BULLETIN CSHPMlSCHPM
November/novembre 2000 Number/Ie numero 27
WHAT'S INSIDE
President's Message [G. Van Brummelen] ...... page 4
Articles
The GodeI-Zermelo Letters [G. Moore] ...... page 6
History of mathematics it Ia fran~aise [T. Archibald] ...... page 10
The Moscow Mathematical Society [Po Buckingham] ...... page 12
Web Review: www.maths.tcd.ie/publHistMath [R.Bradley] ...... page 15
The Princeton Mathematics Community [R. Jantzen]...... page 16
Reports
AMS Western Section ...... page 2
Executive Council Minutes ...... page 3
Call for Papers: AMS Spring Sectional Meeting...... page 5
Minutes of the Annual General Meeting ...... page 9
Canadian Society for History and Philosophy of Mathematics
Societe canadienne d'histoire et de philosophie des mathematiques
ISSN 0835-5924 ABOUT THE SOCIETY History of Mathematics at AMS Western Section Founded in 1974, the Canadian Society for the History and Philosophy of Mathematics/ Societe A special session on history of mathematics was canadienne d'histoire et de philosophie des held at the American Mathematical Society mathematiques (CSHPM/SCHPM) promotes Western Section Meeting at San Francisco State research and teaching in the history and University October 21-22, 2000. The session was philosophy of mathematics. Officers of the organized by Shawnee McMurran, Cal State San Society are: Bernardino, and Jim Tattersall, Providence President: Glen Van Brummelen, Bennington College. College, Bennington, VT 05201,USA,
2 Minutes OF THE CSHPMlCHSPM Polytechnic University on May 25-27, 2002 Executive Council Meeting (Saturday-Monday). Jim will talk with Craig June 11,2000 Hamilton, Ontario Fraser about getting a list of past officers of the Society, which should appear in a future The minutes of the previous Executive Council CSHP M Bulletin. meeting (July 1999) were approved. Bulletin Editor's Report: Sharon Kunoff and Tom Drucker will offer a call for contributions, Annual General Meeting Agenda: and will arrange for new members' names to appear in upcoming Bulletins. 1. Treasurer's Report: Robert Thomas will Webmaster's Report: Rob Bradley was asked to report on the following items: 189 members are obtain the domain name www.cshpm.org for the paid for the year 2000 at this time. He will raise Society's use. the issue of whether it is worth the effort for the Proceedings Editor's Report: Jim Tattersall will CSHPM to apply for charitable status. The announ.ce that 231 copies of the 1999 SSHRC travel subsidies continue to support us. Proceedings have been mailed, and that HSSFC dues for 4/1/99-9/30/99 are $461. After Providence College has graciously covered the doubling the dues (from $5 to $10) for cross mailing costs. It was suggested that future membership between the CSHPS and CSHPM, overseas mailings be sent by surface mail. most ofthe CSHPS members who had taken out Nominating Committee's Report: Craig Fraser reciprocal memberships in the CSHPM failed to will be collecting ballots until tomorrow. renew. Treasurer's Report - Actions Taken: Robert Other Business: will check with Craig Fraser concerning the origin and possible restrictions ofthe K. O. May 1. It was agreed that members who were paid fund, currently dormant and worth about $2000; for the year 2000, and new members in the year he will also look into the situation with regard to 2001, should receive the Proceedings (iterate a possible dues increase. The division oflabour for following years). between Secretary and Treasurer was decided as 2. We discussed, but decided against, pursuing follows: the Secretary will take over the the possibility of establishing a SIGMAA in the membership duties, collect the dues, and keep history of mathematics. the US dollars in an American bank account. 3. The Secretary will send out the first dues The Treasurer will be sent Canadian monies and notice in October. deposit them into a Canadian account. The 4. We propose the following change to the Treasurer will keep the books. Constitution, to be formally moved in the Secretary's Report: Glen Van Brummelen will November Bulletin and voted upon at the next describe the e-mail balloting system introduced AGM in 2001: this year, and report on the production of a French-language CSHPM brochure. Article IV, Section 2: "The Executive Council President's Report: Jim Tattersall will note the shall consist of the Officers of the Society, the following: We will meet with the Leameds at immediate past President, the Editor(s) of the the University of Laval from May 25-27,2001 Proceedings, the Bulletin Editor(s), [the (Friday-Sunday). Amy Ackerberg-Hastings and Webmaster,] and four other members ofthe Society." Adrian Rice will organize the general session; Jim Tattersall will locate a chair for the special The meeting was adjourned. session, which will be on French mathematics. We will meet with the Leameds at UTlRyerson Glen Van Brummelen (former Secretary)
3 President's Message over the next year than administrative meetings. It's hard to imagine how one could be more Dirk Jan Struik (1894-2000) blessed!
As a child, I first became aware of the history of No less than seven meetings and sessions on the mathematics through my father. A high school history and philosophy of mathematics, and mathematics teacher, he had shelves of amazingly several other events, are scheduled in North varied books, to spur interest in his students. One America over the next year. Of particular of them, a thin volume entitled A Concise History excitement is the regularity with which they are of Mathematics, caught my attention early, and I beginning to appear as part of national and often paged through it. Many of us were regional mathematics conferences. The profile of introduced to the history of mathematics through history is rising among our mathematical this book; in fact, it has been said that Struik's text colleagues. This year is an opportunity for us to has increased popular exposure to our field more put our best foot forward: to demonstrate the than any other book. importance and intellectual value of our subject to the mathematics community, in both pedagogical Superlative words hardly seem to suffice to pay and scholarly terms. tribute to Professor Struik. He pursued a long and eminent career in differential geometry at MIT, The list below, long though it is, may be and worked with many of the great mathe incomplete. Please let me know of any other maticians of the early 20th century. His work in the meetings, and we'll announce them in the next history of mathematics, begun relatively late in his BulIetin. career, was insightful, broad, and highly influential. I understand that his knowledge, even • Canadian Mathematical Society Winter late in life, was stunningly encyclopedic, yet he Meetings, Dec. 10-12,2000, Vancouver: J. L. maintained a helpful and encouraging attitude to Berggren, CSHPM Vice-President, is his colleagues. I wish I had had the chance to meet organizing a special session on the history of him. He remained active to the end, contributing mathematics .. to Mathematical Reviews only several months ago.
Above all, Struik was a man of conscience. His • The AMSIMAA Joint Mathematical strongly held political and social beliefs were Meetings, Jan. 10-13,2001, New Orleans: If espoused honestly and with integrity, even as a you'll be attending, don't plan much time Marxist under the scrutiny of Joseph McCarthy. during the meetings to visit New Orleans! Ron His care for the oppressed, part of a universal Calinger is organizing a panel discussion human concern, led to his political beliefs, and I entitled "The Muse of History: Writing believe that this concern·also motivated his pursuit Biographies of Mathematicians", which will of the history of mathematics. He will be missed, include Joe Dauben, Joan Richards, and remembered, and honoured. Manfred KronfeIIner. Joseph Auslander and CSHPM member Bonnie Gold will host a Meetings, meetings, meetings ... session entitled "Philosophy of Mathematics: That Which is ofInterest to Mathematicians". Having moved from a college with more Cheryl Olson and Douglas Ensley are committees than employees to a college with organizing a session on "Great Theorems of virtually no administrative structure at all, I have Mathematics". CSHPM member Eleanor recently felt unusually free from the distaste that Robson will give an MAA Invited Address, the word "meeting" conjures. Academic meetings, "Neither Sherlock Holmes nor Babylon: A on the other hand, are events to be anticipated. I Reassessment of Plimpton 322". CSHPM may be in the unique position of having more member Chuck Lindsey will present his web history of mathematics conferences in my agenda based history of mathematics course. Finally,
4 Robin Wilson will be bringing back his State Ph.D. in algebraic semigroups in 1970. He was popular dramatic presentation on the the abstracts editor of Historia Mathematica from mathematics of Lewis Carroll. 1988 through 1999. His paper on American mathematics in the period 1890-1950 will appear in • AMS Western Sectional Meeting, Apr. 21-22, the Monthly in 2001. 2001, Las Vegas: a historical session is being organized by past CSHPM president Jim Call for Papers: AMS Spring Sectional Meeting Tattersall, and CSHPM members Adrian Rice and Shawnee McMurran. There will be a Special Session on the History of Mathematics to be held at the Spring Eastern • AMS Eastern Sectional Meeting, Apr. 28-29, sectional meeting of the AMS in Hoboken, NJ, on 2001, Hoboken, NJ: CSHPM Secretary Pat April 28-29, 2001. The organizers are Pat Allaire, Allaire and CSHPM Webmaster Rob Bradley
• The big event: the CSHPM Annual Meeting, Submissions of abstracts for 20-minute talks in the May 25-27, 2001, Quebec City. Louis history of mathematics, from any historical Charbonneau is organizing the special session period, relating to any mathematical discipline or on French mathematics; Amy Ackerberg historically informed papers on the philosophy of Hastings and Adrian Rice are organizing the mathematics are welcome. Abstracts should be general session. submitted directly to the AMS. Instructions for abstract submission can be found at • AMS Eastern Sectional Meeting, Oct. 10-12, http://www.ams.org/abstracts/. The deadline for 2001, Williamstown, MA: Jim Tattersall, submission of an abstract is January 9, 2001. If Della Fenster, and I are organizing a historical you intend to submit an abstract, please let one of session. the organizers know at your earliest convenience, even if it will be some time before you make your In addition, the quadrennial meeting of the submission to the AMS. International Congress of History of Science will be held in Mexico City this August. (I smell the The usual AMS policies apply to this session: workings of a certain AMS associate secretary, speakers receive neither fees nor reimbursement of and past CSHPM president, in the large collection expenses, and must even pay their own conference of historical sessions at AMS meetings. Thanks, registration fees, currently running at about US Jim!) Let's keep up the momentum in the years to $40 for AMS members. Pat and Rob have said come. I'll be attending a number of these that they can provide you with a personalized meetings, and hope to see some of you there. letter of invitation, if this will help you to secure Finally, a meeting schedule to view with relish! funding from your institution. Please plan to G. Van Brummelen attend the history session in Hoboken even if you are not in a position to give a paper. It is expected David E. Zitarelli of Temple University will offer a to be an enriching and informative, with Chautauqua course on the history of mathematics in significant participation from the community of America from May 31 to June 2, 2001, in historians of mathematics. Philadelphia. The course covers the development of mathematics and mathematics education in the The organizers can be contacted by email or by United States from the Colonial period up to the post at: Pat Allaire, Dept. of Math & C.S. 1950s. The major emphasis is on the period 1875- Queensborough CC,CUNY, Bayside, NY 11364, 1925, when the U.S. emerged from a backwater observer to an international contributor. Zitarelli has Rob Bradley, Dept. of Math & C.S., Adelphi been at Temple University since receiving his Penn Univ., Garden City, NY 11530 516-877-4496
5 At Cross-Purposes: The Godel-Zermelo responding to critiques which Abraham Fraenkel Letters and John von Neumann had made of the concept of "definit" property used in Zermelo' s 1908 Gregory H. Moore axiomatization of set theory. Zermelo (1929) axiomatized "definit" property in what amounted The eminent mathematicians Ernst Zermeloand to second-order logic, since he quantified over Kurt Godel corresponded briefly, in 1931, but propositional functions. Soon Skolem attacked their letters are still intriguing. Zermelo attacks Zermelo's approach and argued that set theory GOdel's Incompleteness Theorem, gently in his must be formulated in first-order logic instead. He first letter, then forcefully in his last one. Godel insinuated that Zermelo's use of second-order defends his theorem quietly, lecturing Zermelo on logic could make his system contradictory by the rudiments of formal systems. reintroducing Russell's Paradox (1930, 338-339).
When Zermelo initiated this correspondence, his The first sign of Zermelo' s counterattack on career was almost over. It would soon end when Skolem came in a letter which Reinhold Baer, he was removed from the University of Freiburg Zermelo's close friend, wrote to him on 27 May for refusing to give the Hitler salute. By contrast, 1930: "In your war against Skolem, may you have Godel was at the beginning of his. Yet he had victory and lots of booty." Baer was uncertain already achieved two of his three most important whether Zermelo would succeed: "You want to results, the Completeness and Incompleteness prove that a domain of sets in which the Axiom of Theorems. In this correspondence the old and Choice is satisfied cannot be countable in any experienced Zermelo, whose views on logic had more inclusive domain of sets? For that purpose been largely formed decades earlier, was you must have a very sharp Axiom of Separation! confronted with the brilliant young Godel. I am very eager to learn how generally that is valid." Zermelo sent Baer an argument about Both Zermelo and GOdel were influenced by keeping cardinals invariant in larger domains, but Hilbert, but in different ways. Zermelo adopted in his reply of 2 June, Baer was not completely the young Hilbert's approach to the axiomatization convinced. of geometry and the real numbers about 1899- 1900, while Godel was influenced by the mature Zermelo first responded publicly to Skolem's Hilbert's formalization of logic (Hilbert and attack at the annual meeting of the Deutsche Ackermann 1928). Such formalization played Mathematiker-Vereinigung, held in Bad Elster on little part in Zermelo's published work. Nor, 15 September 1931, and spoke there immediately unlike Godel, did he use Principia Mathematica or after G6del's talk on his incompleteness theorems. first-order logic. Zermelo's talk (1932) attacked Skolem' s approach and offered an infinitary logic as an alternative The correspondence also reflects their contrasting foundation for mathematics. But the abstract of personalities. Godel's letter was cautious, the talk also attacked G6del's Incompleteness detailed, at times pedantic. Zermelo's letters were Theorem. short, argumentative, even pugnacious. Throughout his career, Zermelo had been Zermelo's criticism of Skolem and GOdel was a stimulated by spirited intellectual debates. His defense of mathematics against assaults on Cantor first was in the 1890s about thermodynamics. The and Hilbert. Zermelo saw Cantor's work as second, between 1904 and 1908, concerned his threatened by Skolem's relativism. Skolem had Axiom of Choice (see Moore 1982, 85-160). The argued against the existence of sets that were third, with Godel over the Incompleteness uncountable in an absolute sense, since any Theorem, continued a dispute between Zermelo axiomatization of such sets would have a and Thoralf Skolem that began two years earlier. countable model. Zermelo counterattacked by This dispute arose from Zermelo's 1929 article introducing an infinitary logic, modeled on the
6 cumulative type hierarchy that he had recently first letter to G6del argued that G6del's proof of introduced for set theory (1930). The main point the Incompleteness Theorem contained an error. of this infinitary logic was to insure that, within it, Godel's replied by lecturing Zermelo patiently, as every true sentence was provable, and this was his one might lecture a schoolboy, about the answer to G6del's threat to Hilbert. Zermelo had difference between a formula and a term in a no interest in questions of effectivity, perhaps formal system. But GOdel continued by reflecting the earlier debate over the Axiom of emphasizing an important point that was not at all Choice, where his opponents had used effectivity evident in his 1931 paper: the class of true to argue against that axiom. formulas of the system is never expressible in the system, and hence there are true formulas that are Yet in 1929 Zermelo had deviated from Hilbert's not provable. Here Godel clearly indicated the logic on an important point. While Hilbert's logic result, usually credited to Tarski alone, that truth was finitary, Zermelo's new logic was not. is undefinable in a formal system containing Zermelo first made it public in his lectures at the arithmetic. University of Warsaw in May 1929. His first lecture insisted that mathematics was not Zermelo's reaction to the limitations of finitary determined by its subject matter (e.g., space and logic was by no means peculiar to him. No less a number) but was "a systematization of the logician than Rudolf Carnap (1936) was also provable and, as such, an applied logic". He stood driven to infinitary logic by the Incompleteness on the brink of a more general notion of proof Theorem. His new rule of inference with than that accepted by Frege, Peano, and Hilbert: infinitely many premises was intended to reduce "A 'proof is the derivation of a new proposition the gap between truth and provability. Meanwhile from other previously given propositions, by Zermelo (1935) gave the beginnings of an whose truth its own is established through general infinitary proof theory. Despite appearing in a logical rules or laws" (Zermelo in Moore 1980, prominent journal, Zermelo's paper attracted no 135). A proof, he insisted, might not be of finite interest. The time was not yet ripe for infinitary length. In his fourth lecture he argued that logic. "mathematics is infinitistic in its essence and is founded on the assumption of infinite domains; it Zermelo preserved a negative impression from his can be designated precisely as the 'logic of the contacts with Godel. Replying on I October 1941 infinite' " (ibid., 136). to Paul Bernays, who had congratulated him on his 70th birthday, Zermelo regretted that his work From the abstract of his talk, Zermelo's lecture on set theory (except the Axiom of Choice) was might seem highly critical of G6del. In fact, it ignored. In particular, he had not been invited to was not. In a letter of 7 October 1931 to Baer, the conference on foundations held in Zurich Zermelo noted "At Bad Elster I avoided any direct during December 1938. He added that his work polemic against G6del, both in my lecture itself after 1904 was not even mentioned in its and afterwards. One should not frighten off proceedings, "whereas the dubious merit of a enterprising beginners" (Zermelo in Taussky-Todd Skolem or a GOdel was widely promulgated. In 1987, 47). Yet the letter to Baer was bitter: "I that regard I recall that already at the Bad Elster deliberately had G6del's lecture put on before meeting my lecture about systems of propositions mine and asked that they be discussed together. was excluded from the discussion, thanks to an But the sole consequence of my loyalty was that intrigue by the Vienna School represented by the whole discussion was putforther back at the Hahn and Godel. So it goes, apparently, for unjustified suggestion of Fraenkel (who stabs me anyone who has no 'school' or clique behind him. in the back at every opportunity!) and then petered But perhaps the time will come when my works out" (ibid.). too will again be discovered and read."
Six days after the Bad Elster meeting, Zermelo's (See GOdel P. 8)
7 Godel (cont.from P. 7) Taussky-Todd, Olga. 1987. "Remembrances of Kurt Godel", in P. Weingartner et al. (eds.), Godel The day came when Zermelo's works on set Remembered (Naples Bibliopolis), 29-41. theory were read again, but his work on an infinitary logic was not. Infinitary logic was only Zermelo, Ernst. 1929. "Uber den Begriff der accepted as part of logic in the mid-1950s with the Definitheit in der Axiomatik", Fundamenta work of Leon Henkin, Carol Karp, Dana Scott, Mathematicae 14, 339-344. and Alfred Tarski. This flowering of infinitary ----- 1930 "Uber Grenzzahlen und Mengenbereiche", logic was motivated by desires contrary to those of Fundamenta Mathematicae 16,29-47. Zermelo. He had wanted a strong logic in order to eliminate countable models of set theory. Those ----- 1932 "Uber Stufen der Quantifikation und die who worked on infinitary logic in the 1950s Logik des Unendlichen", Jahresbericht der Deutschen Mathematiker-Vereinigung (Angelegenheiten) 41, 85- wanted a weak infinitary logic which stayed close 88. to first-order logic and preserved many of its desirable properties but had more expressive ----- 1935 "Grundlagen einer allgemeinen Theorie der power. In the interim, the earlier work on mathematischen Satzsysteme", Fundamenta infinitary logic (see Moore 1997) was forgotten. Mathematicae 25,136-146.
Yet, in a sense, Zerrnelo had his revenge. By the Frederick V. Pohle Colloquium Series 1960s infinitary logic became an integral part of mathematical logic, despite the wishes of GOdel On October 4, 2000, CSHPM member Amy Shell (1944), who had argued vigorously against it. kicked off the 2000-2001 season of the Frederick V. Pohle Colloquium Series on the History of References Mathematics. Amy, a recent D.A.from UI Chicago is an assistant professor at West Point. She spoke Carnap, Rudolf. 1936. "Truth in Mathematics and on "Mina Rees and Her Influence on Mathematical Logic", Journal ofSymbolic Logic 1,59. Research" to an intimate and appreciative audience.
GOdeJ, Kurt. 1944. "Russell's Mathematical Logic", The Series, now in its third year, is a monthly series The Philosophy ofBertrand Russell (ed. P. A. Schilpp), of talks on the history (and sometimes philosophy) 123-153. of mathematics chaired by Pat Allaire and Rob Bradley at Adelphi University and services mainly Hilbert, David, and Wilhelm Ackermann. 1928. mathematics professors in the Queens/Nassau Grundziige der theoretischen Logik (Berlin Springer). County area of New York State. Fred Pohle, a Moore, Gregory H. 1980. "Beyond First-Order Logic: former chairman of the department, was an applied The Historical Interplay between Mathematical Logic mathematician and an avid student and teacher of and Axiomatic Set Theory", History and Philosophy of the history of mathematics. Logic 1,95-137. CSHPM members, have featured prominently in the ----- 1982 Zermelo's Axiom of Choice: Its Origins, Colloquium's first two years. Future speakers Development and Influence (New York Springer). include Fran Abeles (November 9), Rob Bradley (December 6), Rudiger Thiele (January 24), Glen ----- 1997 "The Prehistory of Infinitary Logic 1885- Van Brummelen (February 7), Greg Moore (March 1955", Structures and Norms in Science: 10'h 7), Agnes Kalemaris (April 4) and Karen Parshall International Congress of Logic, Methodology and (May 2). Philosophy ofScience (Dordrecht Kluwer), vol. II, pp. J05-123. For more information, VISit www.adelphi.edu/ Skolem, Thoralf. 1930. "Einige Bemerkungen zu der ~bradley/fyp, or email Rob at [email protected]. Abhandlung von E. Zermelo 'Uber die Definitheit in Pat and Rob welcome suggestions and volunteers der Axiomatik' ", Fundamenta Mathematicae 15, 337- for the 2001-2002 schedule. 341.
8 Minutes of the Annual General Meeting, June 12, 2000 , May 25-27. • At the AMS-MAA meetings, January 10-13, 2001 in New Orleans, Eleanor The minutes of the 1999 Annual General Meeting Robson of Oxford University will give a plenary were approved. lecture; Karen Parshall and David Zitarelli will organize a joint special session on the history of 1. Treasurer's Report: Robert Thomas reported a mathematics; Fred Rickey and Bill Dunham will small surplus for the year 1999. As of this point in organize a contributed paper session on Euler; 2000 189 members have paid dues. Doug Ensley will organize a contributed paper , Motion: To approval the 1999 financial session on great theorems in mathematics; and statement and the addendum to the 1998 financial Ron Calinger will organize a special session on statement. Carried. The Muse of History: Biography, which will Motion: To table the pursuit of charitable feature talks by Joan Richards and Joseph Dauben. status for the CSHPM until a future need arises. .' Thanks to Greg Moore for Carried. efficiently handling the local arrangements and to Motion: To cover Robert Thomas's out those chairing the sessions for this meeting; to of-pocket expense incurred in his role as Tre~urer McMaster University for their hospitality; to the in the past year (hiring an accountant). Carned trustees of the E. P. May fund for their generosity; 2. Secretary's Report: Glen Van Brummelen to SSHRC for their continued support of travel thanked Robert Thomas for handling a great grants for our speakers; to Louis Charbonneau for proportion of the duties between Secretary and acting as Jim's representative at the Canadian Treasurer over the past year, and reported on the National Committee (CNC); to Ed Cohen for Council's recommendations for distributing the acting as our representative to the HSSFC; to work between the two jobs. He thanked Ariane Sharon Kunoff and Tom Drucker for the Robitaille for her efforts in translating the absolutely marvelous job they do on the society's informational brochure into Frenc.h, and CSHPM/CSHPM Bulletin; to our councilors Rob Bradley for taking over the duties of Rebecca Adams, John Fauvel, Alexander Jones Webmaster. He thanked Jim Tattersall, outgoing and Craig Fraser for their assistance; to Robert President and Proceedings editor, for his fine Thomas, Jacques Lefebvre, Hardy Grant, Israel service to the Society in both these roles. Kleiner, Craig Fraser, Glen Van Brummelen, and 3. President's Report: Jim Tattersall reported on Tom Archibald who were always there to answer the following: what must have seemed a myriad of questions; to • He thanked the general session Providence College for their help publishing and organizers Pat Allaire and Rob Bradl~y, and t~e mailing the CSHPM/SCHPM Proceedings; special session organizer Tom Archibald. ~hls congratulations to Michael Kinyon for assuming joint meeting with the Canadian Mathematical the editorship of the Proceedings beginning with Society has been very fruitful so far. volume 13; to the Nominating Committee (Sharon e The CSHPMlSCHPM's Annual Kunoff, Craig Fraser, and Robert Thomas) for Meeting in 2001 will take place with the HSSFC their hard work in selecting a slate of candidates. Congress (the Learneds) at the University of 4. Proceedings Editor's Report: Jim Tattersall Laval, May 25-27 (Friday-Sunday). The general reported that 227 copies were mailed out as of session will be organized by Amy Ackerberg 6/1/2000 (100 to the USA, 66 to Canada, 26 to the Hastings and Adrian Rice; the topic, for the special UK, and 35 dispersed to Argentina, Australia session will be French Mathematics. Belgium, Bosnia, Brazil, Croatia, Costa Rica, • The CSHPM/SCHPM's Annual Denmark, Malta, Taiwan, Sweden, France, Meeting in 2002 will take place with the Learneds Germany, Iceland, Italy, Israel, Indonesia, Japan, at UTlRyerson Polytechnic University, (See Minutes P. 11)
9 History of mathematics it la fran~aise The other major project concerns Henri Poincare. Tom Archibald Poincare's collected works are published, but this edition will include much of his correspondence, The main purpose of this note is to increase reader largely unpublished, with other mathematicians awareness of the extent and vitality of the history and scientists. The effort is being conducted by the of mathematics community in the hexagon, as the Archives Henri Poincare in Nancy, with the French Republic is often dubbed in its own press. participation of Gerhard Heintzmann, Philippe My knowledge is very lacunary and the treatment Nabonnand, and Scott Walter (among others). is necessarily selective, so I apologize to the many Several publications have already resulted, people whose efforts won't be described. One including a previously unpublished historical specific difference of the French situation is the reflection by Poincare on the discovery of existence of a research body, the CNRS, which Fuchsian functions (edited by Jeremy Gray and employs researchers in nationally-funded Scott Walter); and the correspondence with permanent and short-term positions, which exists Mittag-Leffler, edited by Philippe Nabonnand. in parallel to the universities. Research Groups and Seminars in Paris The Revue d'histoire des mathematiques While there are regular seminars on the history of First of all, I would like to draw attention to the mathematics in other centres (notably Nantes, fact that the Societe mathematique de France Lyon, Lille and Poitiers), Paris is the main seat of (SMF - the CMS- or AMS counterpart) publishes such activity. An extraordinary number of ajournal, the Revue d 'histoire des mathematiques, seminars occur quasi-regularly during the which has articles in both French and English. The academic year (essentially from October to June) current editor in chief is Jeanne Peiffer of the which touch on all periods and all aspects of the Centre Alexandre Koyre. The overseas field. Themes for the seminars vary annually. subscription rate is 420 francs a year (under $100 Contributors are for the most part post-doctoral Canadian), with a reduction for members of the scholars, though graduate students attend and SMF. In the French tradition, you can also order sometimes present their work. Research in the individual numbers. More details, including history of mathematics exists in contact with the abstracts, can be found at http://smf.emath.fr/. history of science and technology, with the Submissions of original research are encouraged. mathematical community, with the philosophy of science, and with educational research. As you Major editorial projects might expect, there are differences in methodology and in research emphasis both within Two major editions of collected works are and between these different communities. currently underway. The D' Alembert edition has funding which should see the publication of its Many of those associated with the history of first fruits within the next two years. Scholars of science community are at the Centre Alexandre the eighteenth century are well aware of the Koyre, a hybrid institution which houses difficulty of accessing D' Alembert's work, much university-based researchers, CNRS researchers, of it produced as monographs or pamphlets, much and people associated with the Museum d'histoire in difficult-to-obtain academy journals. The naturelle. Two of the best-known historians of project, which involves such scholars as Christian mathematics there are Amy Dahan, the author of Gilain, Eric Brian, Irene Passeron, Franyois de a book on Cauchy, who is currently interested in Gandt and Pierre Crepel, envisages the publication US mathematics in the twentieth century (among of his literary works as well as his mathematical other things); and Jeanne Peiffer, who has worked and scientific endeavours, and there will be extensively on the Bernoulli edition and is also detailed commentary on the mathematics. involved with the D' Alembert edition. CSHPM
10 members had the opportunity to hear Amy Dahan French is one of the society's official languages, at the joint meeting with BSHM last year in and to make contact with this remarkable body of Toronto. scholarship. While books and journals published in France are not easily available in Canada and The CNRS researchers are attached to a the US, online ordering makes locating and paying multiplicity of different units with varying for such works far easier than was the case even a missions and emphases. One example is year or two ago. REHSEIS, a group which includes Karine Chemla, the eminent historian of Chinese Tom Archibald, is a member ofthe Dept. ofMath. and mathematics, and Roshdi Rashid, some of whose Stats., Acadia University, NS. He recently spent some works on the history of mathematics in the Arab time in France researching the History ofMathematics world are available in English. Another is the in the French Republic. CRHST (Centre de recherche en histoire des sciences et techniques) which likewise has a focus Minutes (Cont. from P. 9) strongly associated with history of science and technology: This centre is housed at the Cite des Mexico, Spain, and Portugal. Michael Kinyon Sciences et de l'Industrie, a science centre, and was recognized as the next Proceedings editor. recently welcomed Canadian researcher David 5. Bulletin Editor's Report: The editors, Sharon Aubin, supported by a SSHRC post-doctoral Kunoff and Tom Drucker, issued a call for fellowship to work on issues related to the history contributions from members for the next Bulletin. of chaos theory and catastrophe theory. Still 6. Webmaster's Report: Rob Bradley reported another group, to which Liliane Beaulieu (of that the Society now owns the rights to the domain Montreal) is attached, is concerned with the name www.cshpm.org. history of Bourbaki. 7. Election of Officers: Craig Fraser, on behalf of the Nominating Committee (himself, Sharon University mathematics departments also house a Kunoff, and Robert Thomas), announced the number of researchers. The only professorship of results of the election. 51 ballots were cast. The the history of mathematics is held by Christian results are as follows: Glen Van Brummelen Gilain, who has written extensively on the history (President), 51 yes; Len Berggren (Vice of differential equations. A considerable number President), 51 yes; Pat Allaire (Secretary), 51 yes; ofCNRS researchers do some university teaching, Robert Thomas (Treasurer), 50 yes; Rebecca however, and a considerable number of people Adams (Councilor), 50 yes; Roger Godard with mathematics teaching posts are active in (Councilor), 50 yes; Hardy Grant (Councilor), 50 historical research. Here I would mention yes; Alexander Jones (Councilor), 51 yes. All Catherine Goldstein, whose interesting book on candidates are elected. the history of number theory has yet to be 8. Old Business: none. translated into English. Furthermore, in some 9. New Business: cases university researchers with appointments in Motion: To entitle the organizer(s) of pedagogy also have historical interests : Hel~me general and special sessions at the AGM to the Gispert is a case in point. Likewise, various same travel reimbursement benefits as speakers. government offices house researchers : Bruno Carried. Belhoste, for example, author of the Cauchy The Treasurer and Secretary will look into biography published in English by Springer, is at placing some of the Society's funds into an the National Institute for Pedagogical Research. interest-bearing account.
This very short list reveals only a fraction of the The meeting was adjourned. richness of this diverse community. CSHPM members are hereby encouraged to realize that Glen Van Brummelen (with thanks to Jim Tattersall)
11 Challenges to Science in the Revolutionary Era, 1905-1921: The Experience of the Moscow France, Germany, and Great Britain. Mathematical Society The year 1905 also brought a new president for Paul Buckingham the Moscow Mathematical Society. In November 1905, the respected mathematician and physicist, The period between 1905 and 1921 encompasses Nikolai Egorovich Zhukovskii (1847-1921), also a period of great turmoil in Russian history. Two known as the father of Russian aviation, was major revolutions, the First World War, and a elected to lead the Society.3 The new president vicious civil war further complicated broad social, was, like those before him, a major figure in the political, and economic changes taking place in Moscow scientific community. As a scientist, the Russian Empire. All of Russian society faced Zhukovskii made fundamental contributions to the hardship and change. This includes the growing study of aerodynamics, hydrodynamics, and mathematics community in Moscow centered on general mechanics. As president, Zhukovskii . the Moscow Mathematical Society. The would guide the society through one of the most challenges facing science and scientific desperate times in Russian history. These development in Russia can be clearly seen through desperate times were further complicated by the example of the difficulties faced by the political pressures and the ever-present mathematicians in this time of troubles. Political bureaucratic red tape with which scientists and pressures and simple bureaucratic red tape were mathematicians needed to deal. prominent issues in the story of science and mathematics in Russia during the Revolutionary A difficulty widely affecting science in Russia was Era. the centralized nature of the Russian bureaucracy. As a state-sponsored scientific organization, and By 1905, the Moscow Mathematical Society had there were few other kinds, the Society needed to been in existence for nearly forty years having deal with government red tape and make use of been officially organized in 1867. It was the political connections from time to time in order to foremost mathematical society in the Russian achieve its goals. A clear example of the Empire and its membership included over seventy sometimes baffling nature of the bureaucracy in Russian and a dozen foreign members with the Russia that often hindered the normal activities of active core of the society being formed by the the society is demonstrated in an absurd series of mathematics professors and students at the letters from 1907 to 1908. The society had in its University of Moscow. 1 By the same year, the possession a large portrait ofthe late president of Society had also published nearly twenty-five the Society, Nikolai Bugaev (1837-1903). This volumes of its scholarly journal, Matematicheskii portrait was hung in the Physics and Mathematics sbornik.2 The journal was widely distributed Faculty conference room where meetings of the abroad but mostly disseminated among the Society were held. 4 Following the death ofVasilii universities and other mathematical societies in Iakovlevich Tsinger (1836-1907), another Russia. It was, however, the most important, and president, in February of 1907, the Society virtually the only, journal dedicated solely to decided to hang portraits of all of the deceased mathematics in Russia. The future of the society presidents of the Society including Tsinger in their was promlsmg despite ongoing financial meeting room. 5 In the archives, one finds a set of difficulties. Moscow mathematicians were correspondence demonstrating that, in order to becoming more and more connected to the hang these portraits in their meeting hall at the European mathematics community though, indeed, university in Moscow, the society needed to Russia and the Moscow mathematicians were still request permission from at least the Minister of largely behind the great mathematics centers in (See Moscow P. 13)
12 Moscow (Cont. From P. 12.) political pressures to bear on the Society that were believed to be harmful to its overall mission. Public Education in St. Petersburg and possibly, the Tsar himself.6 Here is an excerpt from one For the Moscow Mathematical Society, evidence letter ofthe series: for increasing political pressure on science began at the meeting of the Society on January 20, 1915. [From the Superintendent of the At this meeting, an order from the Rector of Moscow Educational District to Moscow University was read. The order, dated the Rector of Moscow December 22, 1914, commanded scientific University] societies to expel all German, Austrian, and Turkish members, those scientists from countries His Lordship, the Minister of with which Russia was at war. The command was Public Education, based upon the tabled at the meeting so the Society and its statement from the proposal of leadership could frame a proper response9. At the the 31st ofDecember, 1908 (No. next meeting, the Society reported the following 33348), makes it known that on resolution on the order to the Rector: the basis of HIS IMPERIAL MAJESTY'S command ofthe 5th Resolved: Having attached a list of December 1881, he has of all foreign members in decided to place the portrait of accordance with this project, the the late Professor N. D. SOCiety responds, that amongst Brashman in the hall of the new the active members participating building belonging to the Physics in the activities of the Society, and Mathematics Faculty of the there are no foreign subjects and IMPERIAL Moscow University. that insofar as the foreign members listed, the Society notes [Signed] Superintendent that it does not have the ability to Zhdanov7 differentiate its membership by nationality, not having the This is a glimpse of one ofthe great weaknesses of corresponding data. 10 the centralized bureaucracy in Russia. Simple decisions required the permission of high-level The reply to the order suggests that the Society at officials. Perhaps, in this case, there was fear that the very least sidestepped its spirit because more portraits of inappropriate people might be hung in than halfofthe foreign membership of the Society public places. Regardless, it is an example of some was listed as being from cities in either the of the bureaucratic red tape faced by science and German or the Austrian Empirell. By claiming scientific societies in Russia. not to have collected information on the nationalities of its foreign members, the leaders of Throughout the period from 1907 to 1914, the the Society were apparently suggesting that they membership ofthe Moscow Mathematical Society could not determine if any of the society's continued to grow. The number of Russian and members living in Austria and Germany were foreign members increased and its connections actually Austrian or German. Perhaps, one can and exchanges with other scientific institutions imagine them suggesting, those members might be both foreign and domestic were also strengthened. Polish or Czech by nationality but living in the There were now, in 1913, ninety-one members German or Austrian Empire and thus, they should and twenty-three foreign members.8 This was a not be expelled under this rather explicit edict. In high point for the society in the pre-Stalin era. Yet a manner befitting a society of lawyers, this political changes and global events, primarily the loophole was exploited to avoid expelling foreign beginning of World War I, conspired to bring members. Such an act would have severed very
13 important ties between the Russian and Gennan Symposium] mathematics communities. While the Rector's order, undoubtedly passed on from higher in the 3. The society was to hold an extraordinary meeting government, was a part of the general anti-Gennan to elect Zhukovskii in October but the political feelings that swept through those nations opposing unrest of the Revolution of 1905 forced the Gennany, the mathematicians of the Society cancellation ofthe meeting. clearly felt that the war would eventually end and they would still need contacts in Gennany, one of 4. Protokol, November 7, 1906, Matematicheskii the centers for mathematics in Europe at the time. sbornik, v. 26, n. 4, (1908). These contacts were, after all, friends and colleagues. Also, Russian mathematicians still 5. Nikolai Dmitrievich Brashman (1796-1866), needed to go abroad to receive advanced Avgust Iul'evich Davidov (1823-1885), Tsinger, mathematical training. Severing these ties would and Bugaev. severely damage the future of Russian 6. The series is found in TsIAM F. 418, Op. 86, D. mathematics. So, they used every loophole to 571. L. 1 is a copy of the request in the Journal of protect this future. Fortunately, there seemed to the University Council. L. 2 is a letter from the have been no repercussions from this small Dean of the Physics Mathematics Faculty to the resistance to Russian state authority. Rector. L. 4 is the response from the Superintendent to the Rector (see citation below). F. 418. Op. 85, Throughout the period from 1905 and 1921, the D. 552 contains files from the Dean to the Rector Moscow Mathematical Society faced two (L.1-2), from the rector to the Superintendent (L. 3), problems common to Tsarist Era science. As a from the Superintendent to the Rector (L. 4) and government sponsored organization, it faced its from the Rector to the Dean (L. 5). share of red tape as it dealt with a centralized bureaucracy. Also, although not important enough 7. TsIAM F. 418, Op. 86, D. 571. L. 4. Dated to draw significant attention, it did face its share of January 9, 1909. political pressure. Ironically, and perhaps surprisingly, once the society reregistered with the 8. Based on membership data at the beginning of new Bolshevik government in 1922, it did not face Matematicheskii sbornik, v. 29, n. 1, (1913) and significant ideological or political pressure until Buckingham, Appendix B. 1928 with the beginnings of Stalinization. Eventually, in 1930, politicized graduate students 9. Protokol, January 20, 1915, Matematicheskii chaffing under the tutelage of the old guard sbornik, v. 29, n. 4, (1916). Possibly, the tabling of mathematicians seized and reorganized the this resolution is a ploy to delay implementing the Moscow Mathematical Society around Stalinist order so that the society could find a way to values. circumvent it.
End Notes lO. Protokol, February 19, 1915, Matematicheskii sbornik, v. 29, n. 4, (1916). 1. Based on an estimate from Appendix B of Paul Buckingham, "A History of the Moscow 11. Of twenty-one foreign members listed in Mathematical Society, 1861-1931: Mathematics as Matematicheskii sbornik, v. 29, n. 1, (1913), the a Scientific, Moral, and Economic Tool in the same volume in which the minutes containing this Context of a Late-Developing Society," (Ph.D. order are published, the following foreign members Thesis, Bowling Green State University, 1998), were listed as living and working in Gennany: 271-286. Walther Franz Anton von Dyck (Munich), Paul Albert Gorden (ErIangen), Friedrich Emil Prym 2. Appendix E in Buckingham, 289. (Wurtzburg), Matematicheskii sbornik [Mathematics (See Moscow P. 18 )
14 WEB REVIEW: The History of This neatly circumvents the issues surrounding Mathematics: the changes in the scholarly assessment of ancient www.maths.tcd.ie/publHistMath and medieval mathematics that have taken since the book was written in 1908. Nevertheless, it Rob Bradley makes for some very entertaining surfing in waters of modem mathematics from Descartes to When I inherited the CSHPM website from its Babbage. creator Glen Van Brummelen, it came with a health; collection of links to history of math Of much greater scholarly interest will be the resources on the World Wide Web. Among my sections devoted to Berkeley, Hamilton and the favorites is David Wilkins' site others. The choice of these two Trinity College (http://www.maths.tcd.ie/publHistMathI). Since scholars is not coincidental, Wilkins being this site was new to me a few months ago, I asked himself a Lecturer in Mathematics at Trinity. Glen whether it had already been reviewed in the The Berkeley section includes the full text of The pages of this newsletter, and how old he thought Analyst; Berkeley's challenge to Newton and his it was. Glen told me that it had not yet been followers, as well two sequels, the essay A reviewed, and that it's "almost as old as the web Treatise Concerning the Principles of Human itself. " Knowledge, and links to other works by Berkeley published on other websites. Those works Indeed, I emailed David Wilkins and he confirms transcribed by Wilkins himself are available in that his site, The History of Mathematics, dates HTML format, as well as TeX and Postscript. back to October 1994. How old is the web? Many of the later additions on the site are Well, 1994 was the year of the first International additionally available in PDF format. WWW conference. The official release of Mosaic, the first multi-platform web browser, The section on William Rowan Hamilton is the was in late 1993. Lest you get the wrong most extensive piece of the website. Wilkins impression, though, the site is constantly being claims that, with the exception of two books, updated, with changes to the Hamilton section, everything published by Hamilton during his own for example, made just a few weeks ago. lifetime is included in four formats (TeX, DVI, Postscript and PDF) on-line at his site, for a total David Wilkins' site is primarily an archival site, of some1200 pages in each format. The articles with an extensive collection of the writings of are indexed chronologically, as well as Berkeley, Hamilton, and Riemann, as well as thematically, with brief abstracts of the papers material by Newton, Boole, and Cantor. In supplied by Wilkins on the thematic pages. addition, there are substantial excerpts from Rouse Ball's book A Short Account ofthe History Of necessity, all of the material on Wilkins' site is of Mathematics, and an impressive collection of in the public domain. Therefore, for example, he links to resources on the World Wide Web. has not included any of Hamilton's unpublished The Rouse Ball section is the oldest portion ofthe manuscripts, which appeared for the first time in site, and Wilkins is no longer actively the Cambridge University Press's Mathematical maintaining it. It is also the most trafficked part Papers of William Rowan Hamilton, whose of the site: Wilkins reports a lot of hits from fourth and final volume is due to be released any schoolchildren apparently writing reports on day now. Newton, Descartes, Fermat and others. In this Plans for the future include a broader treatment of portion of his site, he has limited himself to the the history of mathematics in Ireland, which will "Third Period" of Rouse Ball's narrative, and likely include further development of the largely limited himself to the biographies therein. (See Web Review P. 18 )
15 "The Princeton Mathematics then two towering figures of twentieth century Community in the 1930s: An Oral science, Einstein and Godel, were among the faculty during this decade when the Institute for History Project" Now On-Line Advanced Studies was conceived, founded and housed together for 6 years with the Princeton The decade ofthe 1930s at Princeton has had far University Mathematics Department in a new reaching consequences for mathematics in university building built sparing no expense to America. Important advances in game theory, foster a truly mathematical community in memory modern topology, linear programming, of Henry Fine. Their students were the generation mathematical statistics and computing had their which contributed to the oral history project of Al origins then in a remarkable community of Tucker in 1984 in an attempt to salvage what mathematicians whose influence spread across the memories were still left forty-five years later after continent through their students and successive World War II brought this era to a close. generations. Encouraged by a fellow Princeton ian and historian . John Nash, a Nobel prize winner in economics for of science Charles Gillispie, with the help of his early work in game theory (1994), was a historian of science William Aspray and then grad student of Albert Tucker ("prisoner's dilemma"), student Rik Nebeker, they compiled 45 taped himself a student of Solomon Lefschetz, a key interviews which were then transcribed and figure in modem topology (a term coined by indexed, but only a few paper copies were then Lefschetz). Tucker in tum had been greatly produced in 1985, available to the public only at influenced by John von Neumann's early studies the Princeton University Math-Physics Fine Hall of game theory. John Tukey, "considered to be Library, the Charles Babbage Institute (Center for one of the most important contributors to modem the History of Computing) at the University of statistics," inventor of the terms "bit" and Minnesota, and American Philosophical Society in "software", had also been a student in that era. Philadelphia. John von Neumann also had enormous influence on the development of computing, as did Alonzo These were accidentally discovered in 1999 by Church through his abstract lambda-calculus myself, Villanova University Professor Robert which later became the foundation for the Jantzen, Abe Taub's last graduate student in computer language LISP, also making major physics at UC Berkeley (1978), while inquiring contributions to recursion theory and about materials that the Princeton University Fine mathematical logic. Of the students of Church, Hall library might have on Taub and Eisenhart, John Kemeny, was the coinventor of the computer not long before Abe's death that year. Another language BASIC and of time-sharing, while accidental coincidence through the Fine Hall Stephen Kleene also contributed to recursion library staff led to a meeting with Gillispie, at theory and computability and Alan Turing, famous which time I suggested that the Oral History for his "Turing machine" did fundamental work in Project should be made available on the web and computability. Von Neumann actually shared a enhanced with background materials. It was clear half position with his close Hungarian friend that the only way to get this done was to do it Eugene Wigner, who won the Nobel Prize in myself, so I undertook a long and tedious Physics in 1963. Abe Taub, a student of H.P volunteer project of scanning and web formatting Robertson who also worked with Veblen and von the project, and finding supporting materials in an Neumann and learned his geometry from amateur effort to provide some context for the Eisenhart, carried on the relativity tradition of that project. This came on line in September, 2000 at era as a physicist with a mathematics degree. http://www.princeton.edu/mudd/math at the Seeley G. Mudd Manuscript Library of Princeton Veblen, Eisenhart, Lefschetz, Weyl, Alexander, University. von Neumann, Wigner, Robertson, Church, and
16 The interviews reveal the personalities of these The board of the society asked 12 of its members famous names, and the atmosphere of the to participate in the work of this HM Committee, community of mathematicians which existed and nominated Prof. Akos Csaszar, member ofthe during that decade. They should be of interest to Hungarian Academy of Sciences to be chairman, anyone who is curious about how great minds and Katalin Munkacsy, associate prof. of the work, and what kind of people lie behind the work Teacher Training Faculty of Eotvos University of that made them famous. Budapest to be its secretary.
With my background in physics and relativity, I The committee held its inaugural meeting on have little knowledge of the field of the history of October 4, 2000 in Budapest. Seven members mathematics, so I would appreciate help from were present, the chairman and secretary, as well more knowledgeable professionals in gathering as: further supporting documents to either include in Laszlo Filep, College of Nyiregyhaza, the site or make reference to. Any suggestions that Istvan Gazda, Hungarian Science History might improve the site are also welcomed, and its Institute, contents will be updated from time to time. Some Elemer Kiss, University of Tirgu Mures, ofthe supporting documents sketch the decade of Romania, the fifties, the students from which are now at Mihaly Szalay, Eotvos University, about the ages that the remaining students from Tibor Weszely, University of Tirgu the thirties were in 1984. Sadly there seems to be Mures, Romania. little interest in continuing this oral history or in archiving materials to record the human At the first meeting the committee discussed the relationships that fill in the history of the following main topics: generations after the Robert Jantzen 1. Preparation of the celebration of coming Department of Mathematical Sciences, Villanova anniversaries of noted Hungarian or Hungarian University, Villanova, PA 19085-1699 USA born mathematicians, such as
17 Moscow (Cont. from P. 14) Web Review (Cont. from P. 15)
Karl Hermann Amandus Schwartz (Berlin), Paul section devoted to George Boole, and possibly Stackel (Kiel), RudolfMehmke (Stuttgardt), and, further material from mid-nineteenth century in G6ttingen, David Hilbert, Felix Klein, and Germany. This would be a welcome addition Woldemar Voight. Robert Daublewsky von alongside the nearly complete collection of papers Sterneck worked in Vienna, the capital of the by Riemann already available. Austro-Hungarian Empire. David Wilkins says he does not "aim for BIBLIOGRAPHY encyclopaedic coverage of the History of Mathematics". However, he has succeeded admirably in providing the on-line community Archival Sources with an impressive depth of coverage in the writings of some pivotal figures in the subject that Central Historical Archive of Moscow (TsIAM) is our shared passion. You can find his site at the Fond 418- Moscow Imperial University, 1799- URL listed above, or by browsing to 1917. www.cshpm.org, selecting "Links" on the main menu, and then choosing "General Resources in Other Sources the History of Mathematics".
Buckingham, Paul. "A History of the Moscow See you in Quebec May 25-27 2001 Mathematical Society, 1861-1931 : Mathematics as a Scientific, Moral, and Economic Tool in the Context of a Late-Developing Society." Ph.D. This year our Annual Meeting will be held in Thesis, Bowling Green State University, 1998. Quebec City in conjunction with the 2001 Congress of the Social Sciences and Matematicheskii sbornik. Vol. 26. no. 4 (1908), Humanities. This will be the first time we are Vol 29. no. 1 (1913), Vol. 29 no. 4. (1916) meeting with this group since 1998.
Dr. Paul Buckingham is a historian of Russian and Our special session in on French Mathematics Soviet science in the Department of History/Political and will be chaired by Louis Charboneau. The Science at the University ofSaint Francis Fort Wayne IN 46818. He can be reached there or by email at general session will be under the leadership of
18 The following have joined the Society since Spring Mary K. Gfeller, Oregon State University, Dept. 1999. The editors appologize for our negligence of Sci. & Math Ed., 237 Weniger Hall, Corvallis, in not recognizing you sooner. A warm welcome OR 97331, USA, to all! William Hackborn, Mathematical Sciences Judy Barrow-Green, Faculty of Mathematics, Augustana University College, 4901-46 Avenue: Walton Hall, The Open University, Milton Camrose, AB T4V 2R3, Canada, Keynes, MK7 6AA U.K.,
19 New Members (Cont from P. 19) Steven Shore, 1523 Sunnymede, South Bend, IN 4700 Keele St., North York, ON M3J IP3, 46615, USA, 20 , Grace Orzech, Queen's University, Dept. of Mathematics and Statistics, Kingston, ON K7L Manuel Valera, Dep Historia de la Medicina, 3N6, Canada,