Fred Rickey andVictor Katz, and HOMSIGMAA sessions with gen-erous doses of philosophy of mathematics, includingthe guest lecture by Chandler Davis and a panel on‘The Intersection of the History and Philosophy ofMathematics’, both of which were co-sponsored bythe philosophy SIGMAA. Additionally, there was ajoint AMS-MAA Special Session on History of Math-ematics organized by Joe Dauben, Karen Parshall,Patti Hunter and Deborah Kent, which was housed inan impressively large room that many speakers man-aged to fill, a testament to the growing interest inhistory among mathematicians in general.

For several years now, Tom Archibald has taken onthe role of bringing history to the CMS at its wintermeeting, and he continued that this past year, jointlyorganizing a session with Alex Jones on History andPhilosophy of Mathematics at the meeting in Ottawain December. A fine slate of speakers presented re-sults across both areas. Thanks to Tom, a sessionin history has become a routine part of programmingfor the CMS winter meeting and so will improve ourconnections with the community of Canadian math-ematicians, as has happened on the US side with theactivities at the Joint Meetings.

A measure of this integration is our upcoming annualmeeting, held in conjunction with the CMS at Memo-rial University in St. John’s, Newfoundland. This isour third joint meeting with the CMS, following meet-ings at McMaster in 2000 and Waterloo in 2005. Weare a society much in demand and have been rotatingour meetings between the CMS, the BSHM and theLearneds. This year, Tom Drucker is the organizerfor the general session and Tom Archibald is coor-dinating the special session on ‘History of the Rela-

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tionship Between Mathematics and the Physical Sci-ences’. With the two sessions combining to featuretwo dozen speakers, there will be plenty of historyand philosophy on offer. Our May speaker this year,advertized as the CSHPM Plenary Speaker, is JeremyGray, who will be speaking on Sunday, June 7, from10:30 to 11:15. We have, as usual, a strong program,thanks to our many speakers and volunteer organiz-ers. I look forward to seeing many of you in St. John’sin June.

Figure 1: Duncan, Peter and the Editor

Along with a busy meeting schedule, another indexof the health of a field is publications, both in jour-nals and as books. Here, history and philosophy ofmathematics has been going through something of aboom, with members of our society at the fore. Injust the past few months have appeared Janet Beeryand Jackie Stedall’s volume, Thomas Harriot’s Doc-trine of Triangular Numbers: The Magisteria Magna,Kim Plofker’s Mathematics in India, Bruce Burdick’sMathematical Works Printed in the Americas, 1554–1700, Glen Van Brummelen’s The Mathematics ofthe Heavens and the Earth: The Early History ofTrigonometry, and Jean-Pierre Marquis’ From a Ge-ometrical Point of View: A Study of the Historyand Philosophy of Category Theory. Meanwhile, RobBradley and Ed Sandifer’s Cauchy’s Cours d’analyse:An Annotated Translation is available for pre-order atAmazon. All this is without mentioning the steadyflow of journal articles, nor the continuing solid ev-idence of our members’ production evinced by ourin-house Proceedings. The field, and the society, isdoing well.

Duncan Melville

Announcements

Congratulations to George Englebretsen, who wasawarded a DCL, honoris causa by Bishop’s Univer-sity in May 2008!

Bravo also for CSHPM Treasurer Nathan Sidoli, whohas accepted a tenure track position at Waseda Uni-versity in Tokyo. (Nathan has been performing logis-tical wizardry to fulfill his CSHPM duties, but he hasannounced that he will step down when we next holdelections in May 2010. It’s not too early for Cana-dian members to consider volunteering themselves orsomeone else for this key Council position.)

Best wishes to Bob Stein, who officially retiredfrom California State University, San Bernardino, inMarch. The event was marked with a big party andpossibly a bigger cleaning out of his office. His cre-ative commute is described at news.csusb.edu/story -full.asp?articleID=7878. Bob has since returned tohis other home base in Portland, OR.

Pat Allaire has been blessed with a second—andinstant—grandchild. Her son, Ken, proposed to hisgirlfriend, Rebeca, in Panama on Christmas Eve 2008.On Christmas Day, he officially adopted Rebeca’stwo-year-old daughter, Magdiel.

Figure 2: Magdiel Allaire

The latest volume in the Studies in the History ofMathematics Series of the Johns Hopkins Univer-sity Press is Bruce Burdick’s Mathematical Works

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Printed in the Americas, 1554–1700. He provides bib-liographic information and descriptions for 39 trea-tises and 220 almanacs written in Latin, Spanish,and English, and printed in Mexico, Lima, and theEnglish colonies of Massachusetts, Pennsylvania, andNew York. Notable titles include Alonso de la VeraCruz’s 1554 logic text, the Recognitio Summularum;El lunario, Regimiento de Salud, y Pronostico de tem-porales, a 1676 almanac by Feliciana Ruiz, the firstwoman to produce a mathematical work in the Ameri-cas; and the English-language Tenebrae (1697) by Ja-cob Taylor, a treatise on solving triangles and otherfigures using basic trigonometry.

Janet Beery and Jackie Stedall have edited ThomasHarriot’s Doctrine of Triangular Numbers: the ‘Mag-isteria Magna’ for the Heritage of European Mathe-matics series of the European Mathematical Society.In addition to the 1618 manuscript treatise, they pro-vide commentary and an introductory essay.

John S. D. Glaus has translated and published the1927 biography, Leonhard Euler and His Friends, byLuis-Gustave du Pasquier. Ronald Calinger con-tributes a historiographical introduction. See theMAA Review by Herbert Kasube, www.maa.org/maa-%20reviews/01211.jpg

Volume 34 of the AMS/LMS History of Mathematicsseries is Pioneering Women in American Mathemat-ics: The Pre-1940 PhD’s, by Judy Green and JeanneLaDuke. Green and LaDuke compiled biographies for228 women. They also provide an extended intro-ductory essay, comparing the women’s family back-grounds, education, careers, and other professionalactivities. Extended biographies and bibliographicalinformation are available from the companion websitefor the book: www.ams.org/bookpages/hmath-34.

Jean-Pierre Marquis’s From a Geometrical Point ofView: A Study of the History and Philosophy of Cate-gory Theory is volume 14 in Springer’s series in Logic,Epistemology, and the Unity of Science. He beginswith Eilenberg and Mac Lane’s work in the early1940s and pays particular attention to the philosoph-ical aspects of the evolution of category theory.

Kim Plofker’s Mathematics in India has appearedfrom Princeton University Press. Covering antiquityto the early modern period, Kim reexamines the fewfacts about Indian mathematics that have become

common knowledge—such as the Indian origin of Ara-bic numerals—and sets them in a larger textual andcultural framework. She shows that Indian mathe-matics appears not as a disconnected set of discover-ies, but as a lively, diverse, yet strongly unified disci-pline, intimately linked to other Indian forms of learn-ing.

Princeton has also published Glen Van Brummelen’sThe Mathematics of the Heavens and the Earth: TheEarly History of Trigonometry. He treats trigonomet-ric precursors in ancient Egypt, Babylon, and Greece,culminating with Hipparchus; traces the developmentof trigonometry as a full-fledged discipline in Indiaand Islam; explores applications to geography andseafaring navigation in the European Middle Agesand Renaissance; and concludes that trigonometryretained its ancient roots at the same time that itbecame an important part of the foundation of mod-ern mathematics.

On March 12, Victor J. Katz delivered the lecture,“Combinatorics in Islamic and Hebrew Sources,” tothe annual Spring Colloquium of the Immaculata Uni-versity Department of Mathematics, Computer Sci-ence, & Physics.

On March 17 at Swarthmore College, Ken Manderspresented “Uniformity and Generality in Mathemat-ics” jointly with Paolo Mancosu’s lecture, “Style inHistory and Philosophy of Mathematics.” The ses-sion was sponsored by a grant from the Mellon Foun-dation.

On May 7, Len Berggren will lecture on “Conflict andSynergy in Islam’s Relation to the Mathematical Sci-ences.” The lecture is part of a colloquium sponsoredby the Center for the Study of Religion at The OhioState University, which will, in the words of the or-ganizers, provide “a substantive examination of howscience, broadly understood to include philosophy aswell, has functioned alongside Islam as a religious sys-tem.”

On June 17, Len Berggren will be giving the last talkin a series of eight lectures on the topic “Science andIslam at the Oxford Centre for Islamic Studies. Histalk is titled, “The Mathematical Legacy of Islam.”The Kuwait Foundation for the Advancement of Sci-ence and the OCIS are sponsoring the series.

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The ORESME Reading Group will hold its next semi-annual meeting on Friday-Saturday, October 2–3,2009, at Xavier University in Cincinnati, OH. Thesubject of the seminar will be a careful and criti-cal reading of Gauss’s work on the theory of errors,now celebrating its bicentennial of publication. Thegroup will approach the “Determination of an Or-bit satisfying as nearly as possible any number ofObservations whatsoever,” the Third Section of theSecond Book of Gauss’s Theory of the motion of theheavenly bodies moving about the sun in conic sec-tions (Theoria motus corporum coelestium in section-ibus conicis solem ambientium, 1809), in its 1857English translation by Charles Henry Davis, pub-lished by Dover in 1963 and often reprinted since.There will be two reading sessions, the first on Fri-day evening, 8:00-10:00, and the second on Saturdaymorning, 10:00-12:00. Participants are invited to jointhe group for dinner Friday evening at 6:00 at a lo-cal restaurant, and for breakfast Saturday morning at9:30 at the university. For further information, con-tact Danny Otero (otero@xavier.edu) or Dan Curtin(curtin@nku.edu), or visit the ORESME web page(www.nku.edu/˜curtin/oresme.html).

The annual meeting of The Euler Society will be July12–15 at Roger Williams University in Bristol, RI.Registration fees are payable in person at the confer-ence, either by check or by cash; they are expectedto be in the neighborhood of US$100. We encour-age papers relevant to Euler’s life and work, includinghis contributions to mathematics, science, philosophy,religion or education, as well as papers related tan-gentially to his life, times or work.Papers may be oftwo lengths.The short format is 20 minutes, with fiveminutes for questions.The long format is 50 minutes,also with five minutes for questions. For accommo-dations, contact the Roger Williams University Con-ference Center at (401) 254-7300.Be sure to identifyyourself as an attendee at the conference. Propos-als are due to Ed Sandifer no later than May 15: byemail to esandifer@earthlink.net, or by postal mail to3 Juniper Road, Newtown, CT 06470, USA.

The ARITHMOS seminar will meet at Western Con-necticut State University in Danbury, Connecticut, onMay 2–3. This seminar will discuss selections fromJakob Bernoulli’s Ars Conjectandi. For more infor-mation, see www.arithmos.org.

Our in-house source on all things HOMSIGMAA,Amy Shell-Gellasch, reports: The MAA Math Festwill take place in Portland, OR, August 6–8. Historyevents include a contributed paper session on “ TheHistory and Philosophy of Mathematics, and TheirUses in the Classroom” (organized jointly with POM-SIGMAA), as well as an invited paper session on theHistory of Mathematics organized by Janet Beery andAmy Shell-Gellasch. Speakers in this session include:Fernando Gouvea, Charlotte Simmons, Janet Beery,and Stacy Langton, as well as Jim Tattersall, who weare happy to welcome back to the circuit! To submitan abstract for the contributed papers session, pleasevisit www.maa.org/mathfest/cps.cfm before May 1.Also, the speaker for the opening banquet is our veryown Ed Sandifer!!!!

There are already several events focusing on the im-portant texts of mathematics planned for the JointMathematics Meetings in San Francisco in January2010. Glen Van Brummelen and Amy Shell-Gellaschare hosting an MAA short course the two days prior tothe meetings on “Exploring the Great Books of Math-ematics.” During the meetings Amy and FernandoGouvea will organize a contributed papers session,“Mathematical Texts: Famous, Infamous and Influ-ential.” Fernando encourages our members to submitabstracts; the deadline is in September. The HOM-SIGMAA annual guest speaker will be Reviel Netz,providing an update on the Archimedes Palimpsest.

There will be a Special Session on History and Phi-losophy of Mathematics at the fall Western Section-Meeting of the American Mathematical Society atthe University of California at Riverside on Novem-ber 7–8, 2009, organized by Shawnee McMurran (Cal.State San Bernardino) and Jim Tattersall (Provi-dence). Participants will include Victor Shapiro (UCRiverside), John Sarli (Cal. State San Bernardino),Janet Beery (University of Redlands), Mario Martelli(Claremont-McKenna), Paul Wolfson (West ChesterUniv.), and Larry D’Antonio (Ramapo).

The Frederick V. Pohle Colloquium in the Historyof Mathematics, hosted by the Department of Math-ematics & Computer Science at Adelphi University,presented the following speakers this past year: Pa-tricia R. Allaire (Queensborough Community College,CUNY), “Yours truly, D. F. Gregory” on 15 October2008; Harold M. Edwards (Courant Institute), “Kro-

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necker’s Lost Theorem: An Insight into the Solvabil-ity of Algebraic Equations that Goes Beyond Galois”on 5 November 2008; Herbert C. Kranzer (Adelphi),“Two Centuries of Shock Wave Theory and Appli-cations” on 3 December 2008; Salvatore J. Petrilli(Adelphi), “Monsieur Francois-Joseph Servois: HisLife and Work on Differential Calculus” on 4 Febru-ary 2009; Dominic Klyve (Carthage College), “AnEmbarrassment of Riches: Euler’s Choice of Num-ber Theory Problems Near the End of His Life” on 4March 2009; Judy Green (Marymount), “New York-ers Among the Pioneering American Women in Math-ematics” on 1 April 2009; and Hugh McCague (York),“The Method of Equal Altitudes, or the Indian Cir-cle, in the History of Mathematics, Cosmology andArchitecture” on 6 May 2009.

Nearly ten years after the collegial and successful firstmeeting, Fred Rickey is considering planning a secondHistory of Undergraduate Mathematics in Americaconference at West Point for summer 2010. Pleasemonitor his web page, www.dean.usma.edu/depart-ments/math/people/Rickey/hm/.

The Department of History at Michigan State Univer-sity is adopting the Women in Science Digital Collec-tion established by Judith Zinsser and previously lo-cated at the University of Ohio-Miami. With the helpof MATRIX, the Department of History will be cre-ating a new website which will include Du Chatelet’spapers. Judith has written wonderful introductionsto these papers, which will also be on the new web-site. The goal of the new Women in Science DigitalCollection is to EXPAND the collection to featuredocuments, with introductions wherever possible, forwomen who made significant contributions to a rangeof sciences and in a range of time periods. Do youhave PDFs, JPEGS, or TIFF files of important docu-ments, illustrations, and/or photos which could bedisplayed on the website? Is your university will-ing to share documents in their special collections?Such collaboration would of course result in a creditline, links to your libraries, links to your publicationsabout the featured scientist, and other mutually ben-eficial arrangements! Please contact Dr. GeorginaMontgomery in the Department of History by emailat montg165@msu.edu or by postal mail at 35 EastHolmes Hall, Michigan State University, East Lans-ing, MI 48825, USA.

Peter Griffiths has prepared an article, “EconomicCycles: Are They Generated by Trade, Credit orLegislation?” He suggests reinstating American gov-ernmental controls on credit and providing a $1500annual housing benefit directly to individuals. Read-ers desiring a copy are asked to contact Peter atlowdith73@yahoo.com.

Deadlines have been extended for the conferencecelebrating the International Year of Astronomy,“Astronomy and its Instruments Before and AfterGalileo”, to be held on San Servolo Island, Venice,Italy, between September 28 and October 3, 2009. Forupdated info, see web.oapd.inaf.it/venice2009/. Pre-sentations may be in oral or poster form. For earlyregistration (before May 31), abstracts are due byMay 15, with notification of acceptance by May 28.The regular conference fee is 280 euros. For late reg-istration (before July 15), the deadline for abstractsubmission is July 1, with notification of acceptanceby July 13. The late registration fee is 330 euros.

Book Review: Descartes, Pascal &Fermat

Michel Serfati & Domiques Descotes (eds), Mathe-maticiens francais au XV IIe siecle, Descartes, Fer-mat, Pascal. Clermont-Ferrand: Centre d’Etudes surles Reformes, l’Humanisme et l’Age Classique, Cen-tre International Blaise Pascal, 2008, 280 pp. ISBN:978-2-8451-6354-6. EUR 20,00.

The editors mean this collection of essays to bridgethe gap between the sciences and the humanities orbetween the scientific and the literary disciplines.Descartes and Pascal are certainly known as philoso-phers and mathematicians—or as a religious thinkerin the case of Pascal—but Fermat, as an amateurmathematician and a professional lawyer, is hardlya man of literacy, except for his epistolary exchanges.The most important mathematician in the triad, Fer-mat, is confined here to a a biographical sketch. Itis, however, interesting to discover that all three ofthem were more or less secretive in their mathemati-cal ventures, suspicious of contradictors, whether re-puted savants or pugnacious unlearneds.

Michel Serfati’s contribution, “Constructivismes et

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obscurites dans la Geometrie de Descartes. Quelquesremarques philosophiques,” offers a balanced view ofDescartes’ geometry, including his geometrical con-structivism (inspired by the Ancients) and his ac-tual (and rather obscure) construction of geometri-cal curves with the help of a compass of his inven-tion. Ivo Schneider’s “Trends in German Mathemat-ics at the time of Descartes’ Stay in Germany” reviewsthe work of seventeenth-century German algebraistsand geometers who could have influenced Descartes’methodology. From a different perspective, MatheusAraujo Silva, in his “L’imagination dans la Geometriede Descartes: retour sur une question ouverte,” showsthat Descartes was prone to using physical analogiesin his construction of geometrical curves, a fact thatcould partly explain the obscurities pointed out bySerfati.

The next article, by Bruno Gagneux, “La regle dessignes de Descartes: le long cheminement d’uneimprecion,” offers a careful analysis of Descartes’ ruleof signs, which determines an upper bound for thevariation of signs in a polynomial, a problem whichwill find its final solution in Sturm’s theorem on thenumber of real roots of an algebraic equation. Kro-necker (not mentioned by Gagneux) would further re-fine Sturm’s result in requiring explicit bounds for theintervals of localization (Isolierung) of roots.

Maryvonne Spiesser, in her “Pierre Fermat, profil etrayonnement d’un mathematicien singulier,” digs intothe biography of Pierre de Fermat after Michael Ma-honey’s initial attempts, but here Fermat’s mathe-matics, e.g. the method of infinite descent, is scarcelytouched upon. Spiesser refers nevertheless to the workof Catherine Goldstein and Giovanna Cifoletti, whohas written a doctoral thesis on Fermat’s syntheticgeometry at the University of Montreal under mydirection jointly with Gonzalo Reyes. For Fermat’smost significant invention in number theory, infinitedescent, one should refer to Paolo Bussotti’s recentwork From Fermat to Gauss. Indefinite Descent andMethods of Reduction in Number Theory, Augsburg:Dr. Erwin Rauner Verlag, 2006—see my review inDialogue 47, no. 2 (2008): 403–407.

The last contributions in the volume are devotedto Pascal. In his “La pensee des ordres dans lestraites sur la roulette de Pascal,” Claude Merker ex-amines the genesis of Pascal’s roulette or cycloid,

while Dominique Descotes’ “Constructions du trian-gle arithmetique de Pascal” deals with Pascal’s tri-angle and its multiple uses. These analyses scrutinizePascal’s main contributions to mathematics in projec-tive geometry and combinatorics, the works of a pre-cocious child who became an inventive mathematicianbefore turning to religion. Descartes also left mathe-matics for metaphysics, which he considered a morenoble pursuit.

The volume is an important addition to the litera-ture on the seventeenth-century great men in Frenchmathematics: Descartes, Fermat and Pascal. Thethree knew each other and corresponded, not alwayson friendly terms. Descartes thought that Fermatwas a good mathematician, but a poor metaphysician,adding that “Monsieur de Fermat est gascon, moinon,” which means that in Descartes’ opinion, Fermatwas a braggart; we know, however, that Descartes,with all his reticence, also had some early bursts ofchutzpah! Pascal, probably the most sincere of thethree, was also deprecated by Descartes; he consid-ered Fermat as the greatest geometer in all of Eu-rope, confessing at the same time that he could notfollow his inventions. Finally, it is Fermat, partly lostin his boring job as a court lawyer, who has left themost enduring heritage of seventeenth-century Frenchmathematics.

Yvon Gauthier

CSHPM/SCHPM & CMS MeetingInformation

As you know, June 6–8, 2009, we will meet jointlywith the Canadian Mathematical Society at Memo-rial University in St. John’s, Newfoundland. To reg-ister for the meeting and to reserve housing, pleasevisit www.cms.math.ca/Events/summer09/. A com-plete schedule for the meeting was not available atpress time, but the Executive Council will meet dur-ing lunch on Saturday, June 6, and the Annual Gen-eral Meeting will be held during lunch on Sunday,June 7.

The May lecturer is Jeremy Gray of Open Universityand the University of Warwick. He will be speakingin the auditorium from 10:30 to 11:15, Sunday, June

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7, on the subject, “Mathematics, motion, and truth:the Earth goes round the Sun”.

Tom Archibald (Simon Fraser) is organizing the spe-cial session, “History of the Relationship BetweenMathematics and the Physical Sciences.” Expectedspeakers include:

• Josipa Petrunic (Edinburgh/Toronto): “The cor-respondence between Sir William Rowan Hamil-ton and the Peter Guthrie Tait on mathematicsin natural philosophy”• David Orenstein (Toronto District School Board):

“Helen Hogg’s mathematical methods in estab-lishing variable star light curves”• Lawrence D’Antonio (Ramapo): “The Develop-

ment of a Mathematical Model for Magnetism inthe 18th Century”• Amy Ackerberg-Hastings (Md. Univ. College):

“John Playfair in the Natural Philosophy Class-room”• Tom Archibald (Simon Fraser): “Mathematics

and the applied sciences in Canada before 1949”• Menolly Lysne (Simon Fraser): Academic Patron-

age and Laplace’s Early Career• Robert Moir (Western Ontario): “The Conversion

of Phenomena to Theory: Lessons on Applicabil-ity from the Early Development of Electromag-netism”

Tom Drucker (Wisc. – Whitewater) is organizing thegeneral session. Speakers on the program include:

• Gregg De Young (American Univ.): “Ziyadat Lit-erature: An Early Form of Commentary in theArabic Euclidean Tradition”• Marina Vulis (Norwalk CC and CUNY): “Early

Mathematics in Russian Mathematical Textbooks”• Bruce Petrie (Toronto): “Why Euler Didn’t Prove

the Irrationality of Pi: A Chapter in the Historyof Transcendence”• James Tattersall (Providence): “A Late 19th Cen-

tury Mathematical Subculture”• Maria Zack (Point Loma Nazarene): “Robert

Hooke and An Attempt to Prove the Motion ofthe Earth from Observations”• Byron Wall (York): “Some 19th Century Argu-

ments for the Rational Assignment of Probabili-ties for Possible Events in Nature”

• Andrew Perry (Springfield): TBA• Roger Godard (Royal Military College): “Some

Examples of Eigenvalue Problems in Mathemati-cal Physics”• Bruce Burdick (Roger Williams): TBA• Michael Molinsky (Maine): “The Mathematical

Education of a Founding Father, John Adams”• Charlotte Simmons (Central Oklahoma): “Ben-

jamin Gompertz: Pioneer of Actuarial Science”• Hardy Grant (York): “Eighteenth Century Math-

ematics: The Naysayers”• V. Frederick Rickey (USMA): “Selecting Chairs at

West Point”• W. Jim Jordan (Waterloo): “Structuralist Mi-

rages on the Road from Antiquity: Why the An-cient Greek Mathematicians Were not Mathemat-ical Structuralists”• Ronny Becker: “Phenomenology of Mathematics”• Gregory Lavers (Concordia): “Frege the Conven-

tionalist and Carnap the Fregean”• Joel Silverberg (Roger Williams): TBA

CSHPM presentations are typically 20 minutes inlength, with 5 minutes for questions and 5 minutesto set up for the next speaker.

Tom Archibald & Tom Drucker

Annals of Science Prize

Submissions are being accepted for the 2009 An-nals of Science best paper prize. This prize is of-fered every two years to the author of an original,unpublished essay in the history of science or tech-nology, which is not under consideration for pub-lication elsewhere. The prize, which is supportedby Taylor & Francis, is intended for those who arecurrently doctoral students, or have been awardedtheir doctorate within the past four years. Essaysshould be submitted to the Editor (T. H. Levere,annals.science@utoronto.ca) in a form acceptable forpublication in Annals of Science. See the webpage ofthe Journal (www.tandf.co.uk/journals/authors/tasc-auth.asp) for a style guide.

The winning essay will be published in the Journal,and the author will be awarded US$500 and 1 year’sfree subscription to Annals of Science!

8

Papers should be submitted by September 30, 2009;the winner will be notified by December 31, 2009.The Editor’s decision is final.

Past winners of the prize include: Luciano Boschiero,“Natural Philosophical Contention Inside the Ac-cademia del Cimento: The Properties and Effectsof Heat and Cold,” 60 (2003): 329-349; David Pan-talony, “Rudolph Koenig’s Workshop of Sound: In-struments, Theories, and the Debate over Combina-tion Tones,” 62 (2005): 57-82; and Daniela Monaldi,“Life of µ: The Observation of the Spontaneous De-cay of Mesotrons and its Consequences, 1938-1947,”62 (2005): 419-455.

[Editor’s Note: A PDF flyer to hang in your depart-ment or distribute to students is available by emailingaackerbe@verizon.net.]

Katharine Brown

2008 Financial Statements

The following financial statements cover the period1/1/2008 through 12/31/2008.

$ Can.Incomedues/subscr. 14146.10SSHRC travel grant 3480.00TOTAL 17626.10ExpensesCFHSS dues (2008) 1786.72Philosophia Mathematica 2318.40Historia Mathematica 3929.26Proceedings 1887.48Postage etc. 970.16Meeting expenses 3319.33May speaker 250.00Travel claims 5094.70Bank charges 24.22CUMC meeting grant 300.00TOTAL 16260.94NET 1365.16Balance 32074.84TD Mortgage Corp. 3850.06TOTAL 35924.90

Comments: Because the Society has 2 accounts, onein US dollars, we keep two different accounting sys-tems. At the request of the editors, we have combinedthe numbers for these accounts. The numbers givenare in Canadian dollars. A conversion factor of 1.26has been used to convert American dollars into Cana-dian ones.

As usual, the TD Mortgage Corporation GIC fundwas rolled over to mature in February 2010.

There was an overall surplus this year after the deficitof $2077.17 in 2007. The 2007 expenses for BSHMreciprocal membership fees ($650.72) and for theCUMC meeting grant ($300.00) were not expendedin 2008: the Canadian Undergraduate MathematicsConference treasurer did not request funds, as hadbeen done in the past; reciprocal fees are charged onlywhen the number of reciprocal members needs to bebalanced out. In 2008, 45 BSHM members requestedreciprocal membership in CSHPM, while 55 of ourmembers requested reciprocal membership in BSHM.The two societies have tried to set rates that are ap-proximately equal in Canadian dollars and Britishpounds. It would thus appear that we owe BSHM for10 reciprocal memberships in 2008. However, aftermember counts were exchanged last year, the BSHMTreasurer did not present a bill for the difference, asis our custom.

Following Council discussions after last year’s finan-cial report, we agreed to pay out travel expenses tothe amount of the SSHRC grant and $250 to the MaySpeaker as honorarium from our operating costs. Ifailed to follow this policy, however, because I mis-placed some of the reimbursement requests the firsttime I calculated the travel expense claims and in-stead of simply telling some members that we couldn’tpay any of their expenses, I ended up paying out morethan the SSHRC grant. The total excess was about$1286, which is about the same amount as our prac-tice before we made the policy change.

The opening bank balance for 2008 was $27430.90.The increase in the ending balance, beyond 2008’snet income of $1365.16, is due to the decline in thevalue of the Canadian dollar compared to the U.S.(The conversion factor in 2007 was 1.01.)

Nathan Sidoli

9

Cauchy in Quebec City

If you were in Vancouver last year for the Learnedsat UBC, you might remember my paper on an 18th-century manuscript on conic sections produced at theSeminaire de Quebec. (See vol. 21 of the Proceedings,pp. 128–134.) This past March, I returned to QuebecCity for another short research visit.

One of my discoveries came while looking for connec-tions with the conservative Catholic French mathe-matician Augustin Cauchy. The result consisted ofseveral of Cauchy’s books, three student notebooks,a copy of a poem and one letter.

The letter was written from Paris in December 1857by one of the teaching fathers, Thomas-EtienneHamel, to his Superieur, Louis-Jacques Cassault.Hamel had been sent to Paris for advanced study atthe Ecole des Carmes, in preparation for the full de-velopment of the newly established Laval University.Cauchy was one of his teachers.

This four-page letter starts with a polite address andthen recommends another priest to teach at the PetitSeminaire. Regarding Cauchy, Hamel recommendsthat Cassault hurry to acquire his collected works,both for their high quality and for Cauchy’s highstanding as a mathematician and a Catholic.

“Monsieur le Superieur. . . .

“Voici d’autre chose. Cette fois, cela re-garde unpeu les sciences – Monsieur Cauchy qui on regardecomme le premier mathematicien de l’Europe, a pub-lie un certain nombre d’ouvrages qui ont change parleur rigueur la face des mathematiques en fixant lesidees sur les bases memes de cette science. Ces ou-vrages seront, dit-on, la base des progres futurs. Orplusieurs sont maintenant hors de vente chez les li-braires quoique leur auteur vive encore – Comme ilajoute continuellement a ce qu’il a deja fait, on nesait pas s’il recommencera une nouvelle edition. Enattendant les ouvrages epuises se vendent d’occasionmais deplus en plus chers a mesure qu’ils deviennentplus rares. J’attire donc l’attention du Seminaire ladessus, en cas qu’il se propose d’acheter les oeuvrescompleters de cet illustre savent, aussi recomandabledu reste par sa piete que par sa science. . . .

“J’ai l’hommeur d’etre

Monsieur le SuperieurVotre tres humble ettres-obeissant serviteurThos. E. Hamel ptre”

David Orenstein

Book Review: A Primer for Mathe-matics Competitions

A Primer for Mathematics Competitions, by Alexan-der Zawaira and Gavin Hitchcock (Oxford, New York:Oxford University Press, 2009), 350 pp. ISBN: 978-0-1995-3988-8. US$45.

Based solely on the title, this new book aimed athelping to prepare students to participate in nationalMathematical Olympiads might seem a questionablechoice for a review in the Bulletin. A glance at thecover, however, reveals the connection: part of thebook’s description is the claim that an “unusual fea-ture of this book is the attention paid throughout tothe history of mathematics—the origins of the ideas,the terminology and some of the problems, and thecelebration of mathematics as a multicultural, co-operative human achievement.” Although obviouslythe book is first and foremost about problem solving,some historical content is certainly provided.

The book is organized into eight “toolchests” ofrelated mathematical topics: geometry, algebraicinequalities and induction, Diophantine equations,number theory, trigonometry, sequences and series,the Binomial Theorem, and counting techniques.Each of these eight chapters is designed to be inde-pendent of the others, and they can be read in anyorder. In most cases, whenever material from a dif-ferent chapter is required for a particular example, areference is provided directing the reader to the ap-propriate section. The final chapter of the book pro-vides a collection of miscellaneous problems requiringthe methods covered in the previous chapters as wellas tying in some other topics not covered in the book.

The sections in each chapter begin with one or more“appetizer” problems; that is, problems that shouldchallenge the student, but that can be solved usingthe techniques and theorems reviewed in the section.For example, the chapter on combinatorics begins

10

with the following problem: “Distinct 3-digit num-bers are formed using only the digits 1, 2, 3 and 4,with each digit used at most once in each numberformed. What is the sum of all possible numbers soformed?”

Each chapter concludes with a set of problems, al-though the number of problems provided varies basedon the length of the chapter; for instance, the chapteron geometry contains 51 problems, but the chapter onthe Binomial Theorem ends with only five. Solutionsto all of the problems are provided.

The claim that attention is “paid throughout to thehistory of mathematics” is something of an overstate-ment. While the earlier chapters, particularly thechapter on geometry, contain many instances of his-torical discussion, the frequency of those discussionsdiminishes dramatically as one moves further into thebook. For example, in the last three chapters, thereare only two extremely brief references to the historyof mathematics: the fact that Pascal’s Triangle canbe traced back to both Blaise Pascal and Halayudha,and the association of Dirichlet with the Pigeon-HolePrinciple. In many other cases, not even this tokenamount of historical context is provided; for example,while the problem solving applications of the Cauchy-Schwarz Inequality, Fermat’s Little Theorem and theWeierstrass Inequality are presented, they are accom-panied by no historical details.

In the earlier parts of the book, the coverage of thehistory of mathematics is more frequent and slightlyless terse. The first chapter begins with a two-pagesummary of the origin of the word “geometry” andsome discussion of geometric knowledge in Babylon,Egypt and Greece. The problems at the end of thefirst chapter include proving the Pythagorean The-orem based on the diagrams from Propositions I.47and VI.31 of Euclid’s Elements; the solution providedfor the second proof briefly discusses incommensu-rable numbers. There is a condensed description ofthe Library and Museum at Alexandria, which listssome of the mathematicians who studied or workedthere and even explains why the title of Ptolemy’sMathematical Collection eventually became the Al-magest. Later chapters contain very short descrip-tions of Bombelli and the discovery of imaginary num-bers, Simon Stevin and decimal representation, andDiophantus.

As the word “primer” in the title suggests, the bookis intended to provide only an introductory founda-tion for problem solving techniques. At the end of thebook, a list of “Further Training Resources” is pro-vided. In addition to other books on problem solv-ing, this list directs readers to history of mathematicstexts by Boyer & Merzbach, Eves, and Katz, as wellas to the MacTutor website.

Although the actual amount of historical material inthe book was small and mostly limited to the firstchapter, the book was still very interesting. Exceptfor a few minor typographical errors and occasionalodd notational choices (for example, in one problem,the area of triangle ABC was labeled A), the materialwas extremely well written and organized. This bookwould be useful not only to students preparing forcompetitions, but also as a reference book for under-graduate students and as a source of interesting andchallenging problems for secondary education and col-lege teachers to use in their classes.

Mike Molinsky

HPM Americas Section

The Americas Section of the International StudyGroup on the Relations Between History and Ped-agogy of Mathematics held its annual meeting at theMAA Carriage House in Washington, DC, on March14–15, 2008. The Friday afternoon before the meet-ing, Fred Rickey and Florrie Fasanelli organized a rarebook tour of the United States Naval ObservatoryLibrary; attendees remarked on their “counterpointcommentary.”

Janet Heine-Barnett (Colo. State-Pueblo) startedthings off Saturday morning with a report to the au-dience of 17 on her work developing and site test-ing three student projects in Boolean algebra. Thesemodules on George Boole, Edward Huntington, andClaude Shannon are available at www.cs.nmsu.edu/-historical-projects/. I then presented a preliminaryversion of the work you all will hear about at theCSHPM AGM. Next, Betty Mayfield (Hood) sharedher experience taking two students to SMURCHOM,the undergraduate history of mathematics conferenceorganized by Sloan Despeaux. Finally, Shirley Gray(Cal. State-Los Angeles) urged us not to let the ongo-

11

ing examination of the Archimedes Palimpsest underthe auspices of the Walters Art Gallery overshadow J.L. Heiberg’s achievements in reading the text between1906 and 1908.

I mentioned last year that I am a fan of lunches fromWhole Foods Market, so let’s move on to the businessmeeting. A variety of upcoming prospective eventswere announced. Florrie managed to engineer an“election” that resulted in my becoming the AmericasSection treasurer and David L. Roberts ascending tothe newly-created position of secretary. Basically, ourfunctions are to provide additional signing authorityfor the Section’s modest bank account, help maintainthe Web site, and make sure the Section continuesshould anything befall president Bob Stein. The Sec-tion still needs to reach out to math historians andpedagogists in Mexico, South America, and Canadaso that we truly reflect the “Americas.”

After the business session, Alexander Karp (Teach-ers College, Columbia) evaluated the state of Sovietmathematics education before and after the CentralCommittee passed a set of resolutions in 1931. Thereforms seemed to improve basic mastery in a largernumber of students but did not prepare talented stu-dents for higher achievements. Marina Vulis (NewHaven) then described the 1703 Russian textbook,Arithmetika, by Leonty Magnitsky. Dave R. closedthe afternoon with his talk on the linkages chapter inTools of American Mathematics Teaching—he, PeggyKidwell, and I could not go through an entire daywithout plugging our book!

Since this correspondent apparently cannot read acalendar and scheduled her church choir’s first per-formance in two years for March 15, I can provideonly titles for the Sunday morning session: Tom Bart-low (Villanova) talked about “Edward V. Hunting-ton on Teaching the Calculus”; Michel Helfgott (E.Tenn. State) discussed the “Pedagogical Implicationsof Cardano’s Ars Magna”; and Ilhan Izmirli (Amer-ican) spoke on “Does a Postmodernist Philosophy ofMathematics Make Sense? Is 2 + 2 = 5 Correct AsLong As One’s Personal Situation or Perspective Re-quired It?”

In 2009, the Americas Section will return to the Car-riage House on March 13–14. There may be a visitto the Dibner Library. We are exploring other loca-

tions for future meetings, including the D. E. Smithcollection at Columbia University, the Chemical Her-itage Building and American Philosophical Societyin Philadelphia, and cities in the Midwest and WestCoast.

Amy Ackerberg-Hastings

From the Webmaster

I always welcome any suggestions for ways to makethe CSHPM website (www.cshpm.org) a more valu-able resource to the Society. In particular, I wouldlike to encourage your advice in improving the fol-lowing sections of the website:

Calendar. Please let me know of any history and/orphilosophy of mathematics events that are missingfrom the calendar.

Links. Although I try to check through the links toother websites of interest relatively frequently, pleasenotify me if you find any broken links. I’d also ap-preciate suggestions for any additional links to onlineresources. In particular, I’ve started a page with linksto undergraduate and graduate programs in the his-tory or philosophy of mathematics. The list currentlycontains the programs at Simon Fraser University, theUniversity of Toronto, York University, the Universityof Chicago, the City University of New York and theUniversity of Virginia, and I would welcome informa-tion on any other available programs.

Archives. The archives section of the website con-tains the past issues of the Bulletin, as well as copiesof the schedules and abstracts from each AnnualMeeting and the table of contents of each meeting’sProceedings. The archives are currently missing theabstracts of the talks at the 2004 (held in Cambridgewith the BSHM) and 2005 (held in Waterloo in con-junction with the CMS) meetings; if anyone couldprovide copies of those abstracts, it would be ex-tremely helpful. This summer, I plan to complete asearchable database of all of the titles and abstractsfrom the Proceedings. Please let me know if you havesuggestions for other archival materials that would behelpful to have online.

Mike Molinsky

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Web Review: Twitter

Based on my unscientific observation that half thearticles in the Washington Post each day mentionit, Twitter appears to be the must-use technology dujour. Established in 2006, Twitter is a social network-ing service in which users are asked to text or postresponses of fewer than 140 characters to the ques-tion, “What are you doing?” At www.twitter.com,a user may also register to follow the “tweets” ofother “twitterers.” Responses to tweets are not ex-pected, though. Twitter employees encourage usersto follow their friends, but famous Twitter feeds in-clude American actor and Demi Moore spouse, Ash-ton Kutcher (581,000 readers) and bicyclist LanceArmstrong (448,000 readers).

I did not recognize any historians or philosophers ofmathematics among the 1000 most popular Twitterusers. Meanwhile, I can’t think of anyone for whom Ipersonally want constant updates on daily life—evenmy husband or Colin Firth. Still, I don’t want to en-tirely turn into the curmudgeon chasing rotten kidsoff my virtual lawn, either. So, I checked to see whatevidence of the history and philosophy of mathemat-ics may be found on Twitter.

Although Twitter permits searching as far back as 1January 2008, a search for “history of mathematics”returned results only to 19 February 2009. On March27, typeqaz, who appears to be a book buyer namedDina, announced Clifford Pickover’s forthcoming TheMath Book: From Pythagoras to the 57th Dimension,250 Milestones in the History of Mathematics. OnMarch 21, mindblink, who sounds like a student incomputing, came into a bunch of history of mathe-matics books and a box of Girl Scout cookies. OnMarch 6, elbieinwaterloo was excited that Steve Fu-rino would be teaching history of mathematics thissummer at the University of Waterloo. Perhaps someof our members know “Steverino”; he was instructorof the year at Waterloo in 1998 and earns high markson the Rate My Professors Web site for his off-topicanecdotes and “math history Fridays” in his regu-lar mathematics classes. On March 1, veraobmanaposted a link to the MacTutor Web site. On Febru-ary 19 and 27, Kapester and TheDarcinator were bothdoing their history of mathematics homework. Mean-while, Matty Reynolds and Dave Gorman had a con-

versation about the origin of zero on February 26.

By searching for “philosophy of mathematics,” I dis-covered that Adam Wagner was reading CharlesSeife’s Zero: The Biography of a Dangerous Ideaon March 23, while Matt Jakob was reading Phi-losophy of Mathematics: Selected Readings, editedby Paul Benacerraf and Hilary Putnam, on March20. On March 19, Todd Suomela linked to his blogpost on “Bias and Naive Philosophy of Mathemat-ics.” On March 4, fidelisera, an Arizona 19-year-old,was thinking about taking philosophy of mathematicsnext semester. On March 1, lareecarucker, a featuresreporter for the Jackson Clarion-Ledger was read-ing “a book about the philosophy of mathematics.”On February 28, pyridine, a neuroscientist in Mel-bourne, name-checked Eugene Wigner’s 1960 article,“The Unreasonable Effectiveness of Mathematics inthe Natural Sciences” and juxtaposed it with “TheUnreasonable Uselessness of Philosophy in the Natu-ral Science,” which appears to be his own phrase. Hedidn’t like the 4th “Futurama” movie, either, while Ifound the DVD acceptable; maybe I don’t care aboutpyridine’s cranky opinions.

Since abbreviating is supposed to be the point of tex-ting, I also checked “hist math” and “phil math.”These searches provided a larger number of results,but they mainly returned students doing their his-tory homework and their mathematics homework. Idid find out that Shawna Bowler of Denver, CO, whotwittered a mind-boggling 100 times on March 26,expected to receive a CD set on the history of math-ematics from the library on March 16. On March 14,Lauren Beaver and Kait Rankins had read part ofDenis Guedj’s novel The Parrot’s Theorem in theirhistory of mathematics class; in trying to remem-ber the plot, Kait commented, “Can you imaginewhen it’s 3.14.15? Math nerds will explode.” OnMarch 8, tsmosca was reading Thomas Heath’s His-tory of Greek Mathematics, in which he “skippedahead to Hippias’ quadratix. Pre-Euclidean construc-tion & subsequent critiques strikingly sophisticated.”On February 27, struthious twittered 2 comments onhis reading: “ Frege on Mill’s phil of math: ‘pebbleand gingerbread arithmetic’” and “Lakatos’ Proofsand Refutations is fun, fun, fun! Brilliant hist/philof math.”

Does Twitter currently have any use for historians

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and philosophers of mathematics? For finding outabout these subjects, the service seems only to pro-vide insights into what non-professionals are thinkingabout. As the paragraphs above may indicate, thisis a rather labor-intensive process with results thatmay not be very scintillating. Might historians andphilosophers of mathematics profitably employ Twit-ter in the future? This is also uncertain, since it isdifficult to imagine any of us exerting the market-ing effort to develop a substantial following (althoughI would enjoy “tagging along” when our interestingmembers travel to interesting destinations). Still, itis useful to know that our students may be twitteringand tracking tweets. I did search for the names ofseveral prominent historians and philosophers, but Ifound multiple references for only one person, JohnConway. Nick Hobson of Hoking, UK, did reprint aquote from Robin Wilson that gives us a pun on whichto end: “I once gave a talk on classical Greek mathe-matics; in honour of Casablanca it was called ‘Here’sLooking at Euclid’.”

Amy Ackerberg-Hastings

CMS Winter Meeting

The CSHPM continued its regular annual presence atthe Winter Meeting of the Canadian MathematicalSociety in Ottawa, December 6-8, hosted by CarletonUniversity. The session, organized by Tom Archibaldand Alex Jones, provided a showcase for recent re-search in both history and philosophy of mathemat-ics. The talks were excellent and the organizers areproud to have been associated with the event.

Pre-modern mathematics was represented by Dun-can Melville (St. Lawrence Univ.), who spoke on therole of problem texts in Old Babylonian mathematics;and by Kim Plofker (Union College), who discussedGreco-Persian geometry in seventeenth-century India.Paul Rusnock of Ottawa and Dirk Schlimm (McGill)spoke on philosophical aspects of the work of Bolzanoand Pasch, respectively. The remainder of the pa-pers covered material from the eighteenth century tothe present. Highlights included Robert Dawson (StMary’s) on reconstruction of a slide rule for complexnumbers; David Bellhouse (Western Ontario) with aniconographic inquiry into engravings in Euler’s Intro-

ductio, and Brenda Davison (SFU) on G. H. Hardy’sCourse of Pure Mathematics. There were also finecontributions from V. Fred Rickey (USMA), CraigFraser (Toronto), Deborah Kent (Hillsdale), FlorinDiacu (Victoria), and Stan Burris (Waterloo).

Abstracts are online at http://www.cms.math.ca/-Events/winter08/abs/

The CMS has been kind enough to schedule anotherhistory and philosophy session for the Winter meet-ing at Windsor, Ontario, December 5-7, 2009. Thoseinterested in presenting their recent research shouldcontact Tom Archibald, tarchi@sfu.ca.

Tom Archibald

Inequalities As Political Argument

You might remember that the Canadian Conserva-tive minority government’s initial response to an im-pending economic crisis was excessively strange. Tocounter this, a Liberal-NDP coalition governmentwith Bloc Quebecois support was proposed.

I was in full agreement with this reasonable re-sponse to government malignity and incompetence,so I joined the pro-coalition rally that filled NathanPhillips Square in front of Toronto City Hall on Sat-urday, December 6, 2008.

I was singularly struck by how much mathematicalargument and symbolism were part of the rally. Par-ticularly noteworthy were the protest signs that saidsimply “62 > 38”. This was the mathematically suc-cinct way of undermining the Conservatives’ argu-ment that the proposed Coalition was undemocratic.The Conservatives had received only 38% of the votein the October 2008 election. The combined opposi-tion parties who supported the coalition (Liberals +Bloquistes + New Democrats + Greens) had polled62%.

Similarly many people sported a campaign buttonwith a colour-coded diagram. The colours and partieswere as follows: blue for Conservative (surrounded bya solid line in the replica illustration accompanyingthis article), red for Liberal (surrounded by a dottedline), green for Bloc Quebecois (surrounded by a dashand 2 dots), and orange for New Democratic (sur-

14

Figure 3: A Colour-coded Diagram

rounded by a dashed line). Thus, the button graph-ically stated that the opposition parties held a ma-jority in the House of Commons. It was circular, ofcourse, and measured about 6 cm in diameter.

Even as I write (March 30, 2009), I still see postersthat say: “I’m Part of the 62% Majority!”

While not Tensor Analysis or Galois Theory, mathe-matical arguments have been part of greatest recentdebate in Canadian political history.

David Orenstein

Erwin Kreyszig (1922-2008)

Erwin Kreyszig, who died suddenly on December 12,2008, was active in the affairs of CSHPM for severalyears, speaking on a variety of subjects in nearly ev-ery annual meeting from 1983 to 2003. But Kreyszig’slifetime also included multiple careers as researcher,supervisor, textbook author and academic adminis-trator in several institutions in four countries. Hismathematical interests were unusually broad and his163 publications include papers in partial differentialequations, mathematical physics, numerics, differen-tial geometry, applied statistics and the history ofmathematics. He worked with renowned 20th cen-tury mathematicians including Stefan Bergman, Ti-bor Rado, John Todd and Garrett Birkhoff.

Erwin was born in Pirna (near Dresden), Germany,on January 6, 1922. He studied Physics and Math-ematics at the University of Darmstadt, obtaining adoctorate in Mathematics (1949) under the supervi-sion of A. Walther. His dissertation on the gener-alized sine integral [1] deals with a special functionof two complex variables, much of it concerning thequestion of how the zeros with respect to one vari-

able vary with the other variable. This work alreadyillustrates some of the qualities which were to char-acterize his later work: information on the history ofthe subject, attention to detail, use of diagrams andvisual aids, and unification of earlier results.

After further work in Germany on complex analy-sis and differential geometry, Kreyszig moved to theUnited States in 1954. His first position was at Stan-ford University, where he interacted especially withStefan Bergman. He started to work on complex the-oretic methods in partial differential equations, oneof his main areas of activity for several subsequentyears. During 1956–60 he was at Ohio State Univer-sity, where he was promoted to the rank of Profes-sor in 1957. One of his activities during this periodwas the writing of Advanced Engineering Mathemat-ics [2], a textbook now in its 9th edition in English,not to mention the various translations that have ap-peared over the years. Wiley was to publish several ofhis other books, including his textbook on functionalanalysis [3], now in the Wiley Classics series.

Those were the days when, even for senior academics,openings were more available than at any time be-fore or since. Kreyszig was much in demand and wasable to leave his mark on several institutions (Graz,Dusseldorf, Karlsruhe) as well as hold various visit-ing positions! Amazingly, in addition to performingadministrative tasks and continuing his mathematicalresearches, he found the time to become involved inwriting textbooks in statistics.

By 1973, Kreyszig was ready to return to NorthAmerica, where he took a position at the Universityof Windsor, moving to Carleton University in 1984.After retirement from Carleton he was given the titleof Distinguished Research Professor. He continued toplay an active role in the Department, maintaininghis office and continuing his research.

Erwin was quick to become involved in the Canadianmathematical community. He served as a member ofthe Board of Directors of the Canadian Mathemat-ical Society in the years 1977–83 and 1987–89 andon Committees of the Society related to publicationsthroughout the 1980s.

Our Society was to profit from his increasing interestin the history of mathematics. One of his first majorprojects in this area was the early history of functional

15

analysis, joint work with Garrett Birkhoff [4]. Thetopics on which he lectured at CSHPM meetings werevery varied: development of the concept of function,history of the calculus of variations, Leonhard Euler,evolution of engineering mathematics, and history ofnumerical analysis were some of the areas on which hespoke. But we also had some overview topics: “Sur-faces and Manifolds —their general impact”, “Curvesand their influence on the development of mathemat-ics”, “On the concept of space in analysis, geometryand physics” and “‘Modern’ starts: Formative periodof 20th century mathematics”, his contribution to the2000 special session, “History of Mathematics at theDawn of a New Millennium”. But Erwin was no dilet-tante. Every one of his talks was meticulously pre-pared, and so were the written versions in the annualproceedings.

Figure 4: Erwin Kreyszig (1922-2008)

Erwin Kreyszig was pre-deceased by his wife Herta(nee Lied) in 1996. She had obtained a doctorate ingeography from the University of Mainz. The couplehad two sons: Walter, who is Professor of Music atthe University of Saskatchewan, and Herbert, a NewYork-based consultant in finance and business strate-gies for investment banks and private corporations.

Much of the biographical information provided herewas taken from [5], which contains many more detailsof Erwins life and career. I am grateful to HerbertKreyszig for further information and comments andfor the photo, taken by Michael Hale in 2007.

References

[1] E. Kreyszig, “Uber den allgemeinen Integralsinus

Si(z, α)”, Acta Mathematica 85 (1951), 117-181; “Derallgemeine Integralkosinus C(z, α)”, ibid. 89 (1953),107-131.[2] E. Kreyszig, Advanced Engineering Mathematics,Wiley, New York, 1962 (9th edition, 2006, 1248 pp.).[3] E. Kreyszig, Introductory Functional Analysis withApplications, Wiley, New York, 1978 (Wiley ClassicsSeries, 1989, 704 pp.).[4] G. Birkhoff and E. Kreyszig, “The establishment offunctional analysis”, Historia Mathematica 11 (1984),258-321.[5] Manfred W. Kracht, “In honor of Professor ErwinKreyszig on the occasion of his eightieth birthday”,Complex Variables 47, no. 6 (2002), 453-461.

Martin Muldoon

Quotations in Context

Arithmetical symbols are written diagrams andgeometrical figures are graphic formulas. –

David Hilbert

This comment may sound a little too pat, like anaphorism purveyed by some “new-age” guru. How-ever, given the awesome credentials of its author, wemust certainly treat his statement with respect, andwe may understand it better by exploring its context.

The statement is quoted in the form provided abovein Robert Edouard Moritz’s compilation of writings,On Mathematics and Mathematicians (formerly titledMemorabilia Mathematica or the Philomath’s Quota-tion Book). Moritz’s referenced source is Hilbert’sarticle, “Mathematical Problems,” in the Bulletin ofthe AMS (8 (1902): 437–479), a translation by MaryWinston Newson of the original Mathematische Prob-leme published in the Gottinger Nachrichten in 1900.This was before a French translation was published in1902 in the Proceedings of the Second InternationalCongress of Mathematicians, held in Paris in 1900and at which Hilbert presented this paper, containingthe 23 open problems that were to become renownedas challenges for the coming century. The completeEnglish text of this article is included in Ben Yan-dell’s vivid book, The Honors Class: Hilbert’s Prob-lems and their Solvers and was also reprinted in theBulletin of the AMS 37 (2000): 407–436 (availableonline at www.ams.org/bull/2000-37-04).

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The quote as given by Moritz turns out to be a trun-cation of the following sentence: “The arithmeticalsymbols are written diagrams and the geometricalfigures are graphic formulas; and no mathematiciancould spare these graphic formulas, any more than incalculation the insertion and removal of parenthesesor the use of other analytical signs.”

Preceding this sentence, Hilbert states his oppositionto the opinion that only the concepts of analysis oreven arithmetic alone are “susceptible of a fully rig-orous treatment.” He argues that regardless of thesource of mathematical ideas, such as from geometryor physics, it is possible to set up an exact axiomaticsystem that “shall be in no respect inferior to those ofthe old arithmetical concepts.” He then discusses hownew signs are developed from new concepts, beingchosen to remind us of their sources, as “geometricalfigures are signs or mnemonic symbols of space intu-ition.” Examples include his claim that the expressiona > b > c is always associated in mathematicians’minds with “the picture of three points following oneanother on a straight line as the geometrical pictureof the idea ‘between’.”

Following this is a paragraph consisting of the sen-tence from which our quotation is taken. ThenHilbert goes on to stress that “in order that thesegeometrical figures may be incorporated in the gen-eral treasure of mathematical signs, there is neces-sary a rigorous axiomatic investigation of their con-ceptual content.” He concludes this section by men-tioning Hermann Minkowski’s work Die Geometrieder Zahlen (The Geometry of Numbers) as “an ex-ample of an arithmetical theory operating rigorouslywith geometrical ideas and signs.”

Figure 5: The Fixed Point Theorem Without WordsTo conclude with a related viewpoint, John Little-

wood (in Littlewood’s Miscellany, a book of his writ-ings compiled by Bela Bollobas) gives a self-described“sermon” against what he calls the (then) increas-ing practice of avoiding pictures in mathematics. Hewrites that his pupils “will not use pictures, even un-officially and when there is no question of expense” (ofprinting), a comment calling to mind Bourbaki’s no-torious aversion to pictures in their expositions. Thenhe goes on: “A heavy warning used to be given thatpictures are not rigorous; this has never had its bluffcalled and has permanently frightened its victims intoplaying for safety. Some pictures, of course, are notrigorous, but I should say most are (and I use themwhenever possible myself).” He claims that they maybe legitimately used not only for definitions but alsofor pictorial arguments, illustrating his point with afigure that is “[f]or the professional the only proofneeded” of the ‘fixed point theorem’ in one dimen-sion. This concept of a “proof without words” makesup part of the currently popular approach of visual-ization in mathematics. It seems that Hilbert wouldhave appreciated this trend.

Dan Sonnenschein

AGM of CFHSS

The Annual General Meeting of the Canadian Fed-eration of Humanities and the Social Sciences tookplace in Ottawa on 7–8 March 2009. Highlights ofthe discussion included:

Funding. The Government of Canada is giving $87.5million per year to higher education—40% of whichgoes to Humanities & Social Science.

Copyright Law. The copyright act in Parliamenthas been dropped (June 2008) because of the electionin October 2008. A new copyright act will be tabled.See also my report in the May 2006 Bulletin.

Digitization: Google. Google (of San Francisco)scanned approximately 7 million titles between 2004and 2007. These are uncorrected PDF OCR materi-als. It has over 2.5 petabytes and is still growing: 2.4billion bytes of works printed before 1923, 2.6 billionbytes of works published between 1923 and 1963, and10 billion bytes of post-1963 works. Google is beingsued and has until June 2009 to give a binary (accept

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or not) decision. It probably has to obey the BerneConvention on copyrights.

Google is not particularly interested in preservation.It is supposed to give $60 for each title to the author.For books still under copyright, it is only supposed topublish about 20% of the manuscript.

Digitization: Implications. There was a talk on“mass digitization”—long term preservation of data& digital research. Questions for the future: (1) Whoshould pay? (2) How should we make the materialavailable? (3) Do we have the capacity? In 2007, theamount of printed material exceeded the amount onecould store electronically.

Upcoming Meetings. In 2009, CFHSS will meet atCarleton University in Ottawa; in 2010, at ConcordiaUniversity in Montreal; in 2011, at University of NewBrunswick and St. Thomas University in Fredericton;in 2012, at the University of Waterloo and WilfridLaurier University.

For information about the Federation’s ongoing pro-jects, please monitor http://www.fedcan.ca.

Ed Cohen

Mathematical Ephemera

This issue’s installment is not ephemera (short-livedor transitory printed matter such as a pamphlet oradvertisement). As with previous columns, though,this excerpt’s historical significance may not be im-mediately obvious.

John Playfair, Outlines of Natural Philosophy, Be-ing Heads of Lectures Delivered in the University ofEdinburgh, vol. 1 (Edinburgh: Archibald Constable,1812), 104-109.

176. The strength of men, and of all animals, is mostpowerful when directed against a resistance that isat rest: when the resistance is overcome, and whenthe animal is in motion, its force is diminished; lastly,with a certain velocity, the animal can do no work,and can only keep up the motion of its own body...

177. Therefore, till experience has led to a more ac-curate result, we may suppose the strength of an-imals to follow the law expressed by the formula,

W = P(1− vc )2.

This equation, supposing W and v variable, is anequation to a parabola, the construction of which willserve to represent this law more clearly to the imagi-nation.

A formula for expressing the law of animal action wasfirst proposed by Euler, in a Dissertation on theForce of Oars. Mem. Acad. de Berlin, 1747. Thatwhich he employed was W = P(1− v2

c2), different from

both those we have mentioned, but a function of thefirst, and one that becomes 0, when v = c. Euler,however, changed this to another, Mem. Acad. deBerlin, 1752, and Nov. Com. Petrop. VIII. p. 244.,the same that we have adopted. He appears to havedone so merely on account of the analogy thus pre-served between the action of animals and fluids. Thephysical fact mentioned above, is a better reason forthe preference.

178. The effect of animal force, then, or the quantityof work done in a given time, will be proportional toWv, or to Pv(1− v

c )2, and will be a maximum whenv = c

3 , and W = 4P9 , that is, when the animal moves

with the one-third of the speed with which it is ableonly to move itself, and is loaded with four-ninths ofthe greatest load it is able to put in motion. . . .

179. It appears to be a certain fact, that when aman carries only his own weight, the quantity of hisaction, that is, the height he is able to ascend in agiven time, multiplied into his weight, is greater thanwhen he carries any additional load; and Coulombthinks it probable, that this diminution of action, isin proportion to the additional load carried. Nowit appeared from his experiments, that when a mancarried a load equal to his own weight, his action wasreduced nearly one-half; and, therefore, supposing thereduction always proportional to the load, if w be theweight of the man’s body, l an additional load, whichhe is made to carry, H the height to which he ascendsin a given time, when walking freely, and h the heightto which he ascends in the same time with the loadl; then his action in the latter case, or (w + l)h, is

reduced wH(1− l2w ); and therefore also h = wH(1− l

2w)

w+l .

Suppose that a man is loaded with one-fourth of

his own weight; then h = wH(1− 18)

w(1+ 14)

= H(

1− 18

1+ 14

)=

H(.699).

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The value of H is deduced from the ascent of the Peakof Teneriffe. Borda, accompanied by eight men, onfoot, ascended in the first day (7h45m), to the heightof 2923 metres, or 9593 feet. This was at the rate of1225 feet in an hour. Had each of the men carried aload equal to the fourth part of his weight, they wouldonly have ascended at the rate of 857 feet an hour.

When 1− l2w = 0, or l = 2w, the height h = 0. With

a load equal to twice a man’s weight, he could notascend.

180. The strength of a man being supposed to followthe law now laid down, its greatest effect in raising aweight, will be when the weight of the man is to thatof his load as 1 to −1 +

√3, or nearly as 4 to 3.

New Members

Congratulations to the following new members whohave joined the Society since our last Bulletin. Welook forward to your contributions.

Janet Heine BarnettColorado State University-PuebloPueblo, COUSA

Sandra CaravellaFlemington, NJUSA

W. J. JordanWaterloo, ONCanada

Francis Jeffry PelletierEdmonton, ABCanada

Bruce J. PetrieNorth York, ONCanada

Mark C. R. SmithQueen’s UniversityKingston, ONCanada

Alison WylieUniversity of WashingtonSeattle, WA

USA

From the Editor

First, I am pleased to welcome Maria Zack of PointLoma Nazarene University as our new Production Ed-itor. She has seen to the printing and mailing of theissue that those of you who have chosen to continuereceiving the Bulletin on paper are now holding inyour hands. Maria has also secured funding from herinstitution for printing and postage. Also, a heartythank you to Pat Allaire and Rob Bradley, who hadbeen serving unofficially and jointly as ProductionEditor since November 2006. Thanks as well to EissoAtzema, who continues as Layout Editor to transformthe raw text I play with into a lovely TeX document.

Second, thanks to everyone who contributed articlesand announcements for this issue. Our Webmas-ter, Mike Molinsky, changed media to review a printsource for a change of pace, while Dan Sonnenscheinalso provided Mike with a break by handling this is-sue’s Quotations in Context column. In the future,Mike would like to don his other hat as our Archivistto launch a new regular column, so there are opportu-nities for others to contribute Web reviews or suggestquotations to place in context.

Similarly, I would love to receive submissions for theongoing Mathematical Ephemera column, which con-tains brief transcripts of those primary sources thatmight otherwise (and perhaps deservedly) slip intoobscurity. I am also interested in launching a MaterialWitness column, for brief accounts of mathematicalinstruments and objects, in addition to a methodol-ogy corner for notes on current or useful approachesin historiography or philosophy.

One of my favorite occasional columns in the Wash-ington Post is Jonathan Yardley’s “Second Reading,”in which he takes another look at novels and memoirswhich were significant in his youth in the 1950s andconsiders whether these books have stood the test oftime. I often wonder which works in math historyand philosophy we ought to pull off of our own shelvesfor reevaluation. Several years ago, we ran a regularfeature, How I Learned to Love the History of Math-ematics. To relaunch this column, I need your storiesabout how you got started in the history or philoso-

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phy of mathematics.

We are trying to increase the breadth of contributors,as well, so I was deeply appreciative when Yvon Gau-thier and Martin Muldoon accepted assignments forthis issue. Remember, you don’t have to step for-ward yourself to write for the Bulletin; volunteer acolleague from whom you’d like to hear, and I willdo the arm-twisting for you. The next submissiondeadline is October 1, 2009.

Finally, don’t forget to look back at the November2008 issue for the text of the proposed constitutionalamendment to permit electronic voting in our biennialCouncil elections. This amendment is on the agendafor St. John’s. I hope to see many of you there!

Amy Ackerberg-Hastings

About the Bulletin

The Bulletin is published each May and Novemberby a team of 3 volunteers: Content Editor AmyAckerberg-Hastings (aackerbe@verizon.net), LayoutEditor Eisso Atzema (atzema@math.umaine.edu),and Production Editor Maria Zack (Mari-aZack@pointloma.edu). Material without abyline or other attribution has been written by theeditors. Les pages sont chaleureusement ouvertesaux textes soumis en francais. Comments andsuggestions are welcome and can be directed to anyof the editors; submissions should be sent to AmyAckerberg-Hastings at the above email address, orby postal mail to 5908 Halsey Road, Rockville, MD20851, USA.

Printed courtesy of:

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