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 ABOUT THE SOCIETY Announcements

Founded in 1974, the Canadian Society for the His- Congratulations to Glen Van Brummelen, 2015 recip- tory and Philosophy of Mathematics / Société cana- ient of the MAA Pacific Northwest Section’s Teaching dienne d’histoire et philosophie des mathématiques Award. This section is the largest geographically in (CSHPM/SCHPM) promotes research and teaching in the MAA, comprising over 130 colleges and universi- the history and philosophy of mathematics. Officers of ties from Oregon to Alaska. the Society are: Umberto Bottazzini received the 2015 AMS Albert President: Elaine Landry, UC Davis, Davis, CA Leon Whiteman Memorial Prize at the Joint Math- 95616, USA, [email protected] ematics Meetings in San Antonio for “his many works Vice-President: Dirk Schlimm, McGill University, in the history of mathematics, notably on the rise of Montréal, QC H3A 2T7, CA, dirk.schlimm@mcgill. modern mathematics in Italy and on analysis in the ca 19th and early 20th centuries.” Also in San Antonio, Secretary: Patricia Allaire, 14818 60th Ave., Flush- Mathematical Reviews celebrated its 75th anniversary. ing, NY 11355, USA, [email protected] Oxton House has issued a second edition of Math Treasurer: David Bellhouse, University of West- through the Ages, by William P. Berlinghoff and Fer- ern Ontario, London, ON N6A 5B7, CA, bellhouse@ nando Q. Gouvêa. The first edition has been adopted stats.uwo.ca as a text by more than 100 colleges and universities Past President: Glen Van Brummelen, Quest Uni- throughout the United States, and it has been trans- versity, Squamish, BC V8B 0N8, CA, [email protected] lated into Portuguese, Chinese, and Slovenian. It was awarded the Mathematical Association of America’s prestigious Beckenbach Book Prize in 2007. Members of Council Michel Serfati has published “Descartes et Schooten. Les aventures d’une division difficile”, Images des Craig Fraser, University of Toronto, Toronto, ON Mathématiques, CNRS, 2014, images.math.cnrs.fr/ M5S 2J7, CA, [email protected] Descartes-et-Schooten-Les.html; and “Order in Jean-Pierre Marquis, Université de Montréal, Mon- Descartes. Harmony in Leibniz: Two regulative princi- tréal, QC H3C 3J7, CA, jean-pierre.marquis@ ples of mathematical analysis”, Studia Leibnitiana 45, umontreal.ca no. 1 (2013): 59–96. Karen Hunger Parshall, University of Virginia, Janet Barnett, Dominic Klyve, Jerry Lodder, Daniel Charlottesville, VA 22904, USA, khp3k@eservices. Otero, Nicolas Scoville, and Diana White contributed virginia.edu “Using Primary Source Projects to Teach Mathemat- Joel Silverberg, Roger Williams University, Bristol, ics” to the AMS Blog On Teaching and Learning Math- RI 02809, USA, [email protected] ematics, 20 January 2015. Peter L. Griffiths’s article on Fermat’s Last Theorem The Society’s Web Page (www.cshpm.org) is main- appeared in the April 2014 issue of M500, a magazine tained by Michael Molinsky, University of Maine at founded in 1973 by Open University mathematics stu- Farmington, Farmington, ME 04938, USA, michael. dents. [email protected]. The Proceedings of the An- nual Meeting are edited by Maria Zack, Point Loma The inaugural Mahoney Prize, commemorating histo- Nazarene University, San Diego, CA 92106, USA, rian of science Michael S. Mahoney, will be awarded in [email protected]. The Society’s Archives are managed 2015. See www.sigcis.org/mahoneyprize. by Michael Molinsky (see above). The position of HOM SIGMAA News: Larry D’Antonio was CMS Liaison is vacant. elected Secretary/Treasurer. Toke Knudsen was elected New Members are most cordially welcome; please con- Program Coordinator. HOM SIGMAA will sponsor a tact the Secretary. reception for Karen Parshall during MathFest, August 5–8, 2015, in Washington, DC. The reception will be held on August 7. MathFest will feature several His- tory of Mathematics sessions.

2 Volume 5, issue 1 (January 2015) of the Journal of Hu- Mathematics, hosted by the Department of Mathemat- manistic Mathematics is now available at scholarship. ics & Computer Science at Adelphi University, pre- claremont.edu/jhm. It includes an article on the sented the following speakers in 2014–2015: Harold Ed- Smithsonian’s kinematic models by Amy Shell-Gellasch wards (NYU) on October 8; William Dunham (Muh- and first-day-of-class strategies for Calculus I by Mar- lenberg) on November 5; Jonathan Sondow on De- ion Cohen. An upcoming special issue will be de- cember 3; Michael J. Barany (Princeton) on March voted to “The Nature and Experience of Mathematical 4; Maria Zack (Point Loma Nazarene) on April 1; and Beauty.” The journal is also seeking referees. Rob Bradley (Adelphi) on May 6. Issue 02 of the Science Museum Group Journal is Michel Serfati announces the second semester program available at journal.sciencemuseum.ac.uk/issues/ for the annual seminar on Epistemology and History autumn-2014/. The National Maritime Museum’s ex- of Mathematical Ideas, held Wednesdays at 2:00 pm at hibition, Ships, Clocks & Stars is reviewed. the Institut Henri Poincaré in Paris: Bernard Leclerc See www.erittenhouse.org/ for recent articles on the (Caen), “Alain Lascoux: de la géométrie à la combi- history of scientific instruments in eRittenhouse. natoire” on February 4; Serge Grigorieff (Paris VII), “Émergence des modèles du concept de calculabilité” Princeton University Press, Tizra, Hebrew University on March 11; Emily Grosholz (Penn State), “Le raison- of Jerusalem, and California Institute of Technology nement ampliatif en théorie des nombres” on March 18; announce the launch of The Digital Einstein Papers. Jean-Paul Allouche (Inst. Math. Jussieu), “Quadra- See einsteinpapers.press.princeton.edu. ture et transcendance: Gregory et Leibniz”, and Michel Cambridge University Press and the British Society for Serfati (IREM), “La Quadrature Arithmétique du Cer- the History of Science have launched a peer-reviewed cle de 1673. Les idées mathématiques de Leibniz” on open access journal for the history of science, BJHS March 25; Sigmund Probst (Archives Leibniz), “La dis- Themes, edited by Jon Agar. Visit www.journals. cussion par Leibniz des mathématiques de Descartes au cambridge.org/BJHSThemes for information and to cours de son séjour à Paris (1673–1676)”, and Michel submit a proposal. Serfati (IREM), “De l’analyse mathématique. Ordre Doctoral dissertations pertaining to the history of sci- versus Harmonie. Descartes versus Leibniz” on April ence and medicine are compiled at www.hsls.pitt. 8; Michel Serfati (IREM), “‘Monsieur Descartes’ et edu/histmed/dissertations. Élisabeth de Bohème. D’une correspondance math- In May 2014, Kostas Kampourakis, Ron Numbers, ématique à la naissance d’une amitié ‘philosophique”’ and Nicolaas Rupke organized a conference on “New- on May 20 (letter-reading to follow); and Bodo Lass ton’s Apple and other Historical Myths about Sci- (CNRS), “Démonstration de la conjecture de Dumont” ence” at Washington & Lee University in Virginia. on May 27. Twenty-six myths were “busted” during the presen- Adrian Rice was the keynote speaker for BSHM’s Re- tations, and John L. Heilbron gave the keynote ad- search in Progress meeting at Queen’s College Oxford dress. An essay collection aimed at teachers is avail- on 21 February 2015. A BSHM/LMS joint celebration able at www.academia.edu/6412084/Newtons_Apple_ of Augustus de Morgan was held May 9; a meeting on and_other_Myths_about_Science. Symmetry and Groups will be held at Birkbeck College Speakers on the 2014–2015 schedule for the Philadel- on May 23; and a one-day conference on the history phia Area Seminar on the History of Mathemat- of the mathematics of space and relativity will be at ics (PASHoM) included: Peggy Kidwell (NMAH) Rewley House Oxford on June 20. on September 18; Victor Katz (UDC) on October Jim Tattersall and Fred Rickey organized a special ses- 23; Shelley Costa (Swarthmore) on November 20; sion on History and Philosophy of Mathematics for Stephanie Dick (Harvard) on December 4; William the AMS Eastern Section Spring Meeting at George- Noel (Penn) on January 22; Robert Bradley (Adel- town University, March 7–8. Speakers included: Karen phi) on February 19; Robert Naugle (Shepherd) on Parshall (Virginia); Andrew Fiss (Mich. Tech.); March 19; and Marianna Bonanome (Manhattan CC) Amy Ackerberg-Hastings (UMUC); Duncan Melville and Margaret H. Dean (CUNY) on April 16. (St. Lawrence); Chris Rorres (Penn); Peggy Kidwell The Frederick V. Pohle Colloquium on the History of (NMAH); Judy Green (Marymount); Lydia Patton

3 (Virginia Tech); Brit Shields (Penn); David L. Roberts ities in Cambridge is hosting a conference on “Objects (Prince George’s CC); Paul Wolfson (West Chester); in Motion: Material Culture in Transition,” June 18– Larry D’Antonio (Ramapo); Jesse Elliott (Cal State- 20. Channel Islands); Andrea Pedeferri (GWU); and Joe The Twelfth Biennial History of Astronomy Work- Mourad (Georgetown). shop will be held June 24–28 at the University of The MAA Seaway Section 2015 spring meeting was Notre Dame, with a side trip to the Adler Planetar- held April 17–18 at Colgate University and included ium and Astronomy Museum. Michio Yano, chief a session on “Preserving and Writing the History of editor of SCIAMVS, is the keynote speaker. See Mathematics Departments in US Colleges and Univer- www.nd.edu/~histast/. sities,” organized by Gary Towsley and Toke Knudsen. Peter Pesic, new director of the Science Institute at The Midwest Junto for the History of Science met St. John’s College in Santa Fe, NM is organizing week- April 17–19 at UW-Madison. See midwestjunto. long seminars for teachers and other scientific profes- wordpress.com/. sionals on “A Tale of Two Geometries: Euclid and Satish C. Bhatnagar organized a special session on Lobachevsky” (June 29–July 3) and “Understanding History of Mathematics for the AMS Western Sec- Relativity: Texts by Albert Einstein” (July 6–10). tion Spring Meeting at the University of Nevada, Las “Dresden Summer—International Academy for the Vegas, on April 18. Speakers included: Alok Ku- Arts,” August 22–29, will focus on globes in the col- mar (SUNY Oswego); Viktoria Savatorova (UNLV); lection of the Mathematisch-Physikalischer Salon. See Andrzej Lenard (indep. scholar); Satish Bhatnagar www.skd.museum/de/forschung/dresden-summer/. (UNLV); Dieudonne Phanord (UNLV); and David Fott The theme of the 34th Symposium of the Scientific (UNLV). Instruments Commission is “Instruments in Conflict.” A workshop on preserving teaching materials in “uni- The meeting is September 7–11 in Turin, Italy. See versity collections” will be held at Jena University, May www.sic.iuhps.org/. 7–9. See http://necs.org/node/104375. ARTEFACTS XX, on using objects in studies of the The 3rd Irish History of Mathematics Conference is history of science and technology, will meet in Milan, May 15 in Belfast. Contact Mark McCartney to regis- September 20–22, to explore the theme, “Scientific Her- ter, [email protected]. itage at World Exhibitions and Beyond. The Long The Commission on Women and Gender Studies XXth Century.” See www.artefactsconsortium. of the Division of History of Science and Tech- org/. nology of the International Union of History and The Fourth International Conference on the His- Philosophy of Science and Technology is holding tory of Mathematics Education will meet in Turin, the conference, “Gendering Science: Women and Italy, September 23–26. See e20.unito.it/ICHME4/ Men Producing Knowledge,” in Prague, June 4–6. default.aspx. See en.zenyaveda.cz/218-gender-science/. Also, Lick Observatory, Mt. Hamilton, CA, will host the DHST is offering a prize for up to five young scholars 24th Annual Convention of the Antique Telescope So- in the history of science or technology, to be awarded ciety on October 9–12. Side trips include Ricard Ob- in 2017. The application deadline is August 31, 2016. servatory, Chabot Observatory, and UC Santa Cruz’s See hpdst.gr/youngscholarsprize. Optical Shop, Mechanical Shop, and Center for Adap- The 16th Annual Meeting of the European Academic tive Optics. See antiquetelescopesociety.net. Heritage Network UNIVERSEUM will be in Athens, The History of Education Society will meet in St. Greece, June 11–13. A new meeting format will fea- Louis, MO, November 5–8. See www.historyofedu- ture four sessions: University Heritage and Cultural cation.org/our-annual-meeting/. Engagement of European Universities; The Most Cru- The UK History of Education Society will hold its cial Issue(s) with University Heritage Today; Univer- annual conference, “Science, Technologies and Mate- sity Heritage, Its Generators and Its Scholars; and a rial Culture,” in Liverpool, November 20–22. Scroll poster session. See www.universeum2015.uoa.gr/. down at historyofeducationsociety.blogspot.co. The Centre for the Arts, Social Sciences, and Human- uk/ for more information.

4 A free exhibition, “Philosophical Transactions: 350 an edition published in 1701, and the translation by years of publishing at the Royal Society,” runs at the William Gardiner that follows was published in Lon- Royal Society of London until July 2015. A conference don in 1715: on the journal’s legacy was held March 19–21. The 2016 HPM meeting will be in Montpellier, France, Ecoutez, Madame, répondis-je, puisque nous July 18–22. sommes en humeur de mesler toûjours des folies de galanterie à nos discourse les plus serieux, The 13th International Congress on Mathematical Ed- les raisonnemens de Mathematique sont faits ucation will be held in Hamburg, Germany, July 24–31, comme l’Amour. Vous ne sçauriez accorder si 2016. See www.icme13.org/. Topic Study Groups will peu de chose à un Amant, que bien-tost après include “The history of the teaching and learning of il ne faille luy en accorder davantage, & puis mathematics.” encore davantage, & à la fin cela va loin. De The University of Glasgow and the Hunterian Museum mesme accordez à un Mathematicien le moin- and Art Gallery are jointly funding 5 PhD projects on dre principe, il va vous en tirer une consequence, the history of science and medicine in 2015–2016. The qu’il faudra que vous luy accordiez aussi, & de National Maritime Museum, Greenwich, and the Uni- cette consequence encore une autre, & malgré versity of Edinburgh are funding a PhD on “Chronom- vous-mesme il vous mene si loin, qu’à peine le etry and Chronometers on British Voyages of Ex- pouvez vous croire. Ces deux sortes de Gens-là ploration, ca 1815–ca 1872,” beginning in fall 2015. prennent toûjours plus qu’on ne leur donne. SUNY-Oneonta is hiring a visiting assistant professor in Ethno-mathematics or History of Mathematics, be- Hear me, Madam, says I, since we are in ginning in fall 2015. Université Blaise Pascal is offering the humour of mingling Amorous Follies with two post-doc positions for foreign philosophers. our most serious Discourse, I must tell you, Information on American Philosophical Society Grants that in Love and the Mathematicks, People rea- and Fellowships may be found at www.amphilsoc.org/ son alike: Allow never so little to a Lover, yet grants/faq. presently after you must grant him more; nay, more and more; which will at last go a great way. In like manner, grant but a Mathemati- Quotations in Context cian one little Principle, he immediately draws a Consequence from it, to which you must nec- “Mathematicians are like lovers. ... Grant a essarily assent; and from this Consequence an- mathematician the least principle, and he will draw from it a consequence which you must other, till he leads you so far (whether you will also grant him, and from this consequence or no) that you have much ado to believe him. another.” These two sorts of People, Lovers and Mathe- I think I first encountered the above quotation by the maticians, will always take more then [sic] you French author Fontenelle (1657–1757) in E. T. Bell’s give ‘em. Men of Mathematics over twenty years ago. The origin of the quotation is Fontenelle’s most famous work, En- You might be surprised to learn that the context in tretiens sur la pluralité des mondes (Conversations on which this quotation appears is a discussion of the like- the Plurality of Worlds), first published in 1686. The lihood of the existence of life on other planets. Here book was intended to explain selected topics in science are the sentences that immediately follow in the En- and astronomy to a popular audience, and Fontenelle glish translation: explains in the preface to the book that this is why he You grant that when two things are like an- chose to write in French rather than Latin. The work other in all visible respects, it is possible they is organized around conversations between a philoso- may be like one another in those Respects that pher and a Marquise that take place over the course of are not visible, if you have not some good reason six consecutive evenings. to believe otherwise: Now this way of arguing The quotation is taken from the conversation on the have I made use of. The Moon, says I, is in- fifth evening. The French text below comes from habited, because she is like the Earth; and the

5 other Planets are inhabited, because they are The first essay examines “Science and Tradition,” both like the Moon; I find the fix’d Stars to be like in mutual opposition and in supporting each other. our Sun, therefore I attribute to them what is “Between a science ancillary to theology . . . and one proper to that: You are now gone too far to be aimed at discovering the truth irrespective of conse- able to retreat, therefore you must go forward quences, the distance is prodigious.” The changes have with a good Grace. been truly revolutionary. “The Ptolemaic world . . . is hopelessly dwarfed by astronomical theories of today.” Mike Molinsky Sarton’s Belgian compatriot, Adolphe Quetelet, en- larged the range of possible knowledge through his ba- sic investigations of the statistical incidence of social Off the Shelf: Horus ills in a given community. Horus: A Guide to the History of Science, A First Despite “the revolutionary nature of science . . . many Guide for the Study of the History of Science With In- of our traditions . . . are the accumulated goodness of troductory Essays on Science and Tradition, by George centuries.” Such rationalist errors as the short-lived Sarton, Waltham, MA: Chronica Botanica, 1952, xviii Technocracy movement followed in Plato’s fallacy of + 316 pp. governance by an intellectual elite. Sarton suggests that part of the reason so many German scientists ac- Our small downtown Toronto synagogue is liberal, pro- tively facilitated the Nazi programme of radical evil gressive, egalitarian and gay positive. Yet, whether at was their technical infatuation with helping to solve Shabbat services or on the High Holy Days, we return the regime’s practical problems in achieving its crimi- to the sources: prayer in Hebrew and a Torah reading nal ends. from a manuscript parchment scroll. Similarly, when I decided to return to the sources for history of mathe- In “The Tradition of Ancient and Mediaeval Science”, matics and science, I sought out the writings of George Sarton examines his own research speciality. He exam- Sarton (1884–1956), the founder of Isis and Osiris. ines the vicissitudes of the transmission of the ancient One of my discoveries was his late work, Horus: A Greek legacy, whether it’s the survival and copying Guide to the History of Science. of manuscripts, or the various translation traditions in Arabic, Hebrew or Latin. Sarton takes pains to demon- Horus was the falcon-headed son of the ancient Egyp- strate that the science of the mediaeval Arab world tian gods Isis and Osiris, a fitting name for the off- was not just a passive heir of the Greeks but also cre- spring of Sarton’s long years researching and promot- ative and that its leaders included not just Muslims ing history of science. Here, there’s insight into Sar- but also Jews such as Maimonides and Ishaq al-Israili. ton’s approach to our field and its status more than The Latin world learned from the Arabs and applied half a century ago. It is also a research tool that can this learning to its own issues. The early giants of the be used directly and analogous to its method. Scientific Revolution built on their mediaeval roots. The last essay asks, “Is It Possible to Teach the History The Essays of Science?” It’s largely a plea for the establishment These original “lectures were delivered with a minimum of history of science as a respectable academic disci- of notes . . . [so] the text . . . does not reproduce them pline. Sarton asserts that history of science can be except in a general way. . . . The lectures . . . explain compared to other relatively recently established and [why] to study the history of science . . . [and] the bib- evolving fields, such as history of art or history of reli- liography gives the means to do so.” gion. Historians of science need to learn the techniques Sarton felt “the history of science was slowly coming of historical research and should be well-versed in at into its own”, though its development had been hin- least one field of science, such as mathematics or geol- dered by unsympathetic but also uncomprehending ad- ogy. ministrators. They did not realize that “historians of science must know science and history. . . . There are The Bibliography but few historians of science completely qualified for The bibliography is based on Sarton’s own library, “a the task of teaching it. . . . [But] that is simply a mat- cause of strength and a cause of weakness.” The struc- ter of training . . . different . . . but not more difficult.”

6 ture reflects his recipe for the education of an historian Horus also supports my Jewish studies. The new State of science who must know both history (six chapters) of Israel was only 4 years old in 1952, so when Sar- and science (seven chapters), then pursue history of ton talks about Israel in “History of Science in Spe- science (seven chapters), and finally become active in cial Cultural Groups”, he means the millennial his- the “Organization of the Study and Teaching of the tory of the Jewish people. General works include the History of Science” (six chapters). two Jewish encyclopedias as well as Cecil Roth’s 1938 There are many ways individual readers can approach The Jewish Contribution to Civilisation and Harry the Horus bibliography. Mine starts with Canadian Friedenwald’s The Jews and Medicine (1944). More science and mathematics. specifically, William Moses Feldman looked at Rabbini- cal Mathematics and Astronomy in 1931; the follow- Only two books form the Canadian section in “His- ing year, Solomon Gandz published The Mishnat Ha- tory of Science in Special Countries”. 1939’s A History Middot, the first Hebrew geometry of about 150 C.E. of Science in Canada is the proceedings of a sympo- In addition to his appearance in Gandz’s volume, Mai- sium held by the History of Science section of the June monides appears twice: Un glossaire de matière médi- 1938 Ottawa Meeting of the American Association for cale de Maimondide (1940)—for the great philosopher the Advancement of Science. The Centennial Volume and theologian earned his living as a physician—and of the Royal Canadian Institute (1949) celebrates the the Maimonides Bulletin, “a journal of medical prac- venerable institution that still presents popular science tice”. lectures in the Toronto area. Both volumes are collec- tions of exploratory surveys of the different scientific fields. These “studies are still in the pioneer stage, they Conclusion must necessarily suffer from pioneer imperfections and Horus: A Guide to the History of Science is one of crudities.” the landmarks of our field. In it, Sarton was able to Other Canadian scientists are present, though. Frank share some of his most evolved understanding of what Dawson Adams (1859–1942), president of the 1913 In- history of science is about. He also gave us the tools ternational Geological Congress in Toronto, published to do our research and the direction to develop our his Birth and Development of the Geological Sciences methods and improve our results. in 1938. Of course Sarton notes it was reviewed by I’m looking forward to a more thorough exploration Michigan’s William H. Hobbs in Isis 32, no. 1 (1940): of the intellectual riches indicated in the bibliography. 218–220. McGill University’s Sir William Osler’s Yale Using the resources of the University of Toronto Li- lectures on The Evolution of Modern Medicine were brary and the internet, I’ll be reading 17th-century published posthumously in 1921, and his 1929 Bilboth- encyclopaedias, histories of science in Belgium, and eca Osleriana is “a catalogue of books illustrating the 19th-century German history of mathematics journals. history of medicine and of science.” Sarton himself re- David Orenstein viewed Harvey Cushing’s biography in Isis 8, no. 2 (1926): 358–361. Chapter 25 tallies the date and location of 53 series of PSA President’s Lunch “International Congresses”. They played “a great part in the organization of science and especially in the def- On November 7, 2014, Helen Longino, president of the inition of new disciplines and the formulation of their Philosophy of Science Association (PSA), organized a methods.” Sarton has certainly validated the choice of lunch with representatives of related societies at its my current major research project: investigating the joint meeting with the History of Science Society in ramifications of the early international scientific con- Chicago. The main idea was to brainstorm about how gresses that took place in Canada. I’ve already stud- we can better work together. Given all the related soci- ied the 1913 International Geological Congress and the eties, there is a great deal of competition for member- 1924 International Mathematical Congress in Toronto. ship money, attendance at conferences, etc. Though But from Sarton I’ve learned that the Americanists attendance at PSA is good and the submissions to the met in Quebec City in 1906 and the Physiologists in journal are back on track, membership in the society Montreal in 1953. is down.

7 Half of what we discussed was more directly about how dip—given the increasing number of societies. 2. What to help the PSA move forward and increase represen- are the advantages to membership; do the numbers tation. (For example, they are considering detaching matter? Response: the number of members does mat- their conferences from HSS after the next two meet- ter for NSF funding. Also, the prizes require member- ings. Helen wanted feedback on this as well as other ship. ideas for strengthening PSA.) But many of the issues Diversity: 1. PSA is currently gathering diversity relate to us as well. data with respect to its editorial board and publica- This year—to encourage more cooperation or visibi- tions. 2. Could diversity be improved by more actively lity—PSA invited a number of other associations to shaping the PSA program? host their own sessions. These sessions all took place Journals: 1. Concerns about open access and the on Sunday morning. The worry was over attendance. problem of package journal prices for library subscrip- The tacked-on extra half day was not noticed by some tions. folks in time to alter travel plans. There were no reg- The PSA Conference in Particular: 1. Relation ular PSA sessions at this time, but with fewer bod- with HSS in question; they are unsure whether to rene- ies to start with, high competition among the soci- gotiate their relationship (due to cost and size of con- eties and conference fatigue, the overall attendance was ference) or to go solo. They have contracts to co-meet not great. However, the attendance at the Philosophy through 2018. 2. Would any of our societies be in- of Mathematics Association (PMA) joint session was teresting in stepping up to fill the hole left by HSS? standing room only (approximately 40–50 people). 3. Perhaps a university could host a smaller association The ideas generated during the brainstorming session before PSA that then meets jointly with PSA. 4. For covered several topics: the related society sessions, Thursday morning might Conferences: 1. Encouraging joint membership agree- work better than Sunday. 5. Someone asked whether ments. How can we determine some general policy for PSA could move to lower-cost cities? Without HSS joint membership? Which societies should be joined? there would not be such a need for giant convention (On this, perhaps CSHPM could survey our members venues. But would enough people come to meetings to find out what other societies they belong to.) An- if not in good cities? 6. One person recommended to other idea might be reduced conference fees for mem- Helen that PSA does not do both at once: detach from bers of a few related societies. 2. It was pointed out HSS and move to smaller cities or a different type of that there could have been better notice and advertis- venue. Costs are high for hotel conferences and work- ing of the Sunday special sessions. 3. The general idea load is huge; this is not a change to be undertaken of joint meetings may be especially useful to smaller so- lightly. It could involve a dramatic increase in fixed cieties. Another option: coordinating meetings so that costs, but PSA already has lower/fluctuating member- they occur sequentially (in the same week) in the same ship. On the other hand, PSA does have fixed income area of the world. This works better for medium-sized from its journal (recently renegotiated with University summer meetings like CSHPM. 4. Add workshops and of Chicago Press to “take home” more of the income). master classes? For example, a pre-conference morn- Elaine Landry ing of workshops by scientists for philosophers (or vice versa); particularly helpful to students or anyone want- ing to get a primer on a new area. 5. Hold poster ses- HPM Americas Section at Wabash & sions for graduate students? 6. Have a mixer for early DC career and/or grad students based on a model such as speed dating. 7. Offer opportunities to give advice to The Americas Section of the International Study grad students regarding non-academic careers. Group on the Relations Between History and Pedagogy Society Memberships: 1. PSA Membership down, of Mathematics met jointly with the biennial Midwest but conference attendance is up dramatically. Worry: History of Mathematics Conference at Wabash College if we change to allowing membership for conferences in Crawfordsville, IN, October 17–19, 2014. Local or- only, (i) we will have to dramatically increase the reg- ganizer Colin McKinney ensured we were fed extremely istration fee for non-members; (ii) our membership will well all weekend. Friday evening, Jeff Oaks gave a ple-

8 nary talk on “Algebraic notation in medieval Arabic.” dergraduate curricula; Marina Vulis’s discussion of his- Conference talks were given all day Saturday and Sun- torical roots of Common Core methods; a tracing of the day morning. Those on the history of mathematics Emerging Scholars Program, a program for increas- included: an examination of John Napier and comput- ing successful completion rates in first-year calculus ing by Pat Baggett and Andrzej Ehrenfeucht; Andrew courses, by Rebecca Vinsonhaler; and Amy Ackerberg- Leahy’s discussion of Archimedes and Torricelli on cen- Hastings’s look at how Jeremiah Day used the concepts ters of gravity; Pierre Boulos’s look at Newton’s rea- of analysis and synthesis in his mensuration textbook. sons for providing diagrams; and Chris Christensen’s On the use of history in the teaching of mathematics, account of how US Navy codebreakers calculated Mar- William Rose explained a course he teaches at a local shall Hall’s “weights” during World War II. magnet high school on logic and the history of mathe- Presentations dealing with the history of mathemat- matical foundations, while Toke Knudsen showed how ics education included: David L. Roberts’s study of history of mathematics students at SUNY Oneonta the content and rhetoric in Daniel H. Hill’s 1857 alge- undertake archival projects. Amy Shell-Gellasch sug- bra textbook; Nerida Ellerton’s discussion of the use of gested ways to use spherometers in classrooms. His- hornbooks in dame schools in the 17th and 18th cen- tory of mathematics presentations included: Roman turies; and Ken Clements’s look at cyphering books Sznajder on Euler’s relationships with mathematicians used in New Paltz, NY, between 1675 and 1850. On from Gdansk, Poland; Ron Calinger on Euler’s activ- pedagogy in the present, Rebecca Vinsonhaler looked ities in the final decade of his life; and Ilhan Izmirli’s at the JAGUAR project’s study of how two middle- discussion of the Mecca problem. school teachers presented justification in proof. The section is currently exploring meeting sites for Talks that provided suggestions for using history in 2015, 2016, and beyond. The officers and other stal- teaching mathematics included: John Curran, “His- warts who organize meetings also greatly desire to in- torical Role-Playing in the Mathematics Classroom”; crease the section’s emphasis on intersections of history classroom-tested sample problems from Adam Parker and pedagogy and to engage with secondary and un- and Fred Rickey; Michael Todd Edwards’s announce- dergraduate teachers. If you can help with any of these ment of a new, student-run mathematics history jour- objectives, please contact the chair, Dave Roberts, nal at Miami University of Ohio; Jim Smith’s report [email protected]. on how he used a 4-minute 1930 radio address by Amy Ackerberg-Hastings David Hilbert (now available on MAA Convergence); and ways to employ divergent series and sectors, re- spectively, in classrooms by Colin McKinney and Amy MAA MathFest Centennial Events Ackerberg-Hastings. The history and philosophy sessions organized by The Americas Section also met March 13–15, 2015, at CSHPM, BSHM, POMSIGMAA, and HOMSIGMAA American University in Washington, DC. The high- will feature over 60 scholarly presentations from Wednes- light of the weekend was a tour of two temporary exhi- day, August 5, to Saturday, August 8. But that’s bitions at The Phillips Collection: “Man Ray—Human not all, as advertisers say, for attendees looking for Equations: A Journey from Mathematics to Shake- academic and other ways to mark the 100th anniver- speare” and “Hiroshi Sugimoto: Conceptual Forms and sary of the MAA’s founding. In addition to the usual Mathematical Models,” led by one of the curators. Be- named lectures (delivered this year by Karen Smith, fore the tour, Peggy Kidwell explained some of the Jeffrey Lagarias, David Bressoud, Erica Walker, Joe models on display, drawing on the Smithsonian collec- Gallian (on 75 years of MAA mathematics compe- tions. On Friday afternoon, the group also viewed rare titions), Noam Elkies, and Terrence Blackman), six mathematics books in the AU Archives. special Centennial lecturers have been recruited: Erik Talks on the history of mathematics education in- Demaine, Jennifer Chayes, Ingrid Daubechies, Car- cluded: David L. Roberts’s examination of number los Castillo-Chavez, Karen Parshall (whose talk also theory proofs in some 19th-century American algebra serves as our May Lecture), and Manjul Bhargava. textbooks; Walter Meyer’s contemplation of whether The POMSIGMAA guest lecture will be given by John Modernism can be observed in early 20th-century un- Burgess on Thursday evening.

9 Special invited paper sessions include Wednesday af- 2014 Financial Statements ternoon’s “Generations of Monthly Gems,” highlight- ing significant papers published between 1894 and the The following financial statements cover the period present. Presenters include Karen Parshall, John Still- 1/1/2014 through 31/12/2014. well, Ron Graham, Bob Devaney, Paul Zorn, and Re- becca Goldin. Victor Katz and Jim Tattersall have $ Can. lined up former MAA presidents to share reminiscences Income on Thursday and Friday afternoons: Henry O. Pol- dues/subscriptions 9,831.00 lak, Lynn A. Steen, Lida K. Barrett, Kenneth Ross, exchange rate differential 53.20 Thomas F. Banchoff, Ann E. Watkins, Ronald L. Gra- TOTAL 9,884.99 ham, Carl C. Cowen, Joseph A. Gallian, David M. Expenses Bressoud, Paul M. Zorn, and Robert L. Devaney. Keynote speaker 1,187.69 Additional history on the program includes a Satur- CFHSS 2014 loss 201.72 day afternoon session honoring Abdulalim A. Shabazz CSHPM Student Prize 750.00 (1927–2014), a prolific mentor of African-American PIMS grad stud. conf. 300.00 mathematicians; a session organized by the Associa- CFHSS dues for 2014 1,851.46 tion of Women in Mathematics on women’s historical Historia Mathematica 3,291.08 contributions to the discipline, also on Saturday after- Philosophia Mathematica 2,443.31 noon; and a minicourse on spherical trigonometry by Postage, office expenses, Bulletin 326.04 Glen Van Brummelen and Joel Silverberg. Bank fees 5.74 Entertainment is also prominent on the schedule. The TOTAL 10,357.04 first night, Wednesday, August 5, will have a large NET (472.05) reception as well as a mathematical carnival—with Bank balance, 12/31/14 39,110.39 acts by Dominic Klyve, Susan Goldstine, Colm Mulc- TD Mortgage Corporation GIC 4,194.75 ahy, Jason Rosenhouse, and Karl Schaffer—and per- TD Mortgage Corporation GIC 4,202.85 formances by Colin Adams, Art Benjamin, Tanya and TOTAL ASSETS 47,507.99 Tim Chartier, and Karl Schaffer. Thursday evening in- cludes an opportunity to preview The Man Who Knew Comments: Infinity, a major feature film about Ramanujan star- Because the Society has 2 accounts, one in US dollars, ring Dev Patel and Jeremy Irons, and musical per- we keep two different accounting systems. At the re- formances by Noam Elkies, Frank Farris, and others. quest of the editors, we have combined the numbers Friday night, MAA members will perform Tom Stop- for these accounts. The numbers given are in Cana- pard’s radio comedy, Albert’s Bridge. dian dollars. A conversion factor of 1.16 has been used Other special events include James R. Olsen’s Friday to convert American dollars into Canadian ones. afternoon workshop on building polyhedra from every- The exchange rate differential is a profit earned in day materials; a contributed paper session on Math transferring $2,266.80 from the Canadian to the Amer- Circle problems, also on Friday afternoon; and Satur- ican account. The first GIC fund earns interest at day afternoon presentations by Richard Guy and John 1,60% and matures 16 September 2016; the second has Conway on the geometry of triangles. a 1,40% rate and matures 26 March 2017. Overall, the To warm up for these events, be sure to visit the Cen- Society’s assets increased $677.85 over last year. tennial webpage: www.maa.org/aboutmaa/maa-his- David Bellhouse tory/celebrating-the-centennial. Don’t forget to register to attend MathFest as soon as possible for the lowest rate; remember to declare yourself a member of 2015 Meeting Outline CSHPM. See you in DC! The 2015 annual meeting of the CSHPM is a joint meeting with the British Society for the History of Mathematics, the History of Mathematics Special In- terest Group of the MAA (HOMSIGMAA) and the

10 Philosophy of Mathematics Special Interest Group of Saturday, August 8 the MAA (POMSIGMAA). The meeting will be held 8:30–11:30 General Sessions on the History and Phi- August 5–8, 2015, in Washington, DC, and is part of losophy of Mathematics the Centennial Celebration of the MAA (Mathemat- 11:30–1:00 Lunch ical Association of America). Over the course of the 13:00–15:30 Special Session in Memory of Ivor Grattan- four days of the meeting, there will be roughly 70 talks Guinness, featuring talks by: Adrian Rice, Albert split between general sessions and special sessions. Be- Lewis, John Dawson, Roger Cooke, and Joe Dauben low is a brief description of the schedule: 15:30–17:30 Closing General Sessions on the History and Philosophy of Mathematics Wednesday, August 5 8:30–17:30 General Sessions on the History and Phi- This is going to be a very rich four days featuring a losophy of Mathematics wide variety of scholarship. The detailed schedule for 15:00–17:30 Session on the Mathematics of Euler, fea- the general sessions is not yet complete, but it will ap- turing talks given by: Sylvio Bistafa, Rob Bradley, pear on the CSHPM website in due course. As you Ronald Calinger, William Hackborn, and Dominic can see elsewhere in this issue, the evenings will in- Klyve clude many special events organized by the MAA to celebrate its Centennial. Thursday, August 6 Maria Zack 8:30–11:30 Special Session in Memory of Jackie Stedall, featuring talks given by: June Barrow-Green, Janet Ivor Grattan-Guinness (1941–2014) Beery, Rosie Cretney, Chris Hollings, Steve Russ, and Robin Wilson As disciplines go, the history of mathematics is rela- 11:30–13:00 Lunch Break (CSHPM Council Meeting) tively small. But in common with most academic pur- 13:00–14:30 General Sessions on the History and Phi- suits, it is a wide and varied field of research, while the losophy of Mathematics focus of most individual research in the subject is of- 14:30–17:00 Special Session on the Philosophy of ten necessarily narrow and specialised. There is noth- Mathematics, featuring talks given by: Elaine Landry, ing particularly unusual or objectionable in this, but a Jean-Pierre Marquis, Jeff Buechner, Alex Manafu, and consequence is that it is entirely possible for one his- Carl Behrens torian of mathematics to be completely unacquainted 5:00–6:00 The POMSIGMAA Lecture on Philosophy with the work of another scholar working outside his or of Mathematics, given by John Burgess her immediate area of interest. Indeed, small though our community may be, it is hard to think of a contem- Friday, August 7 porary historian of mathematics whose name is famil- 8:00–10:30 Special Session on Mathematical Com- iar to every other scholar in our field. However, if such munities, featuring talks given by: Amy Ackerberg- a distinction were ever possible, it is arguable that it Hastings, Janet Barnett, Lawrence D’Antonio, Jane was held by Ivor Grattan-Guinness. Wess, and Diana White The sheer enormity of Ivor’s scholarly output is over- 10:30–11:30 The May Lecture, given by Karen Par- whelming. In a career spanning over four decades, he shall (also one of the MAA Centennial Lectures) published 12 books and more than 250 research papers, 11:30–12:30 Lunch as well as a staggering array of shorter articles, book 12:30–14:00 The CSHPM Annual General Meeting chapters, book reviews, dictionary and encyclopedia 14:00–17:00 Special Session in Honor of Karen Par- entries, and other works. It was not just the volume of shall, featuring talks by: Joe Dauben, Brittany his productivity that was immense: the breadth and Shields, David Zitarelli, Della Dumbaugh, Patti Hunter, range of his contributions to the subject were also re- and Deborah Kent markable. Ivor wrote on everything from the use of 17:00–18:00 Reception in Honor of Karen Parshall, number and magnitude in Euclid’s Elements to the hosted by HOMSIGMAA influence of Max Newman on Alan Turing. His writ- ings encompassed not only the history of mathematics,

11 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 uses of history in mathematics education. His death from heart failure on 12 December 2014 brings a close to both a remarkable career and a formative chapter in the development of the modern discipline of the history of mathematics. Ivor Owen Grattan-Guinness was born on 23 June 1941 in Bakewell, Derbyshire, the son of Henry Grattan- Guinness, a mathematics teacher in Bakewell and later Deputy Director of Education in Huddersfield, and his wife Helena (née Brown). Schooled at Huddersfield New College, Ivor entered Wadham College, Oxford as a mathematics scholar in 1959, graduating with a B.A. in 1962. After a brief career in industry, working as a research mathematician for E.M.I., he re-entered higher education in 1964, joining Enfield College of Technology in north London as a lecturer on the math- Figure 1: Ivor with cat ematics for business degree course. He had met Enid Neville in 1963 while a member of the BBC Choral So- sought to focus on a particular area of mathematics ciety, an amateur choir in which they both sang. Their in which his historical and educational concerns were shared love of music soon blossomed into romance, and prominent. Having already learnt of the connection they were married in January 1965. Enid would re- between Fourier series and fundamental concepts in main his best friend and constant companion for half analysis and set theory, his attention was drawn to a century. the foundational work of Fourier and Cauchy. New to It was Ivor’s experience as a mathematics undergradu- the field, he sought guidance from a scholar who, at ate at Oxford that initiated the curiosity which would this time, was one of the only professional historians ultimately lead to his entrée into the history of mathe- of mathematics in the country, then fully immersed matics. While there, he had been frustrated by the lack in the publication of Newton’s mathematical papers. of interest (and in some cases knowledge) on the part of From Tom Whiteside he received much valuable advice the lecturers with regard to questions concerning both on matters concerning archival research, which would the theoretical motivation and historical development very soon become Ivor’s forte; Whiteside also helped to of the subject matter. In an attempt to begin to an- establish a working relationship with another scholar swer these questions, and simultaneous with the start who had done recent work on Fourier, Jerome Ravetz of his teaching career, Ivor entered the London School at the University of Leeds. of Economics (LSE) as a part-time student in the de- By 1967, Ivor was working on two complementary, but partment of philosophy, logic and scientific method, parallel, projects as a doctoral student in LSE’s de- founded and then run by Karl Popper. Although the partment of mathematics. Under the supervision of departmental atmosphere was not quite as collegial as the analyst and head of department, Cyril Offord, with he might have wished, the intellectual effect on Ivor Ravetz serving as his external supervisor, the study was both stimulating and influential, and included his of Cauchy became his eventual thesis, for which he first exposure to mathematical logic, sparking a fasci- received a Ph.D. from the University of London in nation which was to reverberate throughout his work 1969. With minor changes, this work was published for the rest of his life. He graduated with an M.Sc. in as his first book, The Development of the Foundations the philosophy of science in 1966. of Mathematical Analysis from Euler to Riemann, in Equipped with a philosophical background against 1970. Meanwhile his collaboration with Ravetz on which to frame his unanswered questions, Ivor now Fourier became a full-scale study, not only of the then

12 unpublished 1807 memoir on heat diffusion, but also history of mathematics, retiring from a lectureship in of his life, with prodigious use of a large number of mathematics at Imperial College London in 1967. The previously unpublished manuscript sources—a feature Youngs had been good friends with Cantor, and Tan- that would become a defining characteristic of much of ner was still in touch with his grandchildren; it was Ivor’s work. via this link that Ivor was granted access to Cantor’s At Ravetz’s suggestion, the external examiner on Ivor’s Nachlass, which involved taking a trip behind the Iron Ph.D. committee was Sir Edward Collingwood, a se- Curtain to Halle University in East Germany in 1969. nior figure in British analysis at the time and shortly Ivor’s friendship with Tanner also led to his detailed to become President of the London Mathematical So- study of the mathematical collaboration of her parents, ciety. Collingwood had a deep interest in the history the first of its kind in the history of mathematics. of mathematics in general, but was particularly fas- The network of connections continued to grow wider, cinated by the work of Georg Cantor. The develop- and more international. For many years, via her Ger- mental connections between Cantorian set theory and man connections, Tanner had been one of the few non- the Weierstrassian mathematical analysis so closely re- Germans invited to attend J. E. Hofmann’s annual lated to Ivor’s recent research now led him into a new, meetings on the history of mathematics at the Math- but related, area of research: the history of set the- ematisches Forschungsinstitut in Oberwolfach, which ory. Collingwood had somehow learned that a key had been running since 1954. At her request, Ivor to finding more archival information lay in the former received an invitation to the meeting of 1969. His par- home of Weierstrass’s Swedish disciple Gösta Mittag- ticipation at that meeting marked the beginning of a Leffler, just outside Stockholm, and in 1968, Ivor was new phase in his career: not only was he introduced to dispatched at Collingwood’s own expense on a research a whole new community of historically-minded mathe- trip to Sweden. What occurred there on that first visit maticians, able to impart advice on research and point and again in 1970 was to have a profound impact on him in new directions, but that community was also to Ivor’s research: in the course of searching through the be the source of a number of lifelong friendships, per- largely unsorted documents, he stumbled across liter- haps most notably with Christoph Scriba. The Ober- ally hundreds of manuscripts not widely known to the wolfach meetings also marked the start of a truly inter- history of mathematics community. These documents national career, as Ivor soon became a familiar figure at concerned not only Cantor and Weierstrass, but also conferences first in Europe, then America, then around many of their late-nineteenth-century contemporaries the world. For most of the next forty years, Ivor circled including Sofia Kovalevskaya, Henri Poincaré, Philip the globe, visiting archives, attending conferences and Jourdain and Bertrand Russell. The publication of his giving over 500 invited lectures, or “gigs” as he often findings in 1971 helped establish for Ivor a reputation, used to call them. As he later put it: “My research both for his ability to locate archival sources and for life has always centred largely on two kinds of journey: his eagerness to share that knowledge with the wider to the centre of London, to use the libraries; and to scholarly community. a station or airport, to travel abroad and tell foreign- His association with Collingwood now led him to meet ers about the findings and give lecture courses to their a woman who would influence his career for many students.” But throughout his career, it was the intel- years. Cecily Tanner was born in Göttingen in 1900 lectual immersion, relaxed collegiality and breathtak- as Rosalind Cecilia Hildegard Young, the daughter of ing scenery of Oberwolfach that he always viewed with William and Grace Chisolm Young, the British math- a special fondness, and he and Enid would be regular ematicians who had championed the new set and mea- fixtures at the history of mathematics meetings there sure theory in the opening decades of the 20th cen- for over three decades. tury. Like her parents, she had studied mathematics Back home however, no such community of histori- at Cambridge and like them she was an analyst, re- ans of mathematics existed. The British history of ceiving a Ph.D. on the theory of Stieltjes integration science community was largely apathetic—and indeed in 1929. She had collaborated with Collingwood when the very subject was still viewed by most practicing they were both working at the University College of mathematicians in Britain merely as something to do Wales in Aberystwyth in the 1920s, and for much of in one’s retirement. So when, at the beginning of the her career she had been an active researcher in the 1970s, John Dubbey and Arthur Morley proposed the

13 creation of a learned society specifically devoted to Ivor’s consequent expertise, not only in the history of the history of mathematics, Ivor considered the idea nineteenth-century analysis, but also in the history of to be “hopelessly optimistic”. Nevertheless, on 2 July post-revolutionary French mathematics, led to invita- 1971, he was one of five speakers at a special meet- tions to contribute several biographical studies to the ing held at Thames Polytechnic (now the University Dictionary of Scientific Biography (DSB), then in the of Greenwich) in London. This turned out to be the process of compilation by Charles Gillispie. In addi- first meeting of the British Society for the History of tion to the entries on Fourier, Laurent, Mathieu, Riesz Mathematics, now the oldest such society in the world. and Stäckel, Ivor also wrote a section on the history of Elected its sixth president in 1986, he pushed through the Laplace transform for Gillispie’s book-length biog- a formal constitution and forged stronger relationships raphy of Laplace, first published in volume 15 of the with the international history of mathematics commu- DSB in 1978, and later re-published in book form by nity, via invitations to speak at the society’s meetings Princeton University Press. and active recruitment of members from overseas. As a Work on French mathematics continued through the result, by the end of his presidency in 1988, one quarter 1980s, much of which was occupied by the preparation of the society’s growing membership came from outside of what was arguably his magnum opus: the three- the United Kingdom. volume Convolutions in French Mathematics, 1800– Ivor’s published output was so vast and so wide- 1840: From the Calculus and Mechanics to Mathemat- ranging that it would take a monograph-length paper ical Analysis and Mathematical Physics, published in to provide a detailed survey; even the following sum- 1990. This 1,600-page work remains the most com- mary of his contributions to the history of mathematics prehensive study to date of early nineteenth-century is necessarily incomplete. French mathematics and is a veritable treasure trove Ivor’s research began in an area that was to permeate of previously unpublished sources, biographical and in- much of his work, particularly in the first half of his stitutional information and reference. It treated the career: the history of the foundations of mathematics. development of the mathematical sciences in France Initially, as seen above, this was motivated by a dissat- not as a sequence of great leaps, or “revolutions”, nor isfaction with the presentation of mathematics in his as a story of gradual progress, “evolution”, but rather own education, and this led to an early focus on the as a series of twists and turns; hence the “convolu- development of analysis with the work of Fourier and tions” of the title. Rejecting the one-dimensional in- Cauchy. His first book, The Development of the Foun- ternalist approach to the history of mathematics, Ivor dations of Mathematical Analysis from Euler to Rie- situated the mathematical developments within the mann (1970), centred on an investigation of the math- Parisian mathematical and broader French scientific ematics of Cauchy and his contemporaries, including milieu, so that publication venues, institutional his- Abel and Dirichlet. It also contained a valuable ap- tories, and developments in higher education were all pendix on the history of convergence tests, which still integral to the main narrative. Consequently, since remains a useful resource. His joint work with Ravetz people like Cauchy, Fourier and Laplace did not op- on Joseph Fourier appeared in 1972. Up to this point, erate in isolation, it was not just the famous names Fourier’s key 1807 memoir “Sur la propagation de la that featured; a plethora of minor (but significant) fig- chaleur” only existed in manuscript form in Paris, so ures were also interwoven into the account to provide a historical studies of Fourier had been forced to rely fuller picture of the intellectual environment. Finally, on the greatly expanded and amended published ver- Ivor avoided the common error of viewing mathemat- sion, Théorie analytique de la chaleur (1822). Work- ics as “pure mathematics” by treating developments in ing in the Paris archives, Ivor studied over 6,000 pages analysis, calculus, mechanics, heat diffusion, elasticity, of Fourier’s manuscripts, including many in which the electricity and magnetism, and optics as interrelated handwriting was barely legible, to come up with his components of a cohesive field of study. This inclusive annotated version. The previously unpublished 1807 attitude to mathematics, or rather, “the mathemati- memoir appeared in print for the first time in the col- cal sciences”, was yet another characteristic feature of laborative book Joseph Fourier, 1768–1830, in which Ivor’s work. Ivor provided a detailed commentary on the paper and The path which had led from the history of analysis to on related aspects of Fourier’s life and work. set theory, via Georg Cantor, soon led to an interest in

14 the life and work of Bertrand Russell, to whom in later tions as a stimulus of mathematical progress. A final life Ivor developed a strong physical resemblance. He tour de force was delivered in 2005 with the publica- was one of the very few people who actually attempted tion of his Landmark Writings in Western Mathematics to read Russell and Whitehead’s Principia Mathemat- 1640–1940, a thousand-page collection of 77 chapters ica and was not only familiar with its content, but he by 65 authors surveying 89 important mathematical had also researched the tortuous process of its creation. “writings”, from Descartes’ Géométrie to Hilbert and Again, substantial archival research produced signifi- Bernays’ Grundlagen der Mathematik. All these works cant contributions to our understanding of Russell’s codified vast amounts of information in accessible for- mathematical work, including a reconstruction of the mats, combining first-rate scholarship with deft edito- reasoning which led to Russell’s 1901 discovery of his rial skill to produce valuable and high quality works of paradox, and an edition of his correspondence with reference. Philip Jourdain, Dear Russell–Dear Jourdain, pub- This editorial skill had been honed over many years lished in 1977. Ivor’s The Search for Mathematical as a journal editor, for in addition to serving on the Roots, 1870–1940: Logics, set theories and the foun- editorial board of Historia Mathematica and a number dation of mathematics from Cantor through Russell to of other journals for much of his career, Ivor rescued Gödel, which appeared in 2000, was the culmination of the ailing Annals of Science from pending extinction decades of immersion in the collections of the Russell in 1974, serving as its editor-in-chief until 1981. He archive. This book traced the development of a variety also founded a new journal, History and Philosophy of logical systems in a wide range of national settings, of Logic in 1979, which he edited until 1992. When with the work of Russell forming the centrepiece of the the project to update the century-old Dictionary of study. Key features included the de-emphasis on Frege National Biography was announced in 1994, Ivor was as an influence on Russell, with more focus on the stim- the obvious choice for the associate editor in charge of ulus of the Peano school. Ivor also made an important mathematics and statistics, and when the Oxford DNB distinction between practitioners of what he called “al- finally appeared ten years later, the scores of articles gebraic logic”—namely those who used mathematical on mathematicians and statisticians had all been com- notation to facilitate the study of logic (e.g. Boole, missioned, edited and, in some cases, written by him. De Morgan, Schröder)—and those of “mathematical Ivor’s work found many admirers, but it was not with- logic” (e.g. Frege, Russell, Whitehead)—who sought out controversy. His assertion that Cauchy had plagia- to use logic as a base for the study of mathematics— rised key ideas in analysis from Bolzano’s 1817 paper and remarked upon the distinct lack of communication on the intermediate value theorem was hotly disputed, between the two sides. while a later claim that the substitutional theory of The second half of his career was dominated by work on classes and relations formed the missing link between edited volumes and works of reference. One of the first Russell’s theory of denoting and the Principia Math- of these was his remarkable Companion Encyclopedia ematica also proved contentious. But in truth, Ivor of the History and Philosophy of the Mathematical Sci- never intended his work to be the last word on any ences (1994). Featuring 175 contributions from no subject, and if he stirred up debate along the way, that fewer than 134 authors, this two-volume work is a mas- would serve as the impetus for future research on the terpiece of editorial organisation and a valuable source subject. Elements of his style may not have been to of articles on many topics completely ignored by other everyone’s taste, but in his opinion it was far better for compendia. Ivor’s general survey of the history of the discipline if his work was criticised than if it was the mathematical sciences, The Rainbow of Mathemat- ignored. Thus, whether they agreed with him or not, ics, appeared as the sixth volume of the Fontana His- subsequent historians of mathematics were forced to tory of Science series in 1997. Like the Encyclopedia, engage with his work and respond to his conclusions. this substantial work distinguished itself from many His published output was characterised by the use of of its predecessors by its concentration on post-1800 vast amounts of archival research, the meticulous study mathematical developments, its inclusion of important of primary sources, often in several languages, and the but lesser-known figures, its consideration of national fusion of a wide range of mathematical ideas. Recur- characteristics in the practice of mathematics, and its ring themes included an intense belief in the use of the emphasis on the importance of mathematical applica-

15 history of mathematics in mathematics education—the he or she had made. Such revelations were frequently influence of which has begun to appear in recent years; accompanied by Ivor’s wide-eyed exclamations of “Re- a conviction that the history of mathematics without ally??” To the novice researcher, such expressions of reference to its applications is incomplete; and an in- excitement and interest, the free acknowledgement of sistence on the distinction between the notions of “his- gaps in his own knowledge and the willingness to learn tory” and “heritage” when discussing mathematical de- from his students were the source of tremendous en- velopments. By the latter term he referred to a view of couragement and inspiration. Beyond the Ph.D., Ivor history held by many mathematicians, which centres continued to maintain close and friendly relationships on questions such as “how did we get here?” as op- with all of his former graduate students. Indeed, for posed to the concern of most historians, which tends Ivor, who had no children of his own, this small group to focus more on asking “what happened in the past?” of people came to form what was, for him and Enid, This distinction, as well as its many ramifications, was almost a surrogate family. a subject of immense importance to Ivor and, after Ivor was a man of many eccentricities. In later years many years of gestation, formed the subject of one of he was wont to appear to fall asleep in seminars and his last major papers. conference talks, particularly after lunch, only to wake Institutionally, Ivor remained for his whole career at up and ask a penetrating question at the end. An er- the Enfield College of Technology, although it under- ratic driver, car journeys with Ivor were always memo- went substantial changes in that time. In 1973, the rable, not least for having survived them. Tony Crilly college merged with two other north London schools to recalls being driven back by Ivor after a meeting in form Middlesex Polytechnic, which, as a new and grow- Oxford at high speed so that Ivor could get home in ing institution, soon sought to improve its research time for two editing sessions before bed! In written profile. To complement his own research, Ivor was communications, Ivor’s distinctive scrawl was a chal- encouraged to supervise doctoral students. Beginning lenge even to those well trained in reading barely legi- with Tony Crilly, Ivor went on to successfully supervise ble manuscripts, and the advent of e-mail only height- nine Ph.D. theses, from Crilly’s study of the mathe- ened the need for one’s cryptographic skills to decipher matics of Arthur Cayley to Abhilasha Aggarwal’s sur- his messages. One example (of many) was in reply to vey of higher mathematics education in British India an earlier message and read simply: in 2007. The content of many of these theses, partic- ularly that of Maria Panteki on the relationships be- v god. tanks for rude. no way to get plan to tween algebra, differential equations and logic in early pairs. iv Translation: “Very good. Thanks for nineteenth-century Britain, also influenced the course the ride. On my way to get a plane to Paris. of his own research and the breadth of his publications Ivor.” spread still further. During a long and distinguished career, Ivor was ac- As a research supervisor, Ivor was unparalleled. De- corded many honours. In 1978 the University of spite what may have appeared to those who did not London bestowed the rare distinction of awarding know him well as an intense and rather brusque per- him the prestigious D.Sc., its highest doctoral degree. sona, he was in fact a tremendously kind and generous Elected a membre effectif of the Académie interna- man gifted with a powerful intellect and love of his sub- tionale d’histoire des sciences in 1991, he also held ject. From the moment work began, the student would visiting positions at the Institute for Advanced Study be showered with papers, articles, newspaper cuttings in Princeton, Monash University and the University and other material relevant to their research. Ivor of Western Australia. In 1992, Middlesex Polytech- was a consummate professional and expected his stu- nic was granted university status and became Middle- dents to be likewise, encouraging active participation sex University. The following year, Ivor, who by this in meetings, seminars and conferences, and fostering time had progressed from Senior Lecturer to Reader in connections with others in the history of mathematics Mathematics, was appointed Professor of the History community. Regular weekly or fortnightly meetings of Mathematics and Logic at the university. He would with him, usually over lunch near an archive in cen- hold this title until his retirement in 2002. The two tral London, were the student’s opportunity to discuss honours that perhaps afforded him the most pleasure ideas with Ivor and occasionally reveal any discoveries came late in life: in 2009 he received the Kenneth O.

16 May Prize and Medal from the International Commis- A Centennial History of the MAA Ohio Section will sion for the History of Mathematics for “lifetime schol- be published later this year. A 75-year history, The arly achievement and commitment to the field”, fol- Ohio Section: 1915-1990 is currently available on-line lowed by his election to honorary membership of the at sections.maa.org/ohio/History/index.html. Bertrand Russell Society in 2010. The first annual meeting of the Ohio Section was held The first few years of retirement saw little change in at Ohio State University in April 1916. Because there Ivor’s output as his research continued at its usual was no annual meeting in 1945, due to wartime travel rapid pace. Only with the diagnosis of Parkinson’s restrictions, our 100th annual meeting will occur next disease in 2007 and a heart bypass operation the fol- year, on April 8–9, 2016. We will meet at Ohio North- lowing year did the number of meetings he could at- ern University, where Benjamin F. Finkel, founder of tend begin to decrease and the time taken to prepare The American Mathematical Monthly, earned a B.S. his papers begin to increase. But he was as responsive in 1888 and a M.S. in 1891. Then, the institution was as ever to requests for comments on first drafts, with called Ohio Normal University. work returned almost immediately with references and We welcome anyone interested in attending this meet- comments. His final research paper for Historia Math- ing. As details become available, they will be posted on ematica appeared in February 2014, and his last paper the Ohio section website, sections.maa.org/ohio/. was accepted for publication the week before he died. Copies of “Centennial Notes” can also be found there, It was only in the last few weeks of his life that he in archived issues of Ohio Focus. began to find working at the computer too much of a David Kullman strain. But his fascination with the history of mathe- matics was undiminished to the end. In Britain he leaves the dual legacy of an established Book Review professional discipline and a learned society devoted to it, both non-existent at the start of his career and John Napier: Life, Logarithms, and Legacy, by Julian in both of which he played foundational roles. To the Havil, Princeton: Princeton University Press, 2014, Archives of American Mathematics he leaves his Nach- 296 pp. 64 line illus. 48 tables. ISBN 978-0-691-15570- lass. And to scholars around the world, he leaves his 8,$US35.00 £22.95. vast array of publications—an oeuvre on which future Julian Havil, retired master and long-time teacher of generations of historians of mathematics will continue mathematics at Winchester College, England, 1 is the to build. author of four successful books, published by Prince- Acknowledgements: The author wishes to thank June ton University Press: Gamma, Nonplussed!, Impossi- Barrow-Green, Tony Crilly, Joseph Dauben, Enid ble? and The Irrationals. Grattan-Guinness, Niccolò Guicciardini, Albert Lewis Havil’s book opens with an overview of Napier’s life and Karen Parshall for their valuable help and advice and lineage, devotes a chapter to each of Napier’s five during the preparation of this article. published works, and concludes with a short chapter Adrian Rice on Napier’s legacies, supplemented by no fewer than twelve short appendices that provide many details of the historical, cultural, and mathematical contexts of MAA Ohio Section Centennial the previous material. The strength of this book is that it places each of The Ohio Section of the Mathematical Association Napier’s works within the context of Napier’s personal of America came into being on December 31, 1915, development and within the context of his family and along with the MAA itself. We have been anticipating the times and culture within which he lived. Havil the centennial of our section for the past five years, gives us considerable insight into Napier’s religious fer- with “Centennial Notes” published in the Ohio Fo- vor, the demands and concerns of his aristocratic posi- cus newsletter, “Centennial Minutes” presented at each tion, and his mathematical insights and contributions. Spring and Fall Ohio Section meeting, and tchotchkes distributed to all registrants featuring the message, Napier’s reputation rests primarily on three works: “The Centennial Is Coming.” 1http://www.winchestercollege.org

17 The Plain Discovery, written around 1593, the descrip- manuscripts two years after Napier’s death by his tio and the constructio, each written before 1614. The literary executor and son, Robert Napier. influence of Napier’s mathematical work was greatly • De arte logistica (1839). A collection of notes aided through the efforts of his son Robert, Henry recording Napier’s explorations and musings over Briggs (1st Gresham Professor of Geometry, 1st Savil- two decades into the nature of number. They re- ian Professor of Geometry at Oxford), Edmund Gunter veal Napier’s investigations into natural numbers, (3rd Gresham Professor of Astronomy), and the math- negative integers, rational and irrational numbers, ematical practitioner Edward Wright. and even imaginary numbers, although not un- Havil’s book is unusual in that it devotes a full chap- der those names. Probably written before 1594, ter to each of Napier’s published works, mathematical but not intended for publication. A fair copy in and non-mathematical, published during his lifetime Robert Napier’s hand, intended to be given to and published posthumously. Each of the five works Henry Briggs, survived among the Napier fami- is placed in its proper cultural context, and the con- lies’ private papers. These papers were edited and tent of each of the books, including the mathematical published more than two centuries after Napier’s content, is examined in detail. death by historian Mark Napier, the grandson of the youngest son of John Napier’s grandfather. • A Plaine Discovery of the Whole Revelation of St. John (1593). A work of Calvinist theology, inter- Havil excels in providing a rich context that brings the preting the book of Revelation as a prophecy of world of Napier to life for the modern reader. As a historical and current events. brief example, I include a few of the myriad details of Napier family history taken from Havil’s introductory This massive tome of nearly 400 pages is organized chapter — Life and Lineage. into 36 Propositions, with arguments organized and John Napier, the 8th Laird and Baron of Merchiston, laid out in charts of parallel prophecies and their descended through a line of eldest sons from Alexan- interpretations in the style of Peter Ramus. der, Provost of Edinburgh (bef. 1403) and 1st Laird This work was widely popular, published in four of Merchiston (a rank of minor nobility) (bef. 1438). languages in over two dozen editions. It established Napier’s father, the 7th Laird of Merchiston was made Napier’s reputation as theological scholar of Refor- Master of the Mint, while his ancestors, relatives, and mation Protestant doctrine. in-laws included an array of colorful characters, includ- • Mirifici logarithmorum canonis descriptio (1614). ing several who were involved in alchemy, accused of A description of the concept of logarithms, or ratio- sorcery, and involved in various crimes ranging from numbers, based upon a kinetic model of propor- highway robbery, through witchcraft, to high treason. tional movement in comparison to movement at a On the other hand, the 3rd, 4th, and 5th Lairds died in constant velocity. A set of tables of the logarithms battle in the service of the King, several were knighted, of sines is included, but no table of logarithms of and the 4th Laird became the first Baron of Merchis- numbers. First English edition, 1616. ton, and thus Lord Napier. • Rabdologiae seu numerationis per virgulas libri duo Napier entered the University of St Andrews at the age (1617). Published in the year of Napier’s death. of 13, leaving one year later to spend the next 7 years A description of mechanical aids to multiplication: in Europe. No record survives from his European stay, Napier’s Rods, a Promptuary of lightning multi- but he returned to his home at age 21 in 1571, fully plication, and local arithmetic—a method for ma- trained in Latin and Greek, and assumed his family nipulating markers on a checkerboard to perform duties, while carrying on the theological and mathe- binary arithmetic. matical researches that would occupy him for the next • Mirifici logarithmorum canonis constructio (1619). twenty-five years. In 1593, he initiated a series of pub- Likely written prior to the year in which the de- lications which would earn him the admiration and ap- scriptio was published. This work details pre- preciation of scholars and scientists across Britain and cisely how to produce a table of “artificial numbers” the Continent. from which the table of “artificial sines” in the de- Importantly, in addition to providing the context of scriptio was drawn. Published from John Napier’s Napier’s work, Havil presents the details of both

18 Napier’s theological and mathematical contributions. to place Napier and his work. The richness of details He takes pains to point out the centrality of trigonom- of the politics, religious struggles, and the connections etry, especially spherical trigonometry, to Napier’s con- between Scotland, England, France, Holland and the cerns in astronomy, navigation, and, to some extent, central European continent brings the story to life. cartography. He also points out that Napier thought Furthermore, Havil considers all of Napier’s output, in terms of proportions and ratios and their solution not only a portion of it, and when discussing math- by the “rule of three,” as opposed to the solution of ematical or technical matters, he does not shy away algebraic equations—which is to be expected since Eu- from attempting to present the mathematical details of ropean algebra was still in its embryonic stages. Napier’s work, including the use of logarithms, the me- However, Havil repeatedly retreats from Napier’s chanical inventions for automating arithmetic, and the fifteenth- and sixteenth- century framework to trans- development of logarithmic tables themselves. While late Napier’s accomplishments into modern mathe- intended for a general audience, John Napier: Life, matical terms—terms quite alien to Napier and his Logarithms, and Legacy would also be of considerable contemporaries—an approach which obscures the ex- value to the serious historian wishing a more in-depth position and needlessly complicates it rather than clar- understanding of Napier and his writings, but only if ifies it. read together with Napier’s original exposition, and not as a replacement or substitute. Further, when the reader is most in need of a guide to the intellectual and mathematical train of thought, Joel Silverberg Havil frequently retreats into a modern understanding, stating that such explanations are “best approached New Members through modern notation” or are “best explained in modern terms.” In recasting the situation into mod- Congratulations to the following new members who ern terms, any understanding of the originality and have joined the Society since our last Bulletin. We creativity of Napier, the man, working with the tools look forward to your contributions. that he had at hand, is obscured, distorted, or lost. Valerie Allen When explaining Napier’s more complex reasoning, John Jay College, CUNY Havil couches his explanations in anachronistic terms USA of a fully developed algebra, relying on modern nota- tion, including exponents, subscripted variables, mul- Fiona Ebbertt tipage sequences of inequalities leading to upper and Turnwater, WA lower bounds, and sections of Mathematica computer USA code. This reviewer is strongly of the opinion that Hueston Finlay a historical approach to explaining Napier’s contribu- Windsor tions would have been a better choice. More helpful UK would be a guide to the adaptations Napier made to Enrico Jabara the practices and methods of Regiomontanus, Rheti- Venezia cus, Pitiscus, or Remus—frameworks that Napier most Italy likely encountered during his travels in Europe. An Siobhan Roberts explanation of the doctrine of triangles or the impor- Toronto, ON tance of homogeneity in the pre-Eulerian concepts of Canada trig functions, and the conflict between emerging ideas of algebra and the requirements of homogeneity in cal- culation arising from the Euclidean books on ratio and From the Editor proportion, would do much to illuminate Napier’s ap- proach. Preparations—some of which began a decade ago—are These caveats aside, there is much to enjoy and admire nearly complete for the MathFest marking the Math- in this book. It is a welcome addition to the litera- ematical Association of America’s centennial, August ture and provides a much-needed context into which 5–8, 2015. This event also serves as the annual meet-

19 ing for CSHPM and a joint meeting between CSHPM, BSHM, HOMSIGMAA, and POMSIGMAA. As you About the Bulletin will see elsewhere in this issue, the four days of the meeting are absolutely packed with mathematics his- The Bulletin is published each May and November tory, philosophy, and fun. The full program of our by a team of 3 volunteers: Content Editor Amy joint sessions will be available later this spring at Ackerberg-Hastings ([email protected]), Layout www.cshpm.org and www.maa.org. For information on Editor Eisso Atzema ([email protected]), the pleasures and logistics of the wider Washington, and Production Editor Maria Zack (Maria- DC, area, see our November 2014 issue. [email protected]). Material without a byline or other attribution has been written by the editors. The initiatives launched by the Society over the past Les pages sont chaleureusement ouvertes aux textes couple of years, such as transferring production of soumis en français. Comments and suggestions are our Proceedings to Birkhäuser, continue to move for- welcome and can be directed to any of the editors; ward. If you enjoy the columns CSHPM is contribut- submissions should be sent to Amy Ackerberg- ing to Notes of the Canadian Mathematical Society, Hastings at the above email address, or by postal cms.math.ca/notes/, please consider not only volun- mail to 5908 Halsey Road, Rockville, MD 20851, teering but actually composing a brief piece (about USA. 1,200 words) for a general mathematics audience and submitting it to Hardy Grant, [email protected], and me. We are juggling enough other professional tasks that building a reservoir of completed columns would 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, with memorials for Jim and Jackie planned later. Peace to their memories. The Bulletin reaches your hands or computer screen due to the continued efforts of Eisso Atzema, Lay- out Editor; Maria Zack, Production Editor; Pat Al- laire, Secretary; and Mike Molinsky, Webmaster. I am thankful also for our officers, Councillors, and the volunteers who keep the Society’s other functions op- erating smoothly. The next submission deadline for the Bulletin is 1 October 2015. As always, the editors seek news items of interest to historians and philoso- phers of mathematics, reports on conferences attended, and personal and professional announcements. We also welcome suggestions for memorials, book and web re- views, and informative or thought-provoking column- style articles. Plain text and LaTeX files are easiest for the editors to deal with, but we can (tediously) convert Word’s special characters as well. Submissions may be sent to [email protected].

Amy Ackerberg-Hastings Printed courtesy of:

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