20
BULLETIN May/mai 2015 Number/le numéro 56 WHAT’S INSIDE Articles Announcements ....................................................................................... page 2 Quotations in Context [Mike Molinsky] ................................................................ page 5 Off the Shelf: Horus [David Orenstein] ................................................................. page 6 HPM Americas at Wabash & DC [Amy Ackerberg-Hastings] .......................................... page 8 MAA MathFest Centennial Events ..................................................................... page 9 Ivor Grattan-Guinness (1941–2014) [Adrian Rice] ..................................................... page 10 MAA Ohio Section Centennial [David Kullman] ...................................................... page 17 Book Review: John Napier [Joel Silverberg] .......................................................... page 17 Reports 2014 Financial Statements ............................................................................ page 10 2015 Meeting Outline [Maria Zack] ................................................................... page 11 PSA President’s Lunch [Elaine Landry] ............................................................... page 13 New Members ....................................................................................... page 19 From the Editor ...................................................................................... page 20 Canadian Society for History and Philosophy of Mathematics Société canadienne d’histoire et de philosophie des mathématiques ISSN 0835-5924

CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

  • Upload
    others

  • View
    2

  • Download
    0

Embed Size (px)

Citation preview

Page 1: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

BULLETIN

May/mai 2015 Number/le numéro 56

WHAT’S INSIDEArticlesAnnouncements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 2Quotations in Context [Mike Molinsky] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 5Off the Shelf: Horus [David Orenstein] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 6HPM Americas at Wabash & DC [Amy Ackerberg-Hastings] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 8MAA MathFest Centennial Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .page 9Ivor Grattan-Guinness (1941–2014) [Adrian Rice] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 10MAA Ohio Section Centennial [David Kullman] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 17Book Review: John Napier [Joel Silverberg] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 17Reports2014 Financial Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 102015 Meeting Outline [Maria Zack] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 11PSA President’s Lunch [Elaine Landry] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 13New Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 19From the Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 20

Canadian Society for Historyand Philosophy of Mathematics

Société canadienne d’histoire etde philosophie des mathématiques

ISSN 0835-5924

Page 2: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

ABOUT THE SOCIETY

Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire et philosophie des mathématiques(CSHPM/SCHPM) promotes research and teaching inthe history and philosophy of mathematics. Officers ofthe Society are:President: Elaine Landry, UC Davis, Davis, CA95616, USA, [email protected]: Dirk Schlimm, McGill University,Montréal, QC H3A 2T7, CA, [email protected]: Patricia Allaire, 14818 60th Ave., Flush-ing, NY 11355, USA, [email protected]: David Bellhouse, University of West-ern Ontario, London, ON N6A 5B7, CA, [email protected] President: Glen Van Brummelen, Quest Uni-versity, Squamish, BC V8B 0N8, CA, [email protected]

Members of Council

Craig Fraser, University of Toronto, Toronto, ONM5S 2J7, CA, [email protected] Marquis, Université de Montréal, Mon-tréal, QC H3C 3J7, CA, [email protected] Hunger Parshall, University of Virginia,Charlottesville, VA 22904, USA, [email protected] Silverberg, Roger Williams University, Bristol,RI 02809, USA, [email protected]

The Society’s Web Page (www.cshpm.org) is main-tained by Michael Molinsky, University of Maine atFarmington, Farmington, ME 04938, USA, [email protected]. The Proceedings of the An-nual Meeting are edited by Maria Zack, Point LomaNazarene University, San Diego, CA 92106, USA,[email protected]. The Society’s Archives are managedby Michael Molinsky (see above). The position ofCMS Liaison is vacant.New Members are most cordially welcome; please con-tact the Secretary.

Announcements

Congratulations to Glen Van Brummelen, 2015 recip-ient of the MAA Pacific Northwest Section’s TeachingAward. This section is the largest geographically inthe MAA, comprising over 130 colleges and universi-ties from Oregon to Alaska.Umberto Bottazzini received the 2015 AMS AlbertLeon Whiteman Memorial Prize at the Joint Math-ematics Meetings in San Antonio for “his many worksin the history of mathematics, notably on the rise ofmodern mathematics in Italy and on analysis in the19th and early 20th centuries.” Also in San Antonio,Mathematical Reviews celebrated its 75th anniversary.Oxton House has issued a second edition of Maththrough the Ages, by William P. Berlinghoff and Fer-nando Q. Gouvêa. The first edition has been adoptedas a text by more than 100 colleges and universitiesthroughout the United States, and it has been trans-lated into Portuguese, Chinese, and Slovenian. It wasawarded the Mathematical Association of America’sprestigious Beckenbach Book Prize in 2007.Michel Serfati has published “Descartes et Schooten.Les aventures d’une division difficile”, Images desMathématiques, CNRS, 2014, images.math.cnrs.fr/Descartes-et-Schooten-Les.html; and “Order inDescartes. Harmony in Leibniz: Two regulative princi-ples of mathematical analysis”, Studia Leibnitiana 45,no. 1 (2013): 59–96.Janet Barnett, Dominic Klyve, Jerry Lodder, DanielOtero, Nicolas Scoville, and Diana White contributed“Using Primary Source Projects to Teach Mathemat-ics” to the AMS Blog On Teaching and Learning Math-ematics, 20 January 2015.Peter L. Griffiths’s article on Fermat’s Last Theoremappeared in the April 2014 issue of M500, a magazinefounded in 1973 by Open University mathematics stu-dents.The inaugural Mahoney Prize, commemorating histo-rian of science Michael S. Mahoney, will be awarded in2015. See www.sigcis.org/mahoneyprize.HOM SIGMAA News: Larry D’Antonio waselected Secretary/Treasurer. Toke Knudsen was electedProgram Coordinator. HOM SIGMAA will sponsor areception for Karen Parshall during MathFest, August5–8, 2015, in Washington, DC. The reception will beheld on August 7. MathFest will feature several His-tory of Mathematics sessions.

2

Page 3: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

Volume 5, issue 1 (January 2015) of the Journal of Hu-manistic Mathematics is now available at scholarship.claremont.edu/jhm. It includes an article on theSmithsonian’s kinematic models by Amy Shell-Gellaschand first-day-of-class strategies for Calculus I by Mar-ion Cohen. An upcoming special issue will be de-voted to “The Nature and Experience of MathematicalBeauty.” The journal is also seeking referees.Issue 02 of the Science Museum Group Journal isavailable at journal.sciencemuseum.ac.uk/issues/autumn-2014/. The National Maritime Museum’s ex-hibition, Ships, Clocks & Stars is reviewed.See www.erittenhouse.org/ for recent articles on thehistory of scientific instruments in eRittenhouse.Princeton University Press, Tizra, Hebrew Universityof Jerusalem, and California Institute of Technologyannounce the launch of The Digital Einstein Papers.See einsteinpapers.press.princeton.edu.Cambridge University Press and the British Society forthe History of Science have launched a peer-reviewedopen access journal for the history of science, BJHSThemes, edited by Jon Agar. Visit www.journals.cambridge.org/BJHSThemes for information and tosubmit a proposal.Doctoral dissertations pertaining to the history of sci-ence and medicine are compiled at www.hsls.pitt.edu/histmed/dissertations.In May 2014, Kostas Kampourakis, Ron Numbers,and Nicolaas Rupke organized a conference on “New-ton’s Apple and other Historical Myths about Sci-ence” at Washington & Lee University in Virginia.Twenty-six myths were “busted” during the presen-tations, and John L. Heilbron gave the keynote ad-dress. An essay collection aimed at teachers is avail-able at www.academia.edu/6412084/Newtons_Apple_and_other_Myths_about_Science.Speakers on the 2014–2015 schedule for the Philadel-phia Area Seminar on the History of Mathemat-ics (PASHoM) included: Peggy Kidwell (NMAH)on September 18; Victor Katz (UDC) on October23; Shelley Costa (Swarthmore) on November 20;Stephanie Dick (Harvard) on December 4; WilliamNoel (Penn) on January 22; Robert Bradley (Adel-phi) on February 19; Robert Naugle (Shepherd) onMarch 19; and Marianna Bonanome (Manhattan CC)and Margaret H. Dean (CUNY) on April 16.The Frederick V. Pohle Colloquium on the History of

Mathematics, hosted by the Department of Mathemat-ics & Computer Science at Adelphi University, pre-sented the following speakers in 2014–2015: Harold Ed-wards (NYU) on October 8; William Dunham (Muh-lenberg) on November 5; Jonathan Sondow on De-cember 3; Michael J. Barany (Princeton) on March4; Maria Zack (Point Loma Nazarene) on April 1; andRob Bradley (Adelphi) on May 6.Michel Serfati announces the second semester programfor the annual seminar on Epistemology and Historyof Mathematical Ideas, held Wednesdays at 2:00 pm atthe Institut Henri Poincaré in Paris: Bernard Leclerc(Caen), “Alain Lascoux: de la géométrie à la combi-natoire” on February 4; Serge Grigorieff (Paris VII),“Émergence des modèles du concept de calculabilité”on March 11; Emily Grosholz (Penn State), “Le raison-nement ampliatif en théorie des nombres” on March 18;Jean-Paul Allouche (Inst. Math. Jussieu), “Quadra-ture et transcendance: Gregory et Leibniz”, and MichelSerfati (IREM), “La Quadrature Arithmétique du Cer-cle de 1673. Les idées mathématiques de Leibniz” onMarch 25; Sigmund Probst (Archives Leibniz), “La dis-cussion par Leibniz des mathématiques de Descartes aucours de son séjour à Paris (1673–1676)”, and MichelSerfati (IREM), “De l’analyse mathématique. Ordreversus Harmonie. Descartes versus Leibniz” on April8; Michel Serfati (IREM), “ ‘Monsieur Descartes’ etÉlisabeth de Bohème. D’une correspondance math-ématique à la naissance d’une amitié ‘philosophique” ’on May 20 (letter-reading to follow); and Bodo Lass(CNRS), “Démonstration de la conjecture de Dumont”on May 27.Adrian Rice was the keynote speaker for BSHM’s Re-search in Progress meeting at Queen’s College Oxfordon 21 February 2015. A BSHM/LMS joint celebrationof Augustus de Morgan was held May 9; a meeting onSymmetry and Groups will be held at Birkbeck Collegeon May 23; and a one-day conference on the historyof the mathematics of space and relativity will be atRewley House Oxford on June 20.Jim Tattersall and Fred Rickey organized a special ses-sion on History and Philosophy of Mathematics forthe AMS Eastern Section Spring Meeting at George-town University, March 7–8. Speakers included: KarenParshall (Virginia); Andrew Fiss (Mich. Tech.);Amy Ackerberg-Hastings (UMUC); Duncan Melville(St. Lawrence); Chris Rorres (Penn); Peggy Kidwell(NMAH); Judy Green (Marymount); Lydia Patton

3

Page 4: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

(Virginia Tech); Brit Shields (Penn); David L. Roberts(Prince George’s CC); Paul Wolfson (West Chester);Larry D’Antonio (Ramapo); Jesse Elliott (Cal State-Channel Islands); Andrea Pedeferri (GWU); and JoeMourad (Georgetown).The MAA Seaway Section 2015 spring meeting washeld April 17–18 at Colgate University and includeda session on “Preserving and Writing the History ofMathematics Departments in US Colleges and Univer-sities,” organized by Gary Towsley and Toke Knudsen.The Midwest Junto for the History of Science metApril 17–19 at UW-Madison. See midwestjunto.wordpress.com/.Satish C. Bhatnagar organized a special session onHistory of Mathematics for the AMS Western Sec-tion Spring Meeting at the University of Nevada, LasVegas, on April 18. Speakers included: Alok Ku-mar (SUNY Oswego); Viktoria Savatorova (UNLV);Andrzej Lenard (indep. scholar); Satish Bhatnagar(UNLV); Dieudonne Phanord (UNLV); and David Fott(UNLV).A workshop on preserving teaching materials in “uni-versity collections” will be held at Jena University, May7–9. See http://necs.org/node/104375.The 3rd Irish History of Mathematics Conference isMay 15 in Belfast. Contact Mark McCartney to regis-ter, [email protected] Commission on Women and Gender Studiesof the Division of History of Science and Tech-nology of the International Union of History andPhilosophy of Science and Technology is holdingthe conference, “Gendering Science: Women andMen Producing Knowledge,” in Prague, June 4–6.See en.zenyaveda.cz/218-gender-science/. Also,DHST is offering a prize for up to five young scholarsin the history of science or technology, to be awardedin 2017. The application deadline is August 31, 2016.See hpdst.gr/youngscholarsprize.The 16th Annual Meeting of the European AcademicHeritage Network UNIVERSEUM will be in Athens,Greece, June 11–13. A new meeting format will fea-ture four sessions: University Heritage and CulturalEngagement of European Universities; The Most Cru-cial Issue(s) with University Heritage Today; Univer-sity Heritage, Its Generators and Its Scholars; and aposter session. See www.universeum2015.uoa.gr/.The Centre for the Arts, Social Sciences, and Human-

ities in Cambridge is hosting a conference on “Objectsin Motion: Material Culture in Transition,” June 18–20.The Twelfth Biennial History of Astronomy Work-shop will be held June 24–28 at the University ofNotre Dame, with a side trip to the Adler Planetar-ium and Astronomy Museum. Michio Yano, chiefeditor of SCIAMVS, is the keynote speaker. Seewww.nd.edu/~histast/.Peter Pesic, new director of the Science Institute atSt. John’s College in Santa Fe, NM is organizing week-long seminars for teachers and other scientific profes-sionals on “A Tale of Two Geometries: Euclid andLobachevsky” (June 29–July 3) and “UnderstandingRelativity: Texts by Albert Einstein” (July 6–10).“Dresden Summer—International Academy for theArts,” August 22–29, will focus on globes in the col-lection of the Mathematisch-Physikalischer Salon. Seewww.skd.museum/de/forschung/dresden-summer/.The theme of the 34th Symposium of the ScientificInstruments Commission is “Instruments in Conflict.”The meeting is September 7–11 in Turin, Italy. Seewww.sic.iuhps.org/.ARTEFACTS XX, on using objects in studies of thehistory of science and technology, will meet in Milan,September 20–22, to explore the theme, “Scientific Her-itage at World Exhibitions and Beyond. The LongXXth Century.” See www.artefactsconsortium.org/.The Fourth International Conference on the His-tory of Mathematics Education will meet in Turin,Italy, September 23–26. See e20.unito.it/ICHME4/default.aspx.Lick Observatory, Mt. Hamilton, CA, will host the24th Annual Convention of the Antique Telescope So-ciety on October 9–12. Side trips include Ricard Ob-servatory, Chabot Observatory, and UC Santa Cruz’sOptical Shop, Mechanical Shop, and Center for Adap-tive Optics. See antiquetelescopesociety.net.The History of Education Society will meet in St.Louis, MO, November 5–8. See www.historyofedu-cation.org/our-annual-meeting/.The UK History of Education Society will hold itsannual conference, “Science, Technologies and Mate-rial Culture,” in Liverpool, November 20–22. Scrolldown at historyofeducationsociety.blogspot.co.uk/ for more information.

4

Page 5: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

A free exhibition, “Philosophical Transactions: 350years of publishing at the Royal Society,” runs at theRoyal Society of London until July 2015. A conferenceon the journal’s legacy was held March 19–21.The 2016 HPM meeting will be in Montpellier, France,July 18–22.The 13th International Congress on Mathematical Ed-ucation will be held in Hamburg, Germany, July 24–31,2016. See www.icme13.org/. Topic Study Groups willinclude “The history of the teaching and learning ofmathematics.”The University of Glasgow and the Hunterian Museumand Art Gallery are jointly funding 5 PhD projects onthe history of science and medicine in 2015–2016. TheNational Maritime Museum, Greenwich, and the Uni-versity of Edinburgh are funding a PhD on “Chronom-etry and Chronometers on British Voyages of Ex-ploration, ca 1815–ca 1872,” beginning in fall 2015.SUNY-Oneonta is hiring a visiting assistant professorin Ethno-mathematics or History of Mathematics, be-ginning in fall 2015. Université Blaise Pascal is offeringtwo post-doc positions for foreign philosophers.Information on American Philosophical Society Grantsand Fellowships may be found at www.amphilsoc.org/grants/faq.

Quotations in Context

“Mathematicians are like lovers. . . . Grant amathematician the least principle, and he willdraw from it a consequence which you mustalso grant him, and from this consequence

another.”

I think I first encountered the above quotation by theFrench author Fontenelle (1657–1757) in E. T. Bell’sMen of Mathematics over twenty years ago. The originof the quotation is Fontenelle’s most famous work, En-tretiens sur la pluralité des mondes (Conversations onthe Plurality of Worlds), first published in 1686. Thebook was intended to explain selected topics in scienceand astronomy to a popular audience, and Fontenelleexplains in the preface to the book that this is why hechose to write in French rather than Latin. The workis organized around conversations between a philoso-pher and a Marquise that take place over the course ofsix consecutive evenings.The quotation is taken from the conversation on thefifth evening. The French text below comes from

an edition published in 1701, and the translation byWilliam Gardiner that follows was published in Lon-don in 1715:

Ecoutez, Madame, répondis-je, puisque noussommes en humeur de mesler toûjours des foliesde galanterie à nos discourse les plus serieux,les raisonnemens de Mathematique sont faitscomme l’Amour. Vous ne sçauriez accorder sipeu de chose à un Amant, que bien-tost aprèsil ne faille luy en accorder davantage, & puisencore davantage, & à la fin cela va loin. Demesme accordez à un Mathematicien le moin-dre principe, il va vous en tirer une consequence,qu’il faudra que vous luy accordiez aussi, & decette consequence encore une autre, & malgrévous-mesme il vous mene si loin, qu’à peine lepouvez vous croire. Ces deux sortes de Gens-làprennent toûjours plus qu’on ne leur donne.

Hear me, Madam, says I, since we are inthe humour of mingling Amorous Follies withour most serious Discourse, I must tell you,that in Love and the Mathematicks, People rea-son alike: Allow never so little to a Lover, yetpresently after you must grant him more; nay,more and more; which will at last go a greatway. In like manner, grant but a Mathemati-cian one little Principle, he immediately drawsa Consequence from it, to which you must nec-essarily assent; and from this Consequence an-other, till he leads you so far (whether you willor no) that you have much ado to believe him.These two sorts of People, Lovers and Mathe-maticians, will always take more then [sic] yougive ‘em.

You might be surprised to learn that the context inwhich this quotation appears is a discussion of the like-lihood of the existence of life on other planets. Hereare the sentences that immediately follow in the En-glish translation:

You grant that when two things are like an-other in all visible respects, it is possible theymay be like one another in those Respects thatare not visible, if you have not some good reasonto believe otherwise: Now this way of arguinghave I made use of. The Moon, says I, is in-habited, because she is like the Earth; and the

5

Page 6: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

other Planets are inhabited, because they arelike the Moon; I find the fix’d Stars to be likeour Sun, therefore I attribute to them what isproper to that: You are now gone too far to beable to retreat, therefore you must go forwardwith a good Grace.

Mike Molinsky

Off the Shelf: Horus

Horus: A Guide to the History of Science, A FirstGuide for the Study of the History of Science With In-troductory Essays on Science and Tradition, by GeorgeSarton, Waltham, MA: Chronica Botanica, 1952, xviii+ 316 pp.Our small downtown Toronto synagogue is liberal, pro-gressive, egalitarian and gay positive. Yet, whether atShabbat services or on the High Holy Days, we returnto the sources: prayer in Hebrew and a Torah readingfrom a manuscript parchment scroll. Similarly, when Idecided to return to the sources for history of mathe-matics and science, I sought out the writings of GeorgeSarton (1884–1956), the founder of Isis and Osiris.One of my discoveries was his late work, Horus: AGuide to the History of Science.Horus was the falcon-headed son of the ancient Egyp-tian gods Isis and Osiris, a fitting name for the off-spring of Sarton’s long years researching and promot-ing history of science. Here, there’s insight into Sar-ton’s approach to our field and its status more thanhalf a century ago. It is also a research tool that canbe used directly and analogous to its method.

The EssaysThese original “lectures were delivered with a minimumof notes . . . [so] the text . . . does not reproduce themexcept in a general way. . . . The lectures . . . explain[why] to study the history of science . . . [and] the bib-liography gives the means to do so.”Sarton felt “the history of science was slowly cominginto its own”, though its development had been hin-dered by unsympathetic but also uncomprehending ad-ministrators. They did not realize that “historians ofscience must know science and history. . . . There arebut few historians of science completely qualified forthe task of teaching it. . . . [But] that is simply a mat-ter of training . . . different . . . but not more difficult.”

The first essay examines “Science and Tradition,” bothin mutual opposition and in supporting each other.“Between a science ancillary to theology . . . and oneaimed at discovering the truth irrespective of conse-quences, the distance is prodigious.” The changes havebeen truly revolutionary. “The Ptolemaic world . . . ishopelessly dwarfed by astronomical theories of today.”Sarton’s Belgian compatriot, Adolphe Quetelet, en-larged the range of possible knowledge through his ba-sic investigations of the statistical incidence of socialills in a given community.Despite “the revolutionary nature of science . . .manyof our traditions . . . are the accumulated goodness ofcenturies.” Such rationalist errors as the short-livedTechnocracy movement followed in Plato’s fallacy ofgovernance by an intellectual elite. Sarton suggeststhat part of the reason so many German scientists ac-tively facilitated the Nazi programme of radical evilwas their technical infatuation with helping to solvethe regime’s practical problems in achieving its crimi-nal ends.In “The Tradition of Ancient and Mediaeval Science”,Sarton examines his own research speciality. He exam-ines the vicissitudes of the transmission of the ancientGreek legacy, whether it’s the survival and copyingof manuscripts, or the various translation traditions inArabic, Hebrew or Latin. Sarton takes pains to demon-strate that the science of the mediaeval Arab worldwas not just a passive heir of the Greeks but also cre-ative and that its leaders included not just Muslimsbut also Jews such as Maimonides and Ishaq al-Israili.The Latin world learned from the Arabs and appliedthis learning to its own issues. The early giants of theScientific Revolution built on their mediaeval roots.The last essay asks, “Is It Possible to Teach the Historyof Science?” It’s largely a plea for the establishmentof history of science as a respectable academic disci-pline. Sarton asserts that history of science can becompared to other relatively recently established andevolving fields, such as history of art or history of reli-gion. Historians of science need to learn the techniquesof historical research and should be well-versed in atleast one field of science, such as mathematics or geol-ogy.

The BibliographyThe bibliography is based on Sarton’s own library, “acause of strength and a cause of weakness.” The struc-

6

Page 7: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

ture reflects his recipe for the education of an historianof science who must know both history (six chapters)and science (seven chapters), then pursue history ofscience (seven chapters), and finally become active inthe “Organization of the Study and Teaching of theHistory of Science” (six chapters).There are many ways individual readers can approachthe Horus bibliography. Mine starts with Canadianscience and mathematics.Only two books form the Canadian section in “His-tory of Science in Special Countries”. 1939’s A Historyof Science in Canada is the proceedings of a sympo-sium held by the History of Science section of the June1938 Ottawa Meeting of the American Association forthe Advancement of Science. The Centennial Volumeof the Royal Canadian Institute (1949) celebrates thevenerable institution that still presents popular sciencelectures in the Toronto area. Both volumes are collec-tions of exploratory surveys of the different scientificfields. These “studies are still in the pioneer stage, theymust necessarily suffer from pioneer imperfections andcrudities.”Other Canadian scientists are present, though. FrankDawson Adams (1859–1942), president of the 1913 In-ternational Geological Congress in Toronto, publishedhis Birth and Development of the Geological Sciencesin 1938. Of course Sarton notes it was reviewed byMichigan’s William H. Hobbs in Isis 32, no. 1 (1940):218–220. McGill University’s Sir William Osler’s Yalelectures on The Evolution of Modern Medicine werepublished posthumously in 1921, and his 1929 Bilboth-eca Osleriana is “a catalogue of books illustrating thehistory of medicine and of science.” Sarton himself re-viewed Harvey Cushing’s biography in Isis 8, no. 2(1926): 358–361.Chapter 25 tallies the date and location of 53 series of“International Congresses”. They played “a great partin the organization of science and especially in the def-inition of new disciplines and the formulation of theirmethods.” Sarton has certainly validated the choice ofmy current major research project: investigating theramifications of the early international scientific con-gresses that took place in Canada. I’ve already stud-ied the 1913 International Geological Congress and the1924 International Mathematical Congress in Toronto.But from Sarton I’ve learned that the Americanistsmet in Quebec City in 1906 and the Physiologists inMontreal in 1953.

Horus also supports my Jewish studies. The new Stateof Israel was only 4 years old in 1952, so when Sar-ton talks about Israel in “History of Science in Spe-cial Cultural Groups”, he means the millennial his-tory of the Jewish people. General works include thetwo Jewish encyclopedias as well as Cecil Roth’s 1938The Jewish Contribution to Civilisation and HarryFriedenwald’s The Jews and Medicine (1944). Morespecifically, William Moses Feldman looked at Rabbini-cal Mathematics and Astronomy in 1931; the follow-ing year, Solomon Gandz published The Mishnat Ha-Middot, the first Hebrew geometry of about 150 C.E.In addition to his appearance in Gandz’s volume, Mai-monides appears twice: Un glossaire de matière médi-cale de Maimondide (1940)—for the great philosopherand theologian earned his living as a physician—andthe Maimonides Bulletin, “a journal of medical prac-tice”.

ConclusionHorus: A Guide to the History of Science is one ofthe landmarks of our field. In it, Sarton was able toshare some of his most evolved understanding of whathistory of science is about. He also gave us the toolsto do our research and the direction to develop ourmethods and improve our results.I’m looking forward to a more thorough explorationof the intellectual riches indicated in the bibliography.Using the resources of the University of Toronto Li-brary and the internet, I’ll be reading 17th-centuryencyclopaedias, histories of science in Belgium, and19th-century German history of mathematics journals.David Orenstein

PSA President’s Lunch

On November 7, 2014, Helen Longino, president of thePhilosophy of Science Association (PSA), organized alunch with representatives of related societies at itsjoint meeting with the History of Science Society inChicago. The main idea was to brainstorm about howwe can better work together. Given all the related soci-eties, there is a great deal of competition for member-ship money, attendance at conferences, etc. Thoughattendance at PSA is good and the submissions to thejournal are back on track, membership in the societyis down.

7

Page 8: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

Half of what we discussed was more directly about howto help the PSA move forward and increase represen-tation. (For example, they are considering detachingtheir conferences from HSS after the next two meet-ings. Helen wanted feedback on this as well as otherideas for strengthening PSA.) But many of the issuesrelate to us as well.This year—to encourage more cooperation or visibi-lity—PSA invited a number of other associations tohost their own sessions. These sessions all took placeon Sunday morning. The worry was over attendance.The tacked-on extra half day was not noticed by somefolks in time to alter travel plans. There were no reg-ular PSA sessions at this time, but with fewer bod-ies to start with, high competition among the soci-eties and conference fatigue, the overall attendance wasnot great. However, the attendance at the Philosophyof Mathematics Association (PMA) joint session wasstanding room only (approximately 40–50 people).The ideas generated during the brainstorming sessioncovered several topics:Conferences: 1. Encouraging joint membership agree-ments. How can we determine some general policy forjoint membership? Which societies should be joined?(On this, perhaps CSHPM could survey our membersto find out what other societies they belong to.) An-other idea might be reduced conference fees for mem-bers of a few related societies. 2. It was pointed outthat there could have been better notice and advertis-ing of the Sunday special sessions. 3. The general ideaof joint meetings may be especially useful to smaller so-cieties. Another option: coordinating meetings so thatthey occur sequentially (in the same week) in the samearea of the world. This works better for medium-sizedsummer meetings like CSHPM. 4. Add workshops andmaster classes? For example, a pre-conference morn-ing of workshops by scientists for philosophers (or viceversa); particularly helpful to students or anyone want-ing to get a primer on a new area. 5. Hold poster ses-sions for graduate students? 6. Have a mixer for earlycareer and/or grad students based on a model such asspeed dating. 7. Offer opportunities to give advice tograd students regarding non-academic careers.Society Memberships: 1. PSA Membership down,but conference attendance is up dramatically. Worry:if we change to allowing membership for conferencesonly, (i) we will have to dramatically increase the reg-istration fee for non-members; (ii) our membership will

dip—given the increasing number of societies. 2. Whatare the advantages to membership; do the numbersmatter? Response: the number of members does mat-ter for NSF funding. Also, the prizes require member-ship.Diversity: 1. PSA is currently gathering diversitydata with respect to its editorial board and publica-tions. 2. Could diversity be improved by more activelyshaping the PSA program?Journals: 1. Concerns about open access and theproblem of package journal prices for library subscrip-tions.The PSA Conference in Particular: 1. Relationwith HSS in question; they are unsure whether to rene-gotiate their relationship (due to cost and size of con-ference) or to go solo. They have contracts to co-meetthrough 2018. 2. Would any of our societies be in-teresting in stepping up to fill the hole left by HSS?3. Perhaps a university could host a smaller associationbefore PSA that then meets jointly with PSA. 4. Forthe related society sessions, Thursday morning mightwork better than Sunday. 5. Someone asked whetherPSA could move to lower-cost cities? Without HSSthere would not be such a need for giant conventionvenues. But would enough people come to meetingsif not in good cities? 6. One person recommended toHelen that PSA does not do both at once: detach fromHSS and move to smaller cities or a different type ofvenue. Costs are high for hotel conferences and work-load is huge; this is not a change to be undertakenlightly. It could involve a dramatic increase in fixedcosts, but PSA already has lower/fluctuating member-ship. On the other hand, PSA does have fixed incomefrom its journal (recently renegotiated with Universityof Chicago Press to “take home” more of the income).Elaine Landry

HPM Americas Section at Wabash &DC

The Americas Section of the International StudyGroup on the Relations Between History and Pedagogyof Mathematics met jointly with the biennial MidwestHistory of Mathematics Conference at Wabash Collegein Crawfordsville, IN, October 17–19, 2014. Local or-ganizer Colin McKinney ensured we were fed extremelywell all weekend. Friday evening, Jeff Oaks gave a ple-

8

Page 9: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

nary talk on “Algebraic notation in medieval Arabic.”Conference talks were given all day Saturday and Sun-day morning. Those on the history of mathematicsincluded: an examination of John Napier and comput-ing by Pat Baggett and Andrzej Ehrenfeucht; AndrewLeahy’s discussion of Archimedes and Torricelli on cen-ters of gravity; Pierre Boulos’s look at Newton’s rea-sons for providing diagrams; and Chris Christensen’saccount of how US Navy codebreakers calculated Mar-shall Hall’s “weights” during World War II.Presentations dealing with the history of mathemat-ics education included: David L. Roberts’s study ofthe content and rhetoric in Daniel H. Hill’s 1857 alge-bra textbook; Nerida Ellerton’s discussion of the use ofhornbooks in dame schools in the 17th and 18th cen-turies; and Ken Clements’s look at cyphering booksused in New Paltz, NY, between 1675 and 1850. Onpedagogy in the present, Rebecca Vinsonhaler lookedat the JAGUAR project’s study of how two middle-school teachers presented justification in proof.Talks that provided suggestions for using history inteaching mathematics included: John Curran, “His-torical Role-Playing in the Mathematics Classroom”;classroom-tested sample problems from Adam Parkerand Fred Rickey; Michael Todd Edwards’s announce-ment of a new, student-run mathematics history jour-nal at Miami University of Ohio; Jim Smith’s reporton how he used a 4-minute 1930 radio address byDavid Hilbert (now available on MAA Convergence);and ways to employ divergent series and sectors, re-spectively, in classrooms by Colin McKinney and AmyAckerberg-Hastings.The Americas Section also met March 13–15, 2015, atAmerican University in Washington, DC. The high-light of the weekend was a tour of two temporary exhi-bitions at The Phillips Collection: “Man Ray—HumanEquations: A Journey from Mathematics to Shake-speare” and “Hiroshi Sugimoto: Conceptual Forms andMathematical Models,” led by one of the curators. Be-fore the tour, Peggy Kidwell explained some of themodels on display, drawing on the Smithsonian collec-tions. On Friday afternoon, the group also viewed raremathematics books in the AU Archives.Talks on the history of mathematics education in-cluded: David L. Roberts’s examination of numbertheory proofs in some 19th-century American algebratextbooks; Walter Meyer’s contemplation of whetherModernism can be observed in early 20th-century un-

dergraduate curricula; Marina Vulis’s discussion of his-torical roots of Common Core methods; a tracing of theEmerging Scholars Program, a program for increas-ing successful completion rates in first-year calculuscourses, by Rebecca Vinsonhaler; and Amy Ackerberg-Hastings’s look at how Jeremiah Day used the conceptsof analysis and synthesis in his mensuration textbook.On the use of history in the teaching of mathematics,William Rose explained a course he teaches at a localmagnet high school on logic and the history of mathe-matical foundations, while Toke Knudsen showed howhistory of mathematics students at SUNY Oneontaundertake archival projects. Amy Shell-Gellasch sug-gested ways to use spherometers in classrooms. His-tory of mathematics presentations included: RomanSznajder on Euler’s relationships with mathematiciansfrom Gdansk, Poland; Ron Calinger on Euler’s activ-ities in the final decade of his life; and Ilhan Izmirli’sdiscussion of the Mecca problem.The section is currently exploring meeting sites for2015, 2016, and beyond. The officers and other stal-warts who organize meetings also greatly desire to in-crease the section’s emphasis on intersections of historyand pedagogy and to engage with secondary and un-dergraduate teachers. If you can help with any of theseobjectives, please contact the chair, Dave Roberts,[email protected] Ackerberg-Hastings

MAA MathFest Centennial Events

The history and philosophy sessions organized byCSHPM, BSHM, POMSIGMAA, and HOMSIGMAAwill feature over 60 scholarly presentations fromWednes-day, August 5, to Saturday, August 8. But that’snot all, as advertisers say, for attendees looking foracademic and other ways to mark the 100th anniver-sary of the MAA’s founding. In addition to the usualnamed lectures (delivered this year by Karen Smith,Jeffrey Lagarias, David Bressoud, Erica Walker, JoeGallian (on 75 years of MAA mathematics compe-titions), Noam Elkies, and Terrence Blackman), sixspecial Centennial lecturers have been recruited: ErikDemaine, Jennifer Chayes, Ingrid Daubechies, Car-los Castillo-Chavez, Karen Parshall (whose talk alsoserves as our May Lecture), and Manjul Bhargava.The POMSIGMAA guest lecture will be given by JohnBurgess on Thursday evening.

9

Page 10: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

Special invited paper sessions include Wednesday af-ternoon’s “Generations of Monthly Gems,” highlight-ing significant papers published between 1894 and thepresent. Presenters include Karen Parshall, John Still-well, Ron Graham, Bob Devaney, Paul Zorn, and Re-becca Goldin. Victor Katz and Jim Tattersall havelined up former MAA presidents to share reminiscenceson Thursday and Friday afternoons: Henry O. Pol-lak, Lynn A. Steen, Lida K. Barrett, Kenneth Ross,Thomas F. Banchoff, Ann E. Watkins, Ronald L. Gra-ham, Carl C. Cowen, Joseph A. Gallian, David M.Bressoud, Paul M. Zorn, and Robert L. Devaney.Additional history on the program includes a Satur-day afternoon session honoring Abdulalim A. Shabazz(1927–2014), a prolific mentor of African-Americanmathematicians; a session organized by the Associa-tion of Women in Mathematics on women’s historicalcontributions to the discipline, also on Saturday after-noon; and a minicourse on spherical trigonometry byGlen Van Brummelen and Joel Silverberg.Entertainment is also prominent on the schedule. Thefirst night, Wednesday, August 5, will have a largereception as well as a mathematical carnival—withacts by Dominic Klyve, Susan Goldstine, Colm Mulc-ahy, Jason Rosenhouse, and Karl Schaffer—and per-formances by Colin Adams, Art Benjamin, Tanya andTim Chartier, and Karl Schaffer. Thursday evening in-cludes an opportunity to preview The Man Who KnewInfinity, a major feature film about Ramanujan star-ring Dev Patel and Jeremy Irons, and musical per-formances by Noam Elkies, Frank Farris, and others.Friday night, MAA members will perform Tom Stop-pard’s radio comedy, Albert’s Bridge.Other special events include James R. Olsen’s Fridayafternoon workshop on building polyhedra from every-day materials; a contributed paper session on MathCircle problems, also on Friday afternoon; and Satur-day afternoon presentations by Richard Guy and JohnConway on the geometry of triangles.To warm up for these events, be sure to visit the Cen-tennial webpage: www.maa.org/aboutmaa/maa-his-tory/celebrating-the-centennial. Don’t forget toregister to attend MathFest as soon as possible for thelowest rate; remember to declare yourself a member ofCSHPM. See you in DC!

2014 Financial Statements

The following financial statements cover the period1/1/2014 through 31/12/2014.

$ Can.Incomedues/subscriptions 9,831.00exchange rate differential 53.20TOTAL 9,884.99ExpensesKeynote speaker 1,187.69CFHSS 2014 loss 201.72CSHPM Student Prize 750.00PIMS grad stud. conf. 300.00CFHSS dues for 2014 1,851.46Historia Mathematica 3,291.08Philosophia Mathematica 2,443.31Postage, office expenses, Bulletin 326.04Bank fees 5.74TOTAL 10,357.04NET (472.05)Bank balance, 12/31/14 39,110.39TD Mortgage Corporation GIC 4,194.75TD Mortgage Corporation GIC 4,202.85TOTAL ASSETS 47,507.99

Comments:Because the Society has 2 accounts, one in US dollars,we keep two different accounting systems. At the re-quest of the editors, we have combined the numbersfor these accounts. The numbers given are in Cana-dian dollars. A conversion factor of 1.16 has been usedto convert American dollars into Canadian ones.The exchange rate differential is a profit earned intransferring $2,266.80 from the Canadian to the Amer-ican account. The first GIC fund earns interest at1,60% and matures 16 September 2016; the second hasa 1,40% rate and matures 26 March 2017. Overall, theSociety’s assets increased $677.85 over last year.David Bellhouse

2015 Meeting Outline

The 2015 annual meeting of the CSHPM is a jointmeeting with the British Society for the History ofMathematics, the History of Mathematics Special In-terest Group of the MAA (HOMSIGMAA) and the

10

Page 11: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

Philosophy of Mathematics Special Interest Group ofthe MAA (POMSIGMAA). The meeting will be heldAugust 5–8, 2015, in Washington, DC, and is part ofthe Centennial Celebration of the MAA (Mathemat-ical Association of America). Over the course of thefour days of the meeting, there will be roughly 70 talkssplit between general sessions and special sessions. Be-low is a brief description of the schedule:

Wednesday, August 58:30–17:30 General Sessions on the History and Phi-losophy of Mathematics15:00–17:30 Session on the Mathematics of Euler, fea-turing talks given by: Sylvio Bistafa, Rob Bradley,Ronald Calinger, William Hackborn, and DominicKlyve

Thursday, August 68:30–11:30 Special Session in Memory of Jackie Stedall,featuring talks given by: June Barrow-Green, JanetBeery, Rosie Cretney, Chris Hollings, Steve Russ, andRobin Wilson11:30–13:00 Lunch Break (CSHPM Council Meeting)13:00–14:30 General Sessions on the History and Phi-losophy of Mathematics14:30–17:00 Special Session on the Philosophy ofMathematics, featuring talks given by: Elaine Landry,Jean-Pierre Marquis, Jeff Buechner, Alex Manafu, andCarl Behrens5:00–6:00 The POMSIGMAA Lecture on Philosophyof Mathematics, given by John Burgess

Friday, August 78:00–10:30 Special Session on Mathematical Com-munities, featuring talks given by: Amy Ackerberg-Hastings, Janet Barnett, Lawrence D’Antonio, JaneWess, and Diana White10:30–11:30 The May Lecture, given by Karen Par-shall (also one of the MAA Centennial Lectures)11:30–12:30 Lunch12:30–14:00 The CSHPM Annual General Meeting14:00–17:00 Special Session in Honor of Karen Par-shall, featuring talks by: Joe Dauben, BrittanyShields, David Zitarelli, Della Dumbaugh, Patti Hunter,and Deborah Kent17:00–18:00 Reception in Honor of Karen Parshall,hosted by HOMSIGMAA

Saturday, August 88:30–11:30 General Sessions on the History and Phi-losophy of Mathematics11:30–1:00 Lunch13:00–15:30 Special Session in Memory of Ivor Grattan-Guinness, featuring talks by: Adrian Rice, AlbertLewis, John Dawson, Roger Cooke, and Joe Dauben15:30–17:30 Closing General Sessions on the Historyand Philosophy of Mathematics

This is going to be a very rich four days featuring awide variety of scholarship. The detailed schedule forthe general sessions is not yet complete, but it will ap-pear on the CSHPM website in due course. As youcan see elsewhere in this issue, the evenings will in-clude many special events organized by the MAA tocelebrate its Centennial.Maria Zack

Ivor Grattan-Guinness (1941–2014)

As disciplines go, the history of mathematics is rela-tively small. But in common with most academic pur-suits, it is a wide and varied field of research, while thefocus of most individual research in the subject is of-ten necessarily narrow and specialised. There is noth-ing particularly unusual or objectionable in this, but aconsequence is that it is entirely possible for one his-torian of mathematics to be completely unacquaintedwith the work of another scholar working outside his orher immediate area of interest. Indeed, small thoughour community may be, it is hard to think of a contem-porary historian of mathematics whose name is famil-iar to every other scholar in our field. However, if sucha distinction were ever possible, it is arguable that itwas held by Ivor Grattan-Guinness.The sheer enormity of Ivor’s scholarly output is over-whelming. In a career spanning over four decades, hepublished 12 books and more than 250 research papers,as well as a staggering array of shorter articles, bookchapters, book reviews, dictionary and encyclopediaentries, and other works. It was not just the volume ofhis productivity that was immense: the breadth andrange of his contributions to the subject were also re-markable. Ivor wrote on everything from the use ofnumber and magnitude in Euclid’s Elements to theinfluence of Max Newman on Alan Turing. His writ-ings encompassed not only the history of mathematics,

11

Page 12: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

but related disciplines such as the history of science,the history and philosophy of logic, the history of nu-merology, the philosophy of mathematics, and the usesof history in mathematics education. His death fromheart failure on 12 December 2014 brings a close toboth a remarkable career and a formative chapter inthe development of the modern discipline of the historyof mathematics.Ivor Owen Grattan-Guinness was born on 23 June 1941in Bakewell, Derbyshire, the son of Henry Grattan-Guinness, a mathematics teacher in Bakewell and laterDeputy Director of Education in Huddersfield, and hiswife Helena (née Brown). Schooled at HuddersfieldNew College, Ivor entered Wadham College, Oxfordas a mathematics scholar in 1959, graduating with aB.A. in 1962. After a brief career in industry, workingas a research mathematician for E.M.I., he re-enteredhigher education in 1964, joining Enfield College ofTechnology in north London as a lecturer on the math-ematics for business degree course. He had met EnidNeville in 1963 while a member of the BBC Choral So-ciety, an amateur choir in which they both sang. Theirshared love of music soon blossomed into romance, andthey were married in January 1965. Enid would re-main his best friend and constant companion for halfa century.It was Ivor’s experience as a mathematics undergradu-ate at Oxford that initiated the curiosity which wouldultimately lead to his entrée into the history of mathe-matics. While there, he had been frustrated by the lackof interest (and in some cases knowledge) on the part ofthe lecturers with regard to questions concerning boththe theoretical motivation and historical developmentof the subject matter. In an attempt to begin to an-swer these questions, and simultaneous with the startof his teaching career, Ivor entered the London Schoolof Economics (LSE) as a part-time student in the de-partment of philosophy, logic and scientific method,founded and then run by Karl Popper. Although thedepartmental atmosphere was not quite as collegial ashe might have wished, the intellectual effect on Ivorwas both stimulating and influential, and included hisfirst exposure to mathematical logic, sparking a fasci-nation which was to reverberate throughout his workfor the rest of his life. He graduated with an M.Sc. inthe philosophy of science in 1966.Equipped with a philosophical background againstwhich to frame his unanswered questions, Ivor now

Figure 1: Ivor with cat

sought to focus on a particular area of mathematicsin which his historical and educational concerns wereprominent. Having already learnt of the connectionbetween Fourier series and fundamental concepts inanalysis and set theory, his attention was drawn tothe foundational work of Fourier and Cauchy. New tothe field, he sought guidance from a scholar who, atthis time, was one of the only professional historiansof mathematics in the country, then fully immersedin the publication of Newton’s mathematical papers.From Tom Whiteside he received much valuable adviceon matters concerning archival research, which wouldvery soon become Ivor’s forte; Whiteside also helped toestablish a working relationship with another scholarwho had done recent work on Fourier, Jerome Ravetzat the University of Leeds.By 1967, Ivor was working on two complementary, butparallel, projects as a doctoral student in LSE’s de-partment of mathematics. Under the supervision ofthe analyst and head of department, Cyril Offord, withRavetz serving as his external supervisor, the studyof Cauchy became his eventual thesis, for which hereceived a Ph.D. from the University of London in1969. With minor changes, this work was publishedas his first book, The Development of the Foundationsof Mathematical Analysis from Euler to Riemann, in1970. Meanwhile his collaboration with Ravetz onFourier became a full-scale study, not only of the then

12

Page 13: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

unpublished 1807 memoir on heat diffusion, but alsoof his life, with prodigious use of a large number ofpreviously unpublished manuscript sources—a featurethat would become a defining characteristic of much ofIvor’s work.At Ravetz’s suggestion, the external examiner on Ivor’sPh.D. committee was Sir Edward Collingwood, a se-nior figure in British analysis at the time and shortlyto become President of the London Mathematical So-ciety. Collingwood had a deep interest in the historyof mathematics in general, but was particularly fas-cinated by the work of Georg Cantor. The develop-mental connections between Cantorian set theory andthe Weierstrassian mathematical analysis so closely re-lated to Ivor’s recent research now led him into a new,but related, area of research: the history of set the-ory. Collingwood had somehow learned that a keyto finding more archival information lay in the formerhome of Weierstrass’s Swedish disciple Gösta Mittag-Leffler, just outside Stockholm, and in 1968, Ivor wasdispatched at Collingwood’s own expense on a researchtrip to Sweden. What occurred there on that first visitand again in 1970 was to have a profound impact onIvor’s research: in the course of searching through thelargely unsorted documents, he stumbled across liter-ally hundreds of manuscripts not widely known to thehistory of mathematics community. These documentsconcerned not only Cantor and Weierstrass, but alsomany of their late-nineteenth-century contemporariesincluding Sofia Kovalevskaya, Henri Poincaré, PhilipJourdain and Bertrand Russell. The publication of hisfindings in 1971 helped establish for Ivor a reputation,both for his ability to locate archival sources and forhis eagerness to share that knowledge with the widerscholarly community.His association with Collingwood now led him to meeta woman who would influence his career for manyyears. Cecily Tanner was born in Göttingen in 1900as Rosalind Cecilia Hildegard Young, the daughter ofWilliam and Grace Chisolm Young, the British math-ematicians who had championed the new set and mea-sure theory in the opening decades of the 20th cen-tury. Like her parents, she had studied mathematicsat Cambridge and like them she was an analyst, re-ceiving a Ph.D. on the theory of Stieltjes integrationin 1929. She had collaborated with Collingwood whenthey were both working at the University College ofWales in Aberystwyth in the 1920s, and for much ofher career she had been an active researcher in the

history of mathematics, retiring from a lectureship inmathematics at Imperial College London in 1967. TheYoungs had been good friends with Cantor, and Tan-ner was still in touch with his grandchildren; it wasvia this link that Ivor was granted access to Cantor’sNachlass, which involved taking a trip behind the IronCurtain to Halle University in East Germany in 1969.Ivor’s friendship with Tanner also led to his detailedstudy of the mathematical collaboration of her parents,the first of its kind in the history of mathematics.The network of connections continued to grow wider,and more international. For many years, via her Ger-man connections, Tanner had been one of the few non-Germans invited to attend J. E. Hofmann’s annualmeetings on the history of mathematics at the Math-ematisches Forschungsinstitut in Oberwolfach, whichhad been running since 1954. At her request, Ivorreceived an invitation to the meeting of 1969. His par-ticipation at that meeting marked the beginning of anew phase in his career: not only was he introduced toa whole new community of historically-minded mathe-maticians, able to impart advice on research and pointhim in new directions, but that community was also tobe the source of a number of lifelong friendships, per-haps most notably with Christoph Scriba. The Ober-wolfach meetings also marked the start of a truly inter-national career, as Ivor soon became a familiar figure atconferences first in Europe, then America, then aroundthe world. For most of the next forty years, Ivor circledthe globe, visiting archives, attending conferences andgiving over 500 invited lectures, or “gigs” as he oftenused to call them. As he later put it: “My researchlife has always centred largely on two kinds of journey:to the centre of London, to use the libraries; and toa station or airport, to travel abroad and tell foreign-ers about the findings and give lecture courses to theirstudents.” But throughout his career, it was the intel-lectual immersion, relaxed collegiality and breathtak-ing scenery of Oberwolfach that he always viewed witha special fondness, and he and Enid would be regularfixtures at the history of mathematics meetings therefor over three decades.Back home however, no such community of histori-ans of mathematics existed. The British history ofscience community was largely apathetic—and indeedthe very subject was still viewed by most practicingmathematicians in Britain merely as something to doin one’s retirement. So when, at the beginning of the1970s, John Dubbey and Arthur Morley proposed the

13

Page 14: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

creation of a learned society specifically devoted tothe history of mathematics, Ivor considered the ideato be “hopelessly optimistic”. Nevertheless, on 2 July1971, he was one of five speakers at a special meet-ing held at Thames Polytechnic (now the Universityof Greenwich) in London. This turned out to be thefirst meeting of the British Society for the History ofMathematics, now the oldest such society in the world.Elected its sixth president in 1986, he pushed througha formal constitution and forged stronger relationshipswith the international history of mathematics commu-nity, via invitations to speak at the society’s meetingsand active recruitment of members from overseas. As aresult, by the end of his presidency in 1988, one quarterof the society’s growing membership came from outsidethe United Kingdom.Ivor’s published output was so vast and so wide-ranging that it would take a monograph-length paperto provide a detailed survey; even the following sum-mary of his contributions to the history of mathematicsis necessarily incomplete.Ivor’s research began in an area that was to permeatemuch of his work, particularly in the first half of hiscareer: the history of the foundations of mathematics.Initially, as seen above, this was motivated by a dissat-isfaction with the presentation of mathematics in hisown education, and this led to an early focus on thedevelopment of analysis with the work of Fourier andCauchy. His first book, The Development of the Foun-dations of Mathematical Analysis from Euler to Rie-mann (1970), centred on an investigation of the math-ematics of Cauchy and his contemporaries, includingAbel and Dirichlet. It also contained a valuable ap-pendix on the history of convergence tests, which stillremains a useful resource. His joint work with Ravetzon Joseph Fourier appeared in 1972. Up to this point,Fourier’s key 1807 memoir “Sur la propagation de lachaleur” only existed in manuscript form in Paris, sohistorical studies of Fourier had been forced to relyon the greatly expanded and amended published ver-sion, Théorie analytique de la chaleur (1822). Work-ing in the Paris archives, Ivor studied over 6,000 pagesof Fourier’s manuscripts, including many in which thehandwriting was barely legible, to come up with hisannotated version. The previously unpublished 1807memoir appeared in print for the first time in the col-laborative book Joseph Fourier, 1768–1830, in whichIvor provided a detailed commentary on the paper andon related aspects of Fourier’s life and work.

Ivor’s consequent expertise, not only in the history ofnineteenth-century analysis, but also in the history ofpost-revolutionary French mathematics, led to invita-tions to contribute several biographical studies to theDictionary of Scientific Biography (DSB), then in theprocess of compilation by Charles Gillispie. In addi-tion to the entries on Fourier, Laurent, Mathieu, Rieszand Stäckel, Ivor also wrote a section on the history ofthe Laplace transform for Gillispie’s book-length biog-raphy of Laplace, first published in volume 15 of theDSB in 1978, and later re-published in book form byPrinceton University Press.Work on French mathematics continued through the1980s, much of which was occupied by the preparationof what was arguably his magnum opus: the three-volume Convolutions in French Mathematics, 1800–1840: From the Calculus and Mechanics to Mathemat-ical Analysis and Mathematical Physics, published in1990. This 1,600-page work remains the most com-prehensive study to date of early nineteenth-centuryFrench mathematics and is a veritable treasure troveof previously unpublished sources, biographical and in-stitutional information and reference. It treated thedevelopment of the mathematical sciences in Francenot as a sequence of great leaps, or “revolutions”, noras a story of gradual progress, “evolution”, but ratheras a series of twists and turns; hence the “convolu-tions” of the title. Rejecting the one-dimensional in-ternalist approach to the history of mathematics, Ivorsituated the mathematical developments within theParisian mathematical and broader French scientificmilieu, so that publication venues, institutional his-tories, and developments in higher education were allintegral to the main narrative. Consequently, sincepeople like Cauchy, Fourier and Laplace did not op-erate in isolation, it was not just the famous namesthat featured; a plethora of minor (but significant) fig-ures were also interwoven into the account to provide afuller picture of the intellectual environment. Finally,Ivor avoided the common error of viewing mathemat-ics as “pure mathematics” by treating developments inanalysis, calculus, mechanics, heat diffusion, elasticity,electricity and magnetism, and optics as interrelatedcomponents of a cohesive field of study. This inclusiveattitude to mathematics, or rather, “the mathemati-cal sciences”, was yet another characteristic feature ofIvor’s work.The path which had led from the history of analysis toset theory, via Georg Cantor, soon led to an interest in

14

Page 15: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

the life and work of Bertrand Russell, to whom in laterlife Ivor developed a strong physical resemblance. Hewas one of the very few people who actually attemptedto read Russell and Whitehead’s Principia Mathemat-ica and was not only familiar with its content, but hehad also researched the tortuous process of its creation.Again, substantial archival research produced signifi-cant contributions to our understanding of Russell’smathematical work, including a reconstruction of thereasoning which led to Russell’s 1901 discovery of hisparadox, and an edition of his correspondence withPhilip Jourdain, Dear Russell–Dear Jourdain, pub-lished in 1977. Ivor’s The Search for MathematicalRoots, 1870–1940: Logics, set theories and the foun-dation of mathematics from Cantor through Russell toGödel, which appeared in 2000, was the culmination ofdecades of immersion in the collections of the Russellarchive. This book traced the development of a varietyof logical systems in a wide range of national settings,with the work of Russell forming the centrepiece of thestudy. Key features included the de-emphasis on Fregeas an influence on Russell, with more focus on the stim-ulus of the Peano school. Ivor also made an importantdistinction between practitioners of what he called “al-gebraic logic”—namely those who used mathematicalnotation to facilitate the study of logic (e.g. Boole,De Morgan, Schröder)—and those of “mathematicallogic” (e.g. Frege, Russell, Whitehead)—who soughtto use logic as a base for the study of mathematics—and remarked upon the distinct lack of communicationbetween the two sides.The second half of his career was dominated by work onedited volumes and works of reference. One of the firstof these was his remarkable Companion Encyclopediaof the History and Philosophy of the Mathematical Sci-ences (1994). Featuring 175 contributions from nofewer than 134 authors, this two-volume work is a mas-terpiece of editorial organisation and a valuable sourceof articles on many topics completely ignored by othercompendia. Ivor’s general survey of the history ofthe mathematical sciences, The Rainbow of Mathemat-ics, appeared as the sixth volume of the Fontana His-tory of Science series in 1997. Like the Encyclopedia,this substantial work distinguished itself from manyof its predecessors by its concentration on post-1800mathematical developments, its inclusion of importantbut lesser-known figures, its consideration of nationalcharacteristics in the practice of mathematics, and itsemphasis on the importance of mathematical applica-

tions as a stimulus of mathematical progress. A finaltour de force was delivered in 2005 with the publica-tion of his Landmark Writings in Western Mathematics1640–1940, a thousand-page collection of 77 chaptersby 65 authors surveying 89 important mathematical“writings”, from Descartes’ Géométrie to Hilbert andBernays’ Grundlagen der Mathematik. All these workscodified vast amounts of information in accessible for-mats, combining first-rate scholarship with deft edito-rial skill to produce valuable and high quality works ofreference.This editorial skill had been honed over many yearsas a journal editor, for in addition to serving on theeditorial board of Historia Mathematica and a numberof other journals for much of his career, Ivor rescuedthe ailing Annals of Science from pending extinctionin 1974, serving as its editor-in-chief until 1981. Healso founded a new journal, History and Philosophyof Logic in 1979, which he edited until 1992. Whenthe project to update the century-old Dictionary ofNational Biography was announced in 1994, Ivor wasthe obvious choice for the associate editor in charge ofmathematics and statistics, and when the Oxford DNBfinally appeared ten years later, the scores of articleson mathematicians and statisticians had all been com-missioned, edited and, in some cases, written by him.Ivor’s work found many admirers, but it was not with-out controversy. His assertion that Cauchy had plagia-rised key ideas in analysis from Bolzano’s 1817 paperon the intermediate value theorem was hotly disputed,while a later claim that the substitutional theory ofclasses and relations formed the missing link betweenRussell’s theory of denoting and the Principia Math-ematica also proved contentious. But in truth, Ivornever intended his work to be the last word on anysubject, and if he stirred up debate along the way, thatwould serve as the impetus for future research on thesubject. Elements of his style may not have been toeveryone’s taste, but in his opinion it was far better forthe discipline if his work was criticised than if it wasignored. Thus, whether they agreed with him or not,subsequent historians of mathematics were forced toengage with his work and respond to his conclusions.His published output was characterised by the use ofvast amounts of archival research, the meticulous studyof primary sources, often in several languages, and thefusion of a wide range of mathematical ideas. Recur-ring themes included an intense belief in the use of the

15

Page 16: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

history of mathematics in mathematics education—theinfluence of which has begun to appear in recent years;a conviction that the history of mathematics withoutreference to its applications is incomplete; and an in-sistence on the distinction between the notions of “his-tory” and “heritage” when discussing mathematical de-velopments. By the latter term he referred to a view ofhistory held by many mathematicians, which centreson questions such as “how did we get here?” as op-posed to the concern of most historians, which tendsto focus more on asking “what happened in the past?”This distinction, as well as its many ramifications, wasa subject of immense importance to Ivor and, aftermany years of gestation, formed the subject of one ofhis last major papers.Institutionally, Ivor remained for his whole career atthe Enfield College of Technology, although it under-went substantial changes in that time. In 1973, thecollege merged with two other north London schools toformMiddlesex Polytechnic, which, as a new and grow-ing institution, soon sought to improve its researchprofile. To complement his own research, Ivor wasencouraged to supervise doctoral students. Beginningwith Tony Crilly, Ivor went on to successfully supervisenine Ph.D. theses, from Crilly’s study of the mathe-matics of Arthur Cayley to Abhilasha Aggarwal’s sur-vey of higher mathematics education in British Indiain 2007. The content of many of these theses, partic-ularly that of Maria Panteki on the relationships be-tween algebra, differential equations and logic in earlynineteenth-century Britain, also influenced the courseof his own research and the breadth of his publicationsspread still further.As a research supervisor, Ivor was unparalleled. De-spite what may have appeared to those who did notknow him well as an intense and rather brusque per-sona, he was in fact a tremendously kind and generousman gifted with a powerful intellect and love of his sub-ject. From the moment work began, the student wouldbe showered with papers, articles, newspaper cuttingsand other material relevant to their research. Ivorwas a consummate professional and expected his stu-dents to be likewise, encouraging active participationin meetings, seminars and conferences, and fosteringconnections with others in the history of mathematicscommunity. Regular weekly or fortnightly meetingswith him, usually over lunch near an archive in cen-tral London, were the student’s opportunity to discussideas with Ivor and occasionally reveal any discoveries

he or she had made. Such revelations were frequentlyaccompanied by Ivor’s wide-eyed exclamations of “Re-ally?? ” To the novice researcher, such expressions ofexcitement and interest, the free acknowledgement ofgaps in his own knowledge and the willingness to learnfrom his students were the source of tremendous en-couragement and inspiration. Beyond the Ph.D., Ivorcontinued to maintain close and friendly relationshipswith all of his former graduate students. Indeed, forIvor, who had no children of his own, this small groupof people came to form what was, for him and Enid,almost a surrogate family.Ivor was a man of many eccentricities. In later yearshe was wont to appear to fall asleep in seminars andconference talks, particularly after lunch, only to wakeup and ask a penetrating question at the end. An er-ratic driver, car journeys with Ivor were always memo-rable, not least for having survived them. Tony Crillyrecalls being driven back by Ivor after a meeting inOxford at high speed so that Ivor could get home intime for two editing sessions before bed! In writtencommunications, Ivor’s distinctive scrawl was a chal-lenge even to those well trained in reading barely legi-ble manuscripts, and the advent of e-mail only height-ened the need for one’s cryptographic skills to decipherhis messages. One example (of many) was in reply toan earlier message and read simply:

v god. tanks for rude. no way to get plan topairs. iv Translation: “Very good. Thanks forthe ride. On my way to get a plane to Paris.Ivor.”

During a long and distinguished career, Ivor was ac-corded many honours. In 1978 the University ofLondon bestowed the rare distinction of awardinghim the prestigious D.Sc., its highest doctoral degree.Elected a membre effectif of the Académie interna-tionale d’histoire des sciences in 1991, he also heldvisiting positions at the Institute for Advanced Studyin Princeton, Monash University and the Universityof Western Australia. In 1992, Middlesex Polytech-nic was granted university status and became Middle-sex University. The following year, Ivor, who by thistime had progressed from Senior Lecturer to Reader inMathematics, was appointed Professor of the Historyof Mathematics and Logic at the university. He wouldhold this title until his retirement in 2002. The twohonours that perhaps afforded him the most pleasurecame late in life: in 2009 he received the Kenneth O.

16

Page 17: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

May Prize and Medal from the International Commis-sion for the History of Mathematics for “lifetime schol-arly achievement and commitment to the field”, fol-lowed by his election to honorary membership of theBertrand Russell Society in 2010.The first few years of retirement saw little change inIvor’s output as his research continued at its usualrapid pace. Only with the diagnosis of Parkinson’sdisease in 2007 and a heart bypass operation the fol-lowing year did the number of meetings he could at-tend begin to decrease and the time taken to preparehis papers begin to increase. But he was as responsiveas ever to requests for comments on first drafts, withwork returned almost immediately with references andcomments. His final research paper for Historia Math-ematica appeared in February 2014, and his last paperwas accepted for publication the week before he died.It was only in the last few weeks of his life that hebegan to find working at the computer too much of astrain. But his fascination with the history of mathe-matics was undiminished to the end.In Britain he leaves the dual legacy of an establishedprofessional discipline and a learned society devotedto it, both non-existent at the start of his career andin both of which he played foundational roles. To theArchives of American Mathematics he leaves his Nach-lass. And to scholars around the world, he leaves hisvast array of publications—an oeuvre on which futuregenerations of historians of mathematics will continueto build.Acknowledgements: The author wishes to thank JuneBarrow-Green, Tony Crilly, Joseph Dauben, EnidGrattan-Guinness, Niccolò Guicciardini, Albert Lewisand Karen Parshall for their valuable help and adviceduring the preparation of this article.Adrian Rice

MAA Ohio Section Centennial

The Ohio Section of the Mathematical Associationof America came into being on December 31, 1915,along with the MAA itself. We have been anticipatingthe centennial of our section for the past five years,with “Centennial Notes” published in the Ohio Fo-cus newsletter, “Centennial Minutes” presented at eachSpring and Fall Ohio Section meeting, and tchotchkesdistributed to all registrants featuring the message,“The Centennial Is Coming.”

A Centennial History of the MAA Ohio Section willbe published later this year. A 75-year history, TheOhio Section: 1915-1990 is currently available on-lineat sections.maa.org/ohio/History/index.html.The first annual meeting of the Ohio Section was heldat Ohio State University in April 1916. Because therewas no annual meeting in 1945, due to wartime travelrestrictions, our 100th annual meeting will occur nextyear, on April 8–9, 2016. We will meet at Ohio North-ern University, where Benjamin F. Finkel, founder ofThe American Mathematical Monthly, earned a B.S.in 1888 and a M.S. in 1891. Then, the institution wascalled Ohio Normal University.We welcome anyone interested in attending this meet-ing. As details become available, they will be posted onthe Ohio section website, sections.maa.org/ohio/.Copies of “Centennial Notes” can also be found there,in archived issues of Ohio Focus.David Kullman

Book Review

John Napier: Life, Logarithms, and Legacy, by JulianHavil, Princeton: Princeton University Press, 2014,296 pp. 64 line illus. 48 tables. ISBN 978-0-691-15570-8,$US35.00 £22.95.Julian Havil, retired master and long-time teacher ofmathematics at Winchester College, England, 1 is theauthor of four successful books, published by Prince-ton University Press: Gamma, Nonplussed!, Impossi-ble? and The Irrationals.Havil’s book opens with an overview of Napier’s lifeand lineage, devotes a chapter to each of Napier’s fivepublished works, and concludes with a short chapteron Napier’s legacies, supplemented by no fewer thantwelve short appendices that provide many details ofthe historical, cultural, and mathematical contexts ofthe previous material.The strength of this book is that it places each ofNapier’s works within the context of Napier’s personaldevelopment and within the context of his family andthe times and culture within which he lived. Havilgives us considerable insight into Napier’s religious fer-vor, the demands and concerns of his aristocratic posi-tion, and his mathematical insights and contributions.Napier’s reputation rests primarily on three works:

1http://www.winchestercollege.org

17

Page 18: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

The Plain Discovery, written around 1593, the descrip-tio and the constructio, each written before 1614. Theinfluence of Napier’s mathematical work was greatlyaided through the efforts of his son Robert, HenryBriggs (1st Gresham Professor of Geometry, 1st Savil-ian Professor of Geometry at Oxford), Edmund Gunter(3rd Gresham Professor of Astronomy), and the math-ematical practitioner Edward Wright.Havil’s book is unusual in that it devotes a full chap-ter to each of Napier’s published works, mathematicaland non-mathematical, published during his lifetimeand published posthumously. Each of the five worksis placed in its proper cultural context, and the con-tent of each of the books, including the mathematicalcontent, is examined in detail.

• A Plaine Discovery of the Whole Revelation of St.John (1593). A work of Calvinist theology, inter-preting the book of Revelation as a prophecy ofhistorical and current events.

This massive tome of nearly 400 pages is organizedinto 36 Propositions, with arguments organized andlaid out in charts of parallel prophecies and theirinterpretations in the style of Peter Ramus.

This work was widely popular, published in fourlanguages in over two dozen editions. It establishedNapier’s reputation as theological scholar of Refor-mation Protestant doctrine.

• Mirifici logarithmorum canonis descriptio (1614).A description of the concept of logarithms, or ratio-numbers, based upon a kinetic model of propor-tional movement in comparison to movement at aconstant velocity. A set of tables of the logarithmsof sines is included, but no table of logarithms ofnumbers. First English edition, 1616.

• Rabdologiae seu numerationis per virgulas libri duo(1617). Published in the year of Napier’s death.A description of mechanical aids to multiplication:Napier’s Rods, a Promptuary of lightning multi-plication, and local arithmetic—a method for ma-nipulating markers on a checkerboard to performbinary arithmetic.

• Mirifici logarithmorum canonis constructio (1619).Likely written prior to the year in which the de-scriptio was published. This work details pre-cisely how to produce a table of “artificial numbers”from which the table of “artificial sines” in the de-scriptio was drawn. Published from John Napier’s

manuscripts two years after Napier’s death by hisliterary executor and son, Robert Napier.

• De arte logistica (1839). A collection of notesrecording Napier’s explorations and musings overtwo decades into the nature of number. They re-veal Napier’s investigations into natural numbers,negative integers, rational and irrational numbers,and even imaginary numbers, although not un-der those names. Probably written before 1594,but not intended for publication. A fair copy inRobert Napier’s hand, intended to be given toHenry Briggs, survived among the Napier fami-lies’ private papers. These papers were edited andpublished more than two centuries after Napier’sdeath by historian Mark Napier, the grandson ofthe youngest son of John Napier’s grandfather.

Havil excels in providing a rich context that brings theworld of Napier to life for the modern reader. As abrief example, I include a few of the myriad details ofNapier family history taken from Havil’s introductorychapter — Life and Lineage.John Napier, the 8th Laird and Baron of Merchiston,descended through a line of eldest sons from Alexan-der, Provost of Edinburgh (bef. 1403) and 1st Lairdof Merchiston (a rank of minor nobility) (bef. 1438).Napier’s father, the 7th Laird of Merchiston was madeMaster of the Mint, while his ancestors, relatives, andin-laws included an array of colorful characters, includ-ing several who were involved in alchemy, accused ofsorcery, and involved in various crimes ranging fromhighway robbery, through witchcraft, to high treason.On the other hand, the 3rd, 4th, and 5th Lairds died inbattle in the service of the King, several were knighted,and the 4th Laird became the first Baron of Merchis-ton, and thus Lord Napier.Napier entered the University of St Andrews at the ageof 13, leaving one year later to spend the next 7 yearsin Europe. No record survives from his European stay,but he returned to his home at age 21 in 1571, fullytrained in Latin and Greek, and assumed his familyduties, while carrying on the theological and mathe-matical researches that would occupy him for the nexttwenty-five years. In 1593, he initiated a series of pub-lications which would earn him the admiration and ap-preciation of scholars and scientists across Britain andthe Continent.Importantly, in addition to providing the context ofNapier’s work, Havil presents the details of both

18

Page 19: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

Napier’s theological and mathematical contributions.He takes pains to point out the centrality of trigonom-etry, especially spherical trigonometry, to Napier’s con-cerns in astronomy, navigation, and, to some extent,cartography. He also points out that Napier thoughtin terms of proportions and ratios and their solutionby the “rule of three,” as opposed to the solution ofalgebraic equations—which is to be expected since Eu-ropean algebra was still in its embryonic stages.However, Havil repeatedly retreats from Napier’sfifteenth- and sixteenth- century framework to trans-late Napier’s accomplishments into modern mathe-matical terms—terms quite alien to Napier and hiscontemporaries—an approach which obscures the ex-position and needlessly complicates it rather than clar-ifies it.Further, when the reader is most in need of a guideto the intellectual and mathematical train of thought,Havil frequently retreats into a modern understanding,stating that such explanations are “best approachedthrough modern notation” or are “best explained inmodern terms.” In recasting the situation into mod-ern terms, any understanding of the originality andcreativity of Napier, the man, working with the toolsthat he had at hand, is obscured, distorted, or lost.When explaining Napier’s more complex reasoning,Havil couches his explanations in anachronistic termsof a fully developed algebra, relying on modern nota-tion, including exponents, subscripted variables, mul-tipage sequences of inequalities leading to upper andlower bounds, and sections of Mathematica computercode. This reviewer is strongly of the opinion thata historical approach to explaining Napier’s contribu-tions would have been a better choice. More helpfulwould be a guide to the adaptations Napier made tothe practices and methods of Regiomontanus, Rheti-cus, Pitiscus, or Remus—frameworks that Napier mostlikely encountered during his travels in Europe. Anexplanation of the doctrine of triangles or the impor-tance of homogeneity in the pre-Eulerian concepts oftrig functions, and the conflict between emerging ideasof algebra and the requirements of homogeneity in cal-culation arising from the Euclidean books on ratio andproportion, would do much to illuminate Napier’s ap-proach.These caveats aside, there is much to enjoy and admirein this book. It is a welcome addition to the litera-ture and provides a much-needed context into which

to place Napier and his work. The richness of detailsof the politics, religious struggles, and the connectionsbetween Scotland, England, France, Holland and thecentral European continent brings the story to life.Furthermore, Havil considers all of Napier’s output,not only a portion of it, and when discussing math-ematical or technical matters, he does not shy awayfrom attempting to present the mathematical details ofNapier’s work, including the use of logarithms, the me-chanical inventions for automating arithmetic, and thedevelopment of logarithmic tables themselves. Whileintended for a general audience, John Napier: Life,Logarithms, and Legacy would also be of considerablevalue to the serious historian wishing a more in-depthunderstanding of Napier and his writings, but only ifread together with Napier’s original exposition, andnot as a replacement or substitute.Joel Silverberg

New Members

Congratulations to the following new members whohave joined the Society since our last Bulletin. Welook forward to your contributions.Valerie AllenJohn Jay College, CUNYUSAFiona EbberttTurnwater, WAUSAHueston FinlayWindsorUKEnrico JabaraVeneziaItalySiobhan RobertsToronto, ONCanada

From the Editor

Preparations—some of which began a decade ago—arenearly complete for the MathFest marking the Math-ematical Association of America’s centennial, August5–8, 2015. This event also serves as the annual meet-

19

Page 20: CSHPM Bulletin, May 2015 - michaelmolinsky.org · ABOUTTHESOCIETY Founded in 1974, the Canadian Society for the His-tory and Philosophy of Mathematics / Société cana-dienne d’histoire

ing for CSHPM and a joint meeting between CSHPM,BSHM, HOMSIGMAA, and POMSIGMAA. As youwill see elsewhere in this issue, the four days of themeeting are absolutely packed with mathematics his-tory, philosophy, and fun. The full program of ourjoint sessions will be available later this spring atwww.cshpm.org and www.maa.org. For information onthe pleasures and logistics of the wider Washington,DC, area, see our November 2014 issue.The initiatives launched by the Society over the pastcouple of years, such as transferring production ofour Proceedings to Birkhäuser, continue to move for-ward. If you enjoy the columns CSHPM is contribut-ing to Notes of the Canadian Mathematical Society,cms.math.ca/notes/, please consider not only volun-teering but actually composing a brief piece (about1,200 words) for a general mathematics audience andsubmitting it to Hardy Grant, [email protected],and me. We are juggling enough other professionaltasks that building a reservoir of completed columnswould be very useful. The Council is also aiming to re-vitalize our presence at the CMS Winter Meeting; con-tact President Elaine Landry, [email protected],if you can help.Since last fall, we have sadly lost three historians well-known to our society: member Jim Kiernan and promi-nent BSHM figures Jackie Stedall and Ivor Grattan-Guinness. An obituary for Ivor appears here, withmemorials for Jim and Jackie planned later. Peace totheir memories.The Bulletin reaches your hands or computer screendue to the continued efforts of Eisso Atzema, Lay-out Editor; Maria Zack, Production Editor; Pat Al-laire, Secretary; and Mike Molinsky, Webmaster. Iam thankful also for our officers, Councillors, and thevolunteers who keep the Society’s other functions op-erating smoothly. The next submission deadline forthe Bulletin is 1 October 2015. As always, the editorsseek news items of interest to historians and philoso-phers of mathematics, reports on conferences attended,and personal and professional announcements. We alsowelcome suggestions for memorials, book and web re-views, and informative or thought-provoking column-style articles. Plain text and LaTeX files are easiest forthe editors to deal with, but we can (tediously) convertWord’s special characters as well. Submissions may besent to [email protected] Ackerberg-Hastings

About the Bulletin

The Bulletin is published each May and Novemberby a team of 3 volunteers: Content Editor AmyAckerberg-Hastings ([email protected]), LayoutEditor Eisso Atzema ([email protected]),and Production Editor Maria Zack ([email protected]). Material without a byline orother attribution has been written by the editors.Les pages sont chaleureusement ouvertes aux textessoumis en français. Comments and suggestions arewelcome and can be directed to any of the editors;submissions should be sent to Amy Ackerberg-Hastings at the above email address, or by postalmail to 5908 Halsey Road, Rockville, MD 20851,USA.

Printed courtesy of:

20