BULLETIN CSHPM/SCHPM
May/mai 1998 Number/Ie numero 22
WHAT'S INSIDE
President's Message ...... page 3
Constitutional Changes...... page 14
Articles
Looking Back [U. D' Ambrosio] ...... , ...... page 4
Purveyor of the History of Mathematics [B. Hughes]...... page 9
The Evolution of Magnitude [G. Moore] ...... page 11
Web Review - British Museum for History of Science [G. Van Brummelen] ...... page 15
Reports
History-of-Logic Session - Baltimore [J. Dawson] ...... page 13
Ubi Conference [V . Katz] ...... page 16
Knorr Memorial Conference [L. Berggren] ...... page 17
Session on History of Mathematics - Baltimore [J. Tattersall]...... page 18
Secretary-Treasurers Report [G. Van Brummelen]...... page 19
C'anadian Society for History and Philosophy of Mathematics
Societe canadienne d'histoire et de philosophie des mathematiques
ISSN 0835-5924 ABOUT THE SOCIETY BSHMII
Founded in 1974, the Canadian Society for the Preliminary planning is under way for the History and Philosophy of Mathematics / Societe second joint meeting of the CSHPM and its canadienne d'histoire et de philosophie des sister society the British Society for the mathematiques (CSHPM /SCHPM) promotes research and teaching in the history and philosophy History of Mathematics (BSHM). The first of mathematics. The Society's officers are: such meeting was hosted by the British side, with much panache, at Oxford last July. President: Robert Thomas, Department of Applied Mathematics, University of Manitoba, Winnipeg, Jim Tattersall, who has taken the lead in MB R3T 2N2, Canada, advance planning for the reunion, has
Israel Kleiner, Department of Mathematics and Craig Fraser, who is based at the IHPST, has Statistics, York University, 4700 Keele Street, no bly volunteered to look after local North York, ON M3J IP3, Canada, arrangements if the present proposal goes
2 A message from the President language! It is useful for us to be represented at HSSFC's annual meeting, and it is essential that organizations come to it or it can't happen. I want, Robert Thomas however, to propose a change from the present (and past) custom of our President's going to that My actions as president since I wrote in the last meeting, at some expense, to the policy adopted by Bulletin have been rather limited. I have a number of other organizations, which is to persuaded Len Berggren to step in as a new appoint as representative someone who lives in Nominating Committee, and he has done a fme job Ottawa (or at the most distant Kingston or of lining up folks to stand for the new two-year Montreal). It is little trouble and expense for such terms (at least I hope that with all this warning the a person to attend the meeting. The latter includes terms can be two years long). I have represented a rather good banquet -- adequate recompense for the Society at the annual meeting of the a local representative (along with whatever may be Humanities and Social Sciences Federation of of interest in the meeting itself). This year my Canada in Ottawa at the end ofNovember - more travel cost the Federation, the Society, and me on that in the next paragraph. And I have watched about a hundred dollars each. I think that this is as other members of the Society have done their unnecessary. I shall put this proposal before our jobs, Sharon and Hardy putting out the Bulletin Executive at the May meeting. together while apart, Glen coping with our fmancial affairs while banking out of the country, It is a great pleasure to see this Bulletin Jim organizing our joint meeting with the British blossoming, under the content editorship of Hardy Society in 1999, Fran Abeles organizing the and technical editorship of Sharon, into as good a special session on late-nineteenth-century newsletter as we have ever had. mathematics for the May meeting in Ottawa, Glen putting together the rest of the program for that As historians and philosophers you have an interest occasion, and Ed Cohen making the local in how the world turns. You may therefore be a arrangements. (Ed recently had a stint in hospital; little interested that the department that I have been I'm glad to report that he's doing fine.) acting head and then head of for the last four calendar years is ceasing to exist at the end of my I want to say a bit about the HSSFC and its annual term, June 30. The Department of Applied meeting. Belonging to HSSFC costs us something. Mathematics, created in April, 1974, will be rolled It is well worth it. Not only are we supporting a into the Department of Ivlathematics, whose new very useful lobby group that speaks for the name is not yet decided. I am hoping to recuperate humanities and social sciences in Ottawa and is from my administrative labours next year at listened to, but also we can call upon its good Wolfson College, Oxford. offices in our own dealings with the Social Sciences and Humanities Research Council, a body We have a second joint meeting with the BSHM to that they are adept at dealing with and that both look forward to, beyond our Ottawa meeting this Glen and I have found impossible to deal with May. The BSHM session is tentatively scheduled directly as an unimportant client of a large faceless for July '99, in Toronto (see news item on page 2 bureaucracy. Last year we had our cut-off funding above). The Executive Council has considered the restored. This past fall there seemed to be a real advisability of our also meeting in Mayor June danger that our travel grants would not be next year, as usual -- our regular participation in forthcoming this year. The results of my inquiries the annual "Congress of the Social Sciences and about this at SSHRC were totally Humanities" (the new name for the old "Learned incomprehensible. We handed the matter over to Societies Conference"). The '99 Congress will be HSSFC, and were told that the grants would be in Lennoxville/Sherbrooke, Quebec -- perhaps not coming. It was as though I hadn't spoken the right (See President page 14)
3 LOOKING BACK...
Ubiratan D'Ambrosio
A special conference at the joint AMS-MAA meetings in Baltimore in January celebrated the 65th birthday oflongtime CSHPM member Ubiratan D'Ambrosio; a report on that conference appears on page 16 below. To further mark the occasion, the Bulletin invited "Ubi" to set down some reflections on his career and his philosophy. The photo shows him and his wife Maria relaxing at a resort near their home in Slio Paolo.
THE FORMATIVE YEARS
I begin by relating an experience which led me to student card. It was the only forgery in my life! an obsessive pursuit of peace. And it was worthwhile. For some time I could not sleep. I was afraid of the possible consequences of Brazil entered WWII in 1942, joining the Allied my forgery, but most shocked about the scenes I Forces. War was something remote to us in Brazil. had witnessed. If what was shown were the acts of Newspapers and radios would report on the events, the legally established government of a nation with but everyday life was practically normal for us. the highest standards of civilization, how would I When the war in Europe ended, some cinemas classify my act? Soon after that, I went to see the announced movies about the concentration camps. movie showing the" glorious" drop of the atomic The movies were restricted to people younger than bomb on Hiroshima and Nagasaki. Vlhile the first 14. I was so curious that I forged my age on my of these brutalities was dealt with by the
4 Nuremberg tribunal, the second was reacted with Jaures P. Cecconi, a distinguished Italian analyst, Congressional Medals and honors. The relations of former student of Leonida Tonelli, working in morality, legality and rationality became my main Area Theory and Calculus of V ariations. Cecconi intellectual concern. had been hired, together with two other Italian mathematicians, Achille Bassi and Ubaldo Later I joined civil rights struggles, environmental Richard, to build up a mathematics department in action groups and the Pugwash movement. I am Sao Carlos. convinced that we can pursue peace only if we regard it in its many dimensions: military peace, Cecconi gave me the choice of what direction of environmental peace, social peace and inner research to follow, but it was wiser for me to work peace. with him. And soon I was diverting the focus of my research to Real Analysis, focused on Area I was also much marked by my professional Theory and Calculus of Variations. lowe much to in.itiation. r-T1y father, who was a math teacher, used Cecconi. For him, teaching was as importa.'1t as to tutor groups of students preparing to take research. He taught freshman calculus. Indeed, it examinations for admission to the public was a rigorous course in Real Analysis, in the line administration. It was mainly Finance of Severi and Tonelli. As his Assistant, I was Mathematics. Soon, while 15 years old, I was supposed to attend his lectures and complete and given the responsibility of conducting a few classes elucidate details of the proofs, do problems and on my own. I still remember how much I enjoyed exercises with the students, and occasionally this experience and how well those students, much conduct classes. Later I realized that he saw this as older than their adolescent teacher, reacted to my a mission of the advisor: to prepare the student to classes. After 50 years of professional life, my style be a professor. And to be a human being in the is practically the same, learned from my father. I totality of our actions. Everything is related: was not then a "Mathematics Educator". I was a research, teaching, professional life, family life, math teacher, seemingly a good one. I would citizenship. I was fortunate to have Cecconi as a become what is academically identified as a mentor. Mathematics Educator only in the early seventies. In an academic career, research was -- and After this initiation, I went to the Faculty of continues to be -- very important. I had to complete Sciences at the University of Sao Paulo for a my doctoral thesis in five years in order to get degree in Mathematics. In 1954 I completed a tenure. There were no courses to follow. What are major in Mathematics and was certified to teach in considered the basic courses in the usual graduate public schools. At that time there were no formal programs we had to read on our own, to organize graduate programs in Brazil. The model was seminars and, of course, the professors were European and the doctorate was granted upon the always available. Among the required books, I completion of a thesis. Research was the focus. remember Saks, Caratheodory, van der Waerden, Soon after g,laduation I engaged in a research Hausdorff, Bw.ach, and several volumes of seminar in Number Theory. The influence of Bourbaki, as having excited me most. This is the Andre Weil was still prevailing in the University of right feeling when you belong to a group doing Sao Paulo and my theme was Class Field Theory. mathematics and not merely listening to lectures. In this period I published a couple of papers. I was We read much more than what is required in the struggling with Chevalley's and Weil's seminal usual graduate programs. And the research area papers when a tenure-track position opened at the was always present, from the beginning. Cecconi new campus at Sao Carlos, about 200 miles north thought that the approaches of L.C. Young of Sao Paulo. In those days such an appointment (generalized surfaces / distributions) and of H. was as an Assistant to a Full Professor, in the Federer and W.H. Fleming (currents) might be European style. This position was as Assistant to combined with the R. Cacciopoli and Ennio De
5 Giorgi techniques of Measures and Finite principle and to formulate what I called "dynamical Perimeter. But he felt that to deal significantly with systems with memory" . I needed to study these modern ideas, it was important to understand non-associative actions. What I could see on the classics. And the list of papers to read was non-associative structures were only quasi-groups, substantially increased by adding works of loops and some Grassmannian structures. I did not classical Area and Measure Theory (mainly H. advance much in the study of the dynamical Lebesgue) and of classical direct methods in systems with memory, but my interest in the Calculus of Variations (D. Hilbert and mainly L. philosophical, historical, religious and Tonelli) and the seminal works of Jesse Douglas, psychoanalytical dimensions of time remains. L. Cesari and C.B. Morrey, Jf. Later my thesis These led me naturally to look into Systems, subject focused on semicontinuity theorems in the Complexity and Chaos. My deeper involvement calculus of variations. This was a good research with the History of Mathematics dates from these program. times. I was interested in the generation of mathematical ideas: which factors are involved in BROADENING MY VIEWS OF SOCIETY, the beginnings of mathematical theories, and also OF THE WORLD AND OF MATHEMATICS how these ideas are intellectually organized (epistemology) and how they are appropriated by In 1963, upon completion of my doctorate, I went the establishment and diffused through the media to Brown University to work with W.H. Fleming. and school systems. Once again, my mentor was exempla.ry. I am so hldebted to hhn as a model of the highest academic In 1968 I accepted a permanent position at the standards. As a teacher and a researcher and for his State University of New York at Buffalo. The human qualities, Fleming was very influential in SUNY system had been founded a few years my life. The stay in Brown \-vas rewarding. The before as a very modern university. The Buffalo intellectual and friendly atmosphere in that campus was mainly a graduate center and its focus relatively small department was something I would was interdisciplinary research. The main strengths not see in other places. In Brown I was fortunate to of the university were focused on the emerging learn from Wendell Fleming, Herbert Federer, fields of Molecular Biology, Computational John Wermer, Ennio De Giorgi (who was visiting Linguistic and Computer Music. I benefitted much while I was there) and from the younger from relations with John Eccles, Charles generation, Fred Almgren, William Ziemer, John Waddington, James F. Danielli, Lukas Foss, David Brothers, Yuji Ito and many others. I also met on Hays and many others. My ideas on systems with several occasions L.C. Young and L. Cesari., I memory did not sound so strange in that became familiar with the work of Hassler Whitney. environment. I became Director of a Master's While my research was focused in Geometric Program in the Natural Sciences. It was essentially Measure Theory, I used to benefit also from what an interdisciplinarian program, something new in was going on in the Department of Applied the USA. This was the beginning of my interest in Mathematics and my interest began to broaden to interdisciplinarity, which would eventually lead to include Singularities and Dynamical Systems. Transdisciplinarity .
There I attended the seminars of Rene Thom. But another aspect of my stay in Buffalo would These were the early days of Catastrophe Theory mark me very strongly. The sixties were marked by and I focused my interest on non-linearity. My the protests against the Vietnam War, the struggle feeling was that it would be difficult to deal with against the dictatorships in Latin America, the non-linear phenomena with the instruments of intensification of civil rights movements, the Analysis based on time as an associative structure. effects of the 1968 student rebellion in Paris and My idea was to remove associativity. This led me the sit-ins. I got much involved with all these to some works of Hadamard on Huyghens' social struggles. Only by chance did I not spend a
6 night in jail after a sit-in at the President's Office slave trader! But I was received as a fellow human in SUNYAB. being. I learned of a deep sense of humanity, joy of life and hope. I was soon appointed Graduate Chairman in the Department of Mathematics. As such, I received A good feature of the program was the encounter one morning a call from the high administration of of visiting professors from different countries of the University telling me that among the Ph.D. the world and of different disciplines. It was a candidates, 25% should be blacks. Simply that. multinational interdisciplinary task force. I, like The graduate enrolment was then 60. It was not many of my colleagues, soon developed an interest easy to find 15 qualified black candidates. To in learning about African culture. As a consultant fulfill the quota, I decided to do an aggressive for UNESCO, I was given the opportunity of recruitment, and this put me in touch with the visiting most African countries and of participating reality of racial discrimination in American society. in several scientific events in the region. What one knows through the media does not reveal the deep issues and the historical contradictions in This allowed me to understand many moments of the development of the economic strength of that African history, such as the influence of the country. Kingdom of Mali in the European economy of the Middle Ages, the learning center established in In this same period I was invited by UNESCO to Timbuktu, the visions of man and the universe in join a doctoral program in Africa, devised by a the Dogon tradition, the epics of Sundyata, the Congolese poet, Tchicaya U'Tamsi. The program religious architecture in Mopti and Dejne, the saga was to take place in Bamako, Mali. It was a very of the great heroes of the resistance to the innovative graduate program in situ, in which colonizer, whose names were -- and continued to professors would go to Bamako three or four times be - unmentioned in history, while colonial a year, for two or three weeks, for intensive work governors still give names to the modem avenues with the advisees, conducting seminars and and plazas in these countries. The effects of the proposing books and papers that the students colonial period are felt in the struggle to free the would read on their own. The regular returns of the countries of post-colonial control. advisors would guarantee a good research atmosphere in Bamako. Indeed, it was so and the I had a' beautiful encounter and friendship with an program, which lasted 10 years, was successful. important African young intellectual, Bakary Traore, who was my first and favorite student. This I was visiting Africa for the first time and I was privileged mathematical mind and patriot, deeply able to corroborate my impressions of the involved in the struggle of his people, was brutally uncivilizing mission of the colonial model and of murdered in the revolution of 1991 in Mali. This is the inhumanity of slavery. Of course, colonization an example of the contradictions of the "civilizing" and slavery go together, they are partners in mission imposed on Africa and other regions of the bringing evil to mankind. I often refer to genocide, worid by colonialism. exclusion and economical inequities, but the cultural deprivation of colonized and enslaved In 1972 I returned to Brazil to be the Director of populations deserves equal condemnation. The the Institute of Mathematics, Statistics and exclusion of people in their own countries, so Computer Science (IMECC) of the recently common nowadays, is a consequence of founded State University of Campinas colonization and slavery. In Africa I had some of (UNICAMP). There I was a Professor of my most beautiful human experiences. Most Mathematics, Director of the Institute and amazing in my first contact with Africans, I was Pro-Rector for University Development. The received with no rancor. After all, my lMECC became one of the most important research great-great-great-grandfather might have been a institutions in Latin America.
7 I remained there until my retirement, in 1993, project in Africa was still active and this gave me when I received the title of Emeritus Professor of the opportunity for a comparative study of Mathematics. At the same time, I continued my civilizations and the effects of colonialism. From own research projects in Mathematics and directed these two projects, in Africa and Latin America, others. Simultaneously, I began to engage in grew my broader sense of Mathematics and of educational projects. My interests in Mathematics History of Mathematics, which culminated in Education come from this period. Ethnomathematics.
In the seventies there was a great effort to In 1982, I returned to UNICAMP to be Pro-Rector modernize Science and Mathematics Education in for University Development, something equivalent Latin America. In 1973 I was invited to direct a to a Vice-President for Academic Affairs. It was a major research project on New Trends in Science good experience. I was very involved with several and Mathematics Education, sponsored by the aspects of higher education, such as recognizing Brazilian Ministry of Education and the and supporting emergent projects and programs. I Organization of American States. This was a got involved with prospectives and this was the multimillion-dollar project which had two strands: start of my interest in Studies of the Future. the development of a new curriculum for Mathematics Education for grades 4-8 and the In 1988 I was invited to be the Coordinator of the launching of a Graduate Program in Mathematics Research Institutes of the Secretary of Health of and Science Education. Research Associates and the State of Sao Paulo. This was an entirely new students from all over Br::l7il and Latin America area for me. I had developed some interest in were involved in these projects. We had enough Mathematical Biology while at SUNY at Buffalo, funds to invite people like Hassler Whitney, who and indeed played an active role in founding the would go to Campinas every year for about ten Sociedad Latinoamericanade Biomatematica in the years. late seventies. Even so, to direct institutes doing research in molecular biology, organ transplants, We also had the visit of Seymour Papert and epidemiology, and several other areas on the Marvin Minsky, who came together to Campinas frontier of medical research, and which had at the with the project of finalizing their work on Logo. same time the responsibility of attending to the And we had several other visitors from the USA, population, was a major challenge. Canada, Europe, Japan and other countries. I see my effort to acquire background to run these Soon I realized that to deal with the health projects as my in-service education as a Science problems of such an ethnically diverse population and Mathematics Educator. I learned much about as the Brazilian, I would need to support philosophy of education and about curriculum, "alternative" medicine. Its ideas were very difficult methodology, evaluation, teacher training, and to propose for acceptance by the medical cognition and learning. profession -- as hard as Ethnomathematics had been, and continues to be -- for mathematicians In 1980 I was appointed chief of the unit of and mathematics educators. But the efforts to relate Curriculum and Innovation of Educational both medicine and mathematics to popular culture Systems in Washington, D.C. As part of the project and beliefs expose similar epistemological barriers. and my functions in the headquarters of the The contacts with the medical profession, both O.A.S., I was required to visit regularly every practitioners and researchers, were very instructive coun1rj of Latin America and the Caribbean. This for me. Dealing with a child who is not learning was an excellent opportunity to corroborate the mathematics and with one who is facing death ideas on colonialism and slavery which I had entails different levels of urgency but reveals developed in my work in Africa. The UNESCO similar conflicts. (See Ubi Page 24)
8 Purveyor of the History of Mathematics: A Retrospective
Barnabas Hughes, O.F.M. Science fame, my work was published by the University of Wisconsin Press as Regiomontanus on Triangles (1967), a slight intrusion into the realm of the history of mathematics.
The opportunity arose to pursue the doctorate in history of mathematics at Stanford and it was adequately supported by grants from the Shell Oil Company. With degree in hand I began teaching at San Fernando State College, now California State University, Northridge, fall semester 1970. While my appointment has been in the Department of My history teacher, Father Florian Guest, Secondary Education, I have always taught O.F.M., always wiggled his glasses before courses in the history of mathematics for the making a pronouncement. I was a junior in a Mathematics Department. high school modeled after the typical German Gymnasium. The word came down from on The scope of my historical research has been high, "If you want to learn anything well, late Middle Ages and early Renaissance, with study its history." Yeah, sure! His advice investigations in other times out of curiosity. went sub cerebral until thirteen years later In every phase I have tried to discover how when I was teaching mathematics to high and why the person thought about school juniors. Then I remembered what he mathematics. The major influences in my had said. academic life have been the works and encouragement of Marshall Clagett, Michael First I bought a set of Heath's Euclid (three Mahoney (Princeton), Christoph Scriba volumes at $2.25 each!), next a copy ofD.E. (Hamburg), Menso Folkerts (Munich), Smith's translation of Descartes' Geometrie, Richard Rouse (UCLA), Jens H0)'IUp and then I found a copy of Karpinski's (Roskilde), and Raffaella Franci (Siena). translation of the Latin translation of al-Khwarizmi's al-Jabr. A book collector (a I chose to describe myself as a "Purveyor of very inadequate description of Sam Barchas the History of Mathematics" for a very good whose superb collection of books on and reason. As there is more to physiology than about the history of science is now at Stanford skeletons, so there is more to mathematics University) offered to buy a first edition than theory and applications. The history of (1533) of Regiomontanus' De triangulis mathematics unites these two; it needs to be omnimodis if I would translate and prepare made available to teachers, particularly in the it for publication. That I did. Thanks to secondary schools. And so I have spent much Sam's friend, William H. Stahl of Roman of my time speaking and writing about the
9 history in a way that is at once attractive to problems, all of which are solved by the and useful for the classroom teacher. From students. While the attraction of the text is October 1973 through May 1986 (except for too narrow to interest publishers, the book the eighteen months that I was on leave in has done a good job for its audience. Italy), I wrote 62 columns on the history of mathematics for The Calculator, the (nearly) Needful to say, I've enjoyed my work monthly bulletin of the Los Angeles City immensely: the challenge to trace down an Teachers of Mathematics Association, not to idea and make it understandable, the people overlook almost the same number of talks whom I've met, the students who caught fire. given at local, state, and national teachers' While I have found research to be fascinating, conferences to the present day. An occasional the selling of the history of mathematics has article or book chapter still appears. been a great joy!
In order to comply with new standards for the Publications education of prospective teachers, in 1989 the 1972 Medieval Latin Mathematical Writings in the Chairman of the Department of Mathematics University Library, Basel, A Provisional Catalogue. asked me to organize an undergraduate course California State University, Northridge (private in the history of mathematics for such printh~g). "A Note on DB 186 Sup." Scriptorium 26: 125-27. students. My initial choice of a text proved 1975 "Biographical Information on Jordanus de unfortunate for three reasons: too many Nemore To Date," Janus 62: 151-56. problems, too long, too cumbersome for an 1980 "De Regulis Generalibus: A Thirteenth-Century undergraduate text. (Katz's excellent book English Mathematical Tract on Problem Solving," Viator 11: 209-24. was not available then.) So, in the second 1982 Jordanus de Nemore: De Numeris Datis. offering of the course the next year, I University of California Press. subjected the students to handouts of what "The Medieval LatiIl Tra..'1s1ations of al=Kh\1:/arizmi's became A History of ]Vfathematics from al-Jabr," Manuscripta 26: 31-37. 1983 "Francisc3.iis 3.iid Mathematics, Part I," Archivum Problems in Mathematics. Its range is the Franciscanum Historicum 76: 98-128. mathematics ordinarily taught in secondary 1984 "Franciscans and Mathematics, Part II," schools. About two hundred pages long, it Archivum Franciscanum Historicum 77: 3-66. 1985 "De numeris misticis of John Pecham, O.F.M., A begins with the number systems of the ancient Critical Edition," Archivum Franciscanum Historicum people in the Western hemisphere including 78: 3-28. Hawaii. Thereafter the traditional topics are 1986 "Gerard of Cremona's Translation of covered, with more emphasis on Babylonian, al-Khwarizmi's al-Jabr," Mediaeval Studies 48: 211-63. Chinese, and Arabic mathematics, on the 1987 "An Early 15th -Century Algebra Codex: A development of proof in Greece, and on the Description," Historia Mathematica 14: 167-172. discoveries of the Italian abacists (really 1989 Robert of Chester's Latin Translation of algebraists), than may be found in other texts, al-Khwarizmi's al-Jabr: A New Critical Edition. Stuttgart: Franz Steiner. all useful topics in the secondary classroom. "The Arithmetical Triangle of J ordanus de N emore, " After an in-depth examination of Historia Mathematica , 16: 213-223. 17th-century mathematics that features 1990 "Learning Algebra in 14th Century Italy," in N. analytic geometry and calculus, I conclude van Deusen & A.E. Ford (eds.), Paradigms in Medieval Thought-Applications in Medieval with a sampling of what has happened since Disciplines (Lewiston, NY: Mellen Press), 1-14. the end of the 17th century. There are enough (See Hughes page 12)
10 The Evolution of Magnitude numerable and a magnitude if measurable; a multitude was potentially divisible into Gregory H. Moore discrete parts, a magnitude into continuous parts [p.1020a]. For many centuries, mathematics was the science of quantity or magnitude, which, in Aristotle's view of quantity was criticized by many older dictionaries, was defined as "what the Neo-Platonist Plotinos, who held that can be increased or decreased". Where did "there is no single genus of Quantity. Only this definition originate? It is old, since it number is Quantity, the rest (magnitudes, occurred in 1780 in Euler's Vollstandige space, time, motion) are quantities only in a Anleitung zur Algebra. But it had already secondary degree" [1992, 512]. By contrast, appeared in 1715 in George Cheyne's other ancient commentators on Aristotle , such Philosophical Principles ofReligion. as Ammonios [1991, 76] and Porphyry [1992, 111], continued to characterize quantity as Earlier, in Euclid's Elements, magnitude was what can be equal or unequal. not defined, nor was quantity. However, his It i~ lln('lp~r u,hpn thp riptln;t;l'In f""\-f rn~{Tn~t·llrL::. COIllillon t,J otions appear to be about .A...... a.u ",....".".a.."" .... "" ...... v't'..L...... l. \...1..1...... """" ...... L..I...&..l..I...... l.'-'.l..1. '-'~ ~~.LU5.1..I..l.I.'-'-\..I.'-' magnitudes; e.g. his first: things which are became "what can be increased or decreased". equal to the same thing are also equal to each In the Dictionnaire des arts et des sciences of other; and his third: if equals be subtracted 1694, this definition is not found, but quantity from equals, the remainders are equal. is defined as what can be measured or Aristotle made quantity one of his ten numbered [v.2, p.347]. However, in a later categories (basic predicates), stated that it volume of the same year, quantity is defined must consist of "parts", then divided it into as "a term of philosophy. An accident which two kinds: discrete and continuous. His two makes bodies capable of number or measure" kinds of "discrete" quantities were number [vA, p.287] -- a definition showing a strong and (surprisingly) oral communication, since Aristotelian influence. Magnitude words have short and long syllables. His ("grandeur") is not given any mathematical "'continuous" quantities were line segments, meaning. But in 1762 the Dictionnaire de surfaces, solids, time, and place. For him, I 'A cademie Franc;aise defines magnitude as what characterized quantity was that two what "is said, in Mathematics, of everything quantities are equal or unequal. By contrast, a which can be increased or decreased" [v. 1, p. quality (another of his categories) possessed 836]. by a given object "may vary ... in degree. For example, a body, if white, is called whiter just Cheyne's Philosophical Principles ofReligion now than it was" [1962, 3b]. In sum, A_ristotle (1 715), in its second part ("Containing the does not define magnitude or quantity as what Nature and Kinds of Infinites, their can be increased or decreased. Arithmetick and Uses, and the Philosophick Principles of Reveal'd Religion") is the In the Metaphysics, Aristotle gave a somewhat earliest source we have found that adopts the different treatment of quantity, defining it as increase/decrease definition: "QUANTITY is nTh~t i~ r1;v;~;hlp lntl'l "h"lTI'I I'Ir lTIl'lrp n~rt~ A what may be encreas'd or diminished. Tho' VV~.I."""1. ~u ,--,"..1.V.l..U..1.I.J.l."" .... .I..L"''-' ",;tv,", '-'.l...... a. .... ""' .... "" 1:-' ...... , • ..L quantity was said to be a multitude if this Definition may not exhaust the
11 Metaphysical Nature of Quantity; yet it points References out that Quality in it, that is here chiefly regarded" [Part II, 1]. By the way he presents Ammonios 1991: On Aristotle's Categories this definition, it is unlikely he originated it. (London: Duckworth). Aristotle 1962: Categories (Cambridge, MA: Harvard Although Dr. Johnson's famous dictionary University Press). Plotinos 1992: The Enneads (1764) cited Milton as an example of (New York: Larson). Porphyry 1992: On magnitude in the sense of "grandeur", and Aristotle's Categories (Ithaca: Cornell cited Newton for magnitude as "comparative University Press). bulk", it cited Cheyne for quantity as what "can be increased or decreased". Already in Gregory H Moore (ghmoore@mcmail. CIS 1728, Ephraim Chambers' Cyclopaedia: or an McMaster. CA) is currently editing volume 5 Universal Dictionary of Arts and Sciences ofRussell's papers (1906-08) and preparing a adopted a defInition of quantity that is close to source book on the infinite in mathematics, Cheyne's: "any thing capable of Estimation, or physics and philosophy. Mensuration; or, which being compared with another thing of the same kind, may be said to Hughes (Cont.from page 10) be greater, or less, than; equal, or unequal to, it" [1728, 934]. Yet he then all but reversed 1994 "Problem-Solving by Ajjub I-Basri, An Early himself by adding: "Quantity is a general Algebraist," J for the History ofArabic Science 10: Attribute, apply'd in a very different Manner 31-39. 1995 "Indian Roots for Latin Problems?" Ganita to things of very different Nature; whence it is Bharati (Bulletin of the Indian Society for the History impossible to give any universal DefInition of Mathematics) 17: 1-9. thereof." Nevertheless, he regarded mathe 1996 "The Earliest Correct Algebraic Solutions of matics as the science of quantity. Cheyne's Cubic Equations", in Ronald Calinger (ed.), Vita Mathematica Historical Research and Integration with general defInition of magnitude lasted in Teaching. Notes No. 40 of the Mathematical textbooks until the 20th century. Thus G. A. Association of America. Wentworth's College Algebra stated: "Arabic Algebra. Victi.m of Religious and Intellectual "Whatever admits of increase or decrease is Animus," in Menso Folkerts (ed.), Mathematische Probleme im Miltelalter: Der lateinische und called a magnitude. Every magnitude must arabische Sprachbereich (Wiesbaden: Harrassowitz therefore admit of comparison with another Verlag),197-220 .
...... nrT....,,~+"r1.a r"\.++ha C"In~.o. 1r; ...... rl ; ...... l"'I,'~h n '''1:71''''\''1:7 nn llla5.ulLUU.\.- Vl L.ll\.- ,:)CUll\.- ..l\..lllU. III ,:)U\.-ll a vvay a':) 1997 "tv1athematics and Geometry," in F.A.C. ivlantello to determine whether the fIrst is greater than, & A.G. Rigg (eds.), Medieval Latin (Catholic less than, or equal to the other" [1902, 1]. University of America Press), 348-354 "Intellectual Mathematical Activity in the Thirteenth Century," in Nancy Van Deusen (ed.), The Intellectual It is a poignant historical irony that, when Climate ofthe Early University -- Essays in Honor of "magnitude" was made precise in the late 19th Otto Grundler (Kalamazoo: Western Michigan century, the basis of that concept was University), 73-lO0. 1998 "J ordanus de N emore's Theory of Figurate Aristotle's: what can be equal or unequal. Yet Numbers: an historico-mathematical analysis of two the mathematicians who made it precise - books from De Elementis Arithmetic Artis with Otto Stolz and Rodolfo Bettazzi - did not Implications for Learning" (in preparation). credit the idea to Aristotle, but to Hermann Grassmann.
12 HISTORY-OF-LOGIC SESSION IN BALTIMORE
John Dawson of the well- ordering theorem in a theorem A special session on the history of that correlates well-orderings with injective mathematical logic, organized by John W. mappings from the power set of a set X into X Dawson, Jr. of Penn State University, was itself. The morning session concluded with held January 7 in Baltimore, Maryland, as part Professor van Dalen's survey of the role of the joint annual meeting of the American Abraham Fraenkel played in expounding Mathematical Society and the Mathematical L.E.J. Brouwer's doctrine of intuitionism. The Association of America. Speakers in the talk was based upon the speaker's study of the morning half of the session were Professors correspondence between the two men that is Wim Ruitenburg of Marquette University, preserved in the Brouwer Archive. Jean Larson of the University of Florida, Akihiro Kanamori of Boston University, and The afternoon session featured talks by Dirk van Dalen of the University of Utrecht. Professors Wilfried Sieg of Carnegie Mellon Professor Anil N erode of Cornell was also University, John Corcoran of the State scheduled to speak, but withdrew at the last University of New York at Buffalo, and moment on account of illness. Gregory H. Moore of McMaster University. Professor Sieg analyzed the consistency Professor Ruitenburg spoke on the relatively proofs that Hilbert gave in his lecture courses sudden appearance, during the years prior to at Goettingen during the years 1917- 1923; 1914, of several non- classical approaches to details are preserved in Hilbert's unpublished the foundations of mathematics, including notes for those lectures, wrtich are preserved intuitionism. Professor Larson then engaged in his Nachlass. Next, Professor Corcoran the audience members in a participatory delineated various senses in which logic may L:>"U'"..-.L-, .... ,..,+~r.~ r.+ +h.,.~r '=lI1",..,r!.,.'t"'I-"\~1" rr..r..t" T;tl.,.r! hop rplY'=lIrr!pr! ,..,,, 't"'I-"\'=lIthp't"'I-"\~+;I""" 1 ~ ..... r! aV",.., ...... ~ ..... ar! \.JAP.lV.lc.l.l..LV.l.l V.L \,.1.1.\.d1. u."""u.u,,",,1.1.1.1.,,",, 1. VV \,.oJ. .L 1.\,.1."",,U v"",, 1. """5u.l. u"""u u.oJ 1.1.1.U\,.1.1."",,1.1.1.(.I.\,.1.,,",,U1., u.l.1.U "",,Au.l..l1.1.1.1.\.JU "Set-theory genealogy", her talk presented the extent to which, in those senses, Aristotle preliminary reconstructions of the academic might be regarded as a mathematical logician. family trees of numerous prominent logicians, Finally, Professor Moore surveyed the history with special emphasis on the descendants of the notion of infinitesimals, from attempts (under the doctoral advisor/student relation) of to treat the problem of hom angles to Alfred Tarski and Alonzo Church. Abraham Robinson's development of nonstandard analysis. pJ. focal point of his Professor Kanamori gave an overview of his presentation was Cantor's vehement paper "The Mathematical Import of Zermelo's opposition to the idea of infinitesimal Well-ordering Theorem", recently published quantities, despite his development of the in the Bulietin of Symboiic Logic; in it he theory of infinite magnitudes. stressed the importance (and belated recognition) of the distinction between set Much to the organizer's gratification, both the inclusion and set membership and isolated the morning and afternoon sessions were very guiding principle underlying Zermelo's proofs well attended.
13 CONSTITUTIONAL CHANGES President's Message (Cont. from page 3)
The following changes in the Society's the ideal location in terms of access or adventure; constitution were recommended by the I suspect that a meeting there of our Society, with executive a year ago but did not reach the another scheduled six weeks later, would not be membership in time to be voted on at the 1997 well attended. I have preferred therefore to skip the Congress for that year and to combine our own Annual Meeting; they will therefore be voted annual meeting with the BSHM session, and the on at this year's Annual Meeting in Ottawa. Executive has now formally endorsed this idea. For rationales one may consult the President's message in Bulletin issue 20, May 1997. A I am not aware of other pressing issues for me to copy of the present version of the constitution remark on at this time. I am looking forward to can be obtained from the Secretary, Glen Van seeing many of you in May and hoping that we can Brummelen, Department of Mathematics and have some way of knowing how to keep (or get) in Statistics, Simon Fraser University, Burnaby, touch with one another while we are there. I am B.C. V5A 1S6 (Canada),
De plus, les changements suivantes au version Fred Rickey will continue on Council for another franc;aise des reglements ont ete recommandes par year if the Ottawa meeting ratifies the appropriate Jacques Lefebvre: constitutional change (see page 14). A ballot accompanies this issue of the Bulletin; Article III, Section I: remplacer "et" par "ou". please return yours to Sharon Kunoffby May 25 at Article III, Section 3: " ... aux membres au moins the address on the bailot. trente jours ... ". Article IV, Section 3: remplacer "communiquer" par "communiquee". BOOK REISSUED Article IV, Section 4: " ... L'election de leurs Good news for admirers of A Mathematical successeurs, et les membres du Conseil sont elus History of the Golden Number by iong-time pour une periode de deux ans ou jusqu 'a I' election Society member (and former Bulletin editor) Roger de leurs successeurs. Les membres du Conseil Herz-Fischler. Roger's book has been reissued by Dover Publications (ISBN 0-486-40007-7; $14.95 executif ... ". , Article VI, remplacer "Finance" par "Finances". . U.S., $20.95 Cdn). I
14 Web Review real experience. Those four special exhibits contain roughly one hundred images each, and each image Web Site of the Semester: appears in three sizes: a small one for browsers British Museum for History of (human ones, that is), and two larger ones for those Science, Oxford who wish a closer look. Detailed text for most of http://www .mhs.ox.ac. uk the images allow one to learn as much or as little as one pleases. It's not quite the same as being in the same room as the world's only remaining intact Glen Van Brummelen spherical astrolabe, but it's a much shorter walk to get there! For me one of the highlights of the CSHPM's joint meeting with the British Society for History of Three of the four special exhibits are of special Mathematics last summer was a visit to the British interest to the history of mathematics: "The Museum for History of Science, just a few blocks Measurers: A Flemish Image of Mathematics in the away from our quarters at Oriel College. Our tour 16th Century", "The Geometry of War, 1500- ieader gave us a detaiied and informative 1750", and "Images of Tycho Brahe". The fIrst exposition, at least for the fIrst half. Then he lost at two are virtual siblings, emphasizing the role of least one member of his entourage when he swept practical mathematics in the development of past the real reason for my visit: the world's largest mathematics and science. Thus we are treated to atl collection of astrolabes. I wandered among the impressive array of mathematical instruments and roughly 70 Islamic and European astrolabes until treatises for gunnery and rangefInding, surveying, the last possible minute, when I had to hurry back gauging, and measuring commercial products, and to the conference for the next talk. I vaguely heard so on. Extended and well-informed essays argue rumours of other special exhibits of great interest that the mathematics lying between theory, as in the museum, but I had found my home and taught in history of mathematics texts and wasn't about to leave. practice, as found in daily and military lif~, may have played a larger role in the shaping of modem Fortunately, when I returned to Canada I was able mathematics than it is usually given credit fOf. The to extend my all-too-short visit to the Museum to Tycho Brahe exhibit revolves around a those 'other exhibits, at least virtually. The MHS 19th-century painting of Brahe demonstrating a was one of the fIrst museums to try to use the celestial globe to Emperor Rudolph II. It uses this Internet to extend their audience (over two years and other surviving images of Brahe to compare ago!), and to my pleasure I found that the },.1HS's the public images of historical scientists -with four major special exhibits over the past two years reality. The non-linear structure of this exhibit is live on, at least as fIles of image and text, stored on well captured in its virtual version. (The fourth the Web. My addiction to astrolabes had not exhibit, on the history of camera technology, may entirely cost me the experience of the rest of the end up as a self-referential display within itself, as museum. it were, in a few decades.) A museum on the Internet might seem like a A lunchtime visit to the MRS is not on the cards contradiction in terms. A museum is intended to for most of us, but a visit to the Web site is a good bring history, culture, and other aspects of our substitute. Spend as much or as little time as you world to us face to face. Can you really wander like, and be sure to dig a little to explore some of from artifact to artifact, browse through exhibits, the breathtaking images; include a few astrolabes. and get a good close look at, say, an astrolabe, It's a pleasant educational experience that intrigues while sitting with a mouse in one hand, staring at the casual visitor and satisfIes the expert, and that a ten-inch-square monitor? Simply put, you can't. is after all the hallmark of a great museum. But the MHS does get you surprisingly close to the
15 Glen will give perhaps the first-ever academic going strong at age 103, who spoke on talk actually presented solely through the "Ethnomathematics at the Beginning". Internet, to the ICMI Study Group on the Among the other speakers were Bill Barton history of mathematics, in April, in Luminy, (New Zealand), "The Philosophical France. Appropriately enough, the talk is Background to D'Ambrosio's Conception of entitled "Resources for the History of Ethno- mathematics"; Gelsa Knijnik (Brazil), Mathematics on the World Wide Web ", and "Ethnomathematics, the Politics of this method of presentation is meant to Knowledge, and Postmodernism"; Marcia illustrate first-hand both the available Ascher (Ithaca College), "Mongolian Board resources of the new medium and its Games"; Claudia Zaslavsky (New York), possibilities and shortcomings. Participants "Ethnomathematics in Alaska and Peace in will use Web browsers to experience the the World"; Paulus Gerdes (Mozambique), presentation, and will engage in discussion "Ubiratan D'Ambrosio and Ethnomathemat (technology permitting) with Glen - who will cal Research in Mozambique"; John Fauvel be in Vancouver, Canada. (UK), "The Role of the History of Mathematics in Building a Democratic and Just Society"; and Reuben Hersh (New CSllPM members will be able to see the Mexico), "The Secret About the Hungarian presentation, when it is completed, at http: Mathematics Miracle". Other speakers Ilwww.kingsu.ab.cal--gJeniluminyltitle.htm included Diana Coben, Larry D'Antonio, Walter Sizer, Rebecca Berg, Nkechi Agwu, Alejandro Garciadiego, Helena Pycior, UBI CONFERENCE Marilyn Frankenstein, Beatrice Lumpkin, Gloria Gilmer, Swapna Mukhopadhyay, Jose Victor Katz Segarra, Munir Fasheh, and Arthur Powell.
Over eighty people from countries all around At the festive birthday dinner in the evening, the world gathered at the Ornni Hotel in Jeremy Kilpatrick, Vice-President of the Baltimore on January 6 to honor long-time International Commission on Mathematical CSHPM member Ubiratan D'Ambrosio on his Instruction, gave the toast and brought 65th birthday. Some twenty-five speakers greetings from ICML Kilpatrick, Alvin dealt with issues related to Ubi's work in White, and Martin Hoffman also made Ethnomathematics, the History of remarks during dinner. After he blew out the Mathematics, and Mathematics and the candles on his birthday cake and the guests Search for Justice. It was clear from the talks sang the requisite "Happy Birthday", Ubi that Ubi has had both a broad and a deep himself spoke m.ovingly on how he felt about influence on mathematics education, since the the gathering and about his long career in range of topics, each of which was related to mathematics education. The program of the his work, was so wide. conference was organized by Marilyn Frankenstein, Gloria Gilmer, Arthur Powell, One of the speakers was Dirk Struik, still and Victor J. Katz.
16 WILBUR KNORR MEMORIAL CONFERENCE AT STANFORD
Len Berggren' The talk centered on the models of planetary motion by means of homocentric spheres A conference was held at Stanford University from developed by Eudoxus and modified by Callipus of March 12 to March 14 to honor the memory of Cyzicus. An impressive display of these models by Wilbur Knorr, whose sudden death from a means of modern computer animations showed the melanoma early last year shocked his many friends kind of insight modern computing technology and colleagues in the history-of-mathematics could provide into the models and, consequently, community. The meeting was generously funded the possible reasons for their rejection. by the School of Humanities and Sciences and by the Departments of Classics, of Philosophy and of Saturday, March 14 History and Philosophy of Science. The organizers of the conference were three long-time friends David Nivison (Stanford University) "The Key to of Wilbur's: Professors Henry Mendell the Chronology of the Three Dynasties: the (Department of Philosophy at Cal State University, 'modern text' Bamboo Annals" Los Angeles) and Julius Moravcsik and Patrick The speaker presented the results of two decades of Suppes (Philosophy Department, Stanford), who his own work on these documents, which had once jointly arranged the following program of invited been labeled as forgeries, to show how modem talks: scholarly detective work, using - among other tools - astronomical records, could shed light on the Friday, March 13 early history of China. Commentator: Jeffrey Riegel David Fowler (University of Warwick) "Techniques of Fractions in Ancient Greece" J. L. Berggren (Simon Fraser University) "The The speaker followed up on what had been (at the Tradition of Analysis in Ancient Mathematics from time ofWiibur's death) an ongoing debate between Greece to tv1edieval Islam" him and Wilbur on how the historian should The speaker, reporting on work he has done jointly interpret the way Greek mathematici311S conceived with Glen van Brummelen, reviewed evidence of fractions in view of the papyrological (and from Greek mathematical and philosophical other) evidence for their representation and sources for what analysis was and how it was used, arithmetic. and he introduced new evidence from Islamic writers of the tenth and eleventh centuries to show Charles Burnett (Warburg Institute) "The how the role of analysis had changed during allnost Coherence of the Arab-Latin Translation Program one and a half millennia. in Twelfth Century Toledo" The focus of the talk was the translation activity of Judith V. Grabiner (Pitzer College) "Maclaurin Gerard of Cremona and a few others associated Among the Molasses Barrels: Archimedean with the Frankish hierarchy of the cathedral in Geometry Meets the Modem State" Toledo in the twelfth century, and the speaker The speaker presented some beautiful argued that there was both an internal coherence mathematical results on frustra of conoids of and a rationale for Gerard's more than seventy revolution from a memoir of Colin Maclaurin on translations. gauging the contents of molasses barrels, written around 1735, and then examined the social and Henry Mendell (Cal. State U., L.A.) "The Trouble economic reasons behind the production of this with Eudoxus" mathematical work.
17 Although only one of the talks had an official After the conclusion of the conference on Saturday commentator the whole audience gladly took on afternoon the West Coast Aristotelian Society met that role for all of the talks, and the two hours to discuss Aristotle's Posterior Analytics B6, and allotted to each talk were barely sufficient to on the following day those participants who were accommodate the lively discussion following each able to remain gathered on the Stanford Campus to of the contributions. plant a tree in Wilbur's memory in the New Guinea Garden.
SPECIAL SESSION ON HISTORY OF MATHEMATICS IN BALTIMORE
Jim Tattersall Modem State: The Case of Colin Maclaurin"; David Kullman (Miami), "Mathematics Problems Karen Parshall (Virginia) and Jim Tattersall Appearing in the Ohio Journal ofEducation"; (Providence) organized a Joint Special Session on Erwin Kreyszig (Carleton), Interrelationships History of Mathematics at the 104th Annual Between Early Topology and Analysis; Meeting of the American Mathematical Society Mark McKinzie (Wisconsin), "Euler's and the 81 st Annual Meeting of the Mathematical Factorization of the Sine Function: One Aspect of Association of American held in Baltimore, the Prehistory of the Riemann Integral"; January 7-10. Joel Goldstein (Drexel), "Some Roots of a Revolution: The Conflict Over Arithmetization in Among the speakers were; Sixteenth-, Seventeenth-, and Eighteenth-Century English Editions of Euclid's Elements Books I Through VI: 1570-1795"; Shai Simonson (Stonehill), "The Mathematics of Diann Porter (Arizona) "William Fogg Osgood at Levi ben Gershon"; Harvard"; Helena Pycior (Wisconsin-Milwaukee) "George Berkeley's Mathematical, Philosophical, and Ubi D'Ambrosio (Brazilian Society of History of Science), Mathematics in the XIX and First Half Religious Ideas: the Intersections, 1732-1735"; of the XX Century in South America"; Peter Duren (Michigan), "Continuous Nowhere (Illinois), "The Search for L.C. Differentiable Functions"; Bruce Reznick Walker", Craig Fraser (Toronto), "Adolph Kim Plotker (Brown), "Women and Mathematical Mayer's Early Work in the Calculus of Variations"; Education in India"; (The Open University), The Origin John Fauvel (The Open University), "The Robin Wilson of the Fifteen School Girls Problem". Mathematical Love Letters of Barnes Wallis"; Della Fenster (Richmond), "Leonard Eugene Dickson: One Quote, One Question - An Inextricable Link?"~ "The mathematician Euclid, working in a Rebecca A. Adams (Southern California I convention of abstractions, shows us reiations I College), "The Beginnings of General Topology"; between the distances of our unwieldy and Len Berggren (Simon Fraser), "Three cluttered-up environment upon which we are able Geometrical Jewels of AI-KuhI"; to count. A drama of Sophocles also indicates Marcia Ascher (Ithaca), Divination In relations between the various human impulses, Madagascar: A Case ofEthnomathematics"; which appear so confused and dangerous ... [N]ot Hourya Sinaceur (Centre National de la only do both Euclid and Sophocles satisfy us by Recherche Scientifique), "F ourier's Analysis of making patterns, they make much the same kind of Inequalities (1831) and Tarski's Definable Sets of patterns." Real Numbers"; 1-- Edmund Wilson Judith Grabiner (Pitzer), "Mathematics and the
18 Secretary-Treasurer's Report, 1997
Once again, the CSHPM enjoyed considerable success this year. The implementation of our cross membership arrangements with the BSHM and CSHPS produced a membership increase of 220/0, from 154 to 188. We recorded a surplus of over $1000 for the fourth year running, even though our SSHRC administrative grant was cut in half This places the Society on firm financial ground, heading into the first year in which the SSHRC administrative grant is completely eliminated.
Financial Statement (must be approved at the Annual General Meeting)
Credit Debit
SSHRC grant $669.00 Publications Membership dues $10453.81 (Bulletin, Proceedings) $2779.01 TTC"C"T.'f""' .J .. __ <1'1"\,",,",1"\1"\ Gain in US$ currency exchange $66.67 n...,...,r~ UUI;;~ -l)7L.L..VV Other (sale of Proceedings) $145.88 Historia Mathematica $4179.77 Philosophia A1athematica $1676.98 Conference expenses (keynote) $131.10 Sponsorship ofICRS '97 dues (for Canadian delegates to general assembly) $270.00 President's trip to HSSFC annual meeting $133.42 Misc. (postage, copying, bank charges, etc.) $167.43
TOTAL: $11335.36 TOTAL: $10259.71
Surplus: $1075.65 Amount carried forward (1996): $5677.70 YEAR-END BALANCE: $6753.35
Graph ofRevenues and Expenses:
Two major items in the above statement (Historia Mathematica and Philosophia Mathematica subscriptions) are "in-out" budget items, and may obscure what our dues money actually gets spent on. The graphic below illustrates the ways in which income, apart from journal subscriptions, was actually received and spent.
19 Expenses
Revenues
$0 $1,000 $2,000 $3,000 $4,000 $5,000 $6,000
Projection for 1998
Our SSHRC administrative grant shrank from $1339 to $669 in 1997, and completely vanishes in 1998. Also, we expect the conference keynote expenses for 1998 to be greater than usual, since some of the expenses for the 1997 keynote speaker were processed early in 1998. Hence, given our recent trend of $1000 surpluses, I expect that we will come close to breaking even in 1998.
1997
1996 _11111111111 ..111
1995
1994 1993._".
$0 $1,000 $2,000 $3,000 $4,000 $5,000 $6,000 $7,000
Membership Totals
Our membership totals have been increasing strongly for several years now. Our record growth in 1998 is due mostly to our cross-membership agreements with the CSHPS and BSHM, both of which took effect in 1997. The graphic below shows our recent membership history, as well as the breakdown of the number of members we received through the cross-membership arrangements. Conversely, we sent 44 members to the BSHM, and 37 members to the CSHPS.
20 1997 ...... -=====1
1996 _"I11IIIII1II.. "".". 1995 ..I11IIIII1II ..... 1994 _ ...._.
1993 ......
100 120 140 160 180 200
CSHPM members who took memberships in the CSHPS through the affiliation agreement were left off the mailing list due to some administrative problems within the CSHPS. Those problems have now been resolved, and memberships extended through 1998.
Glen Van Brummelen, Secretary-Treasurer
"PM" HOt~OURED
Philos9phia Mathematica, the CSHPM's South Africa. PM (www.amath.umanito philosophical j oumal, has been named the ba.caIPMI) is the only journal in the world 1997 runner-up for the Phoenix Award of devoted exclusively to the philosophy of the Council of Editors of Learned Journals mathematics. It was founded in 1964 at (CELl). The award was presented at the Chicago by J. Fang, who edited it through Toronto meeting of the Modem Language two series, 1964-77 and 1986-91. Series Assocation in late December and \vas III was then taken on by the present editor accepted by Israel Kleiner of the Society's and the CSHPM, and since 1992 it has Executive Council. The Phoenix Award is appeared two and then three times a year. given annually for what is officially called It is distributed world-wide (abstracted in "significant editorial achievement" but can Chinese and Russian as well as English perhaps be more precisely described (as its and French) by Wilfrid Laurier University name suggests) as improvement in an Press in Waterloo, Ontario (www.wlu.ca! existing journal. ~wwwpressl).
"PM", as it is known around the CSHPM, The CEL] (www.msu.eduluser/podlceljl) is edited in Winnipeg by Robert Thomas is an organization for editors of learned - who of course happens also to be (pro journals, all over the world but mostly in tern) the Society's President. Robert was North America. It presents awards previously the founder (in 1971) and annually in five categories: best journal managing editor of Utilitas Mathematica, design, best new journal, best special which was published at the University of issue, distinguished retiring editor, and the Manitoba until its recent migration to Phoenix Award. The singling out of Ply!
21 was the only award or runner-up prize IS InSpIrIng. N ow ensconced in a lovely conferred this year outside the U.S.A. At cover, each number impressed with its the presentation ceremony, a judge was depth and coverage". quoted as writing, in praise of PM, " The improvement manifested in the third series Congratulations, Robert!
OTTAWA MEETING
As Society members will know, the InfoEng.html, en fran9ais a www.hssfc. Annual General Meeting is to be held ca/cong/CongressInfoFr.html. from May 29 to May 31 at the University of Ottawa. Ed Cohen has generously The printed Registration Guide contains agreed to look after local arrangements, several errors, whose corrections are: and welcomes enquiries -- by phone to * The Convention Number to quote to Air 613-728-9526 or bye-mail to Canada is CV981127.
22 arrange for a group visit to one of these include a meeting with curators who will facilities. Information about a number of display some of the special treasures from tours can· be found in the Registration the Literary Manuscripts, Rare Books, Guide; the following two tours are not Music and Jacob M. Lowy collections. descri bed there: National Archives. 27 May, 9:30 to 12:00. National Library. General tour of the Special group tour of the most Reference and Information Services and state-of-the-art preservation building in the Reading Room, including a visit of the the world -- the National Archives' exhibition "Cultivating Canadian Gatineau Preservation Centre. Tour an Gardens", which traces the history of award-winning building whose purpose is gardening in Canada through published to protect Canada's documentary heritage materials. This group tour will also for the next 500 years.
REDEEMER CONFERENCE
An international conference on "Science and Vice Versa". The abstract reads in in Theistic Contexts: Cognitive part: "A deeply neglected factor in the Dimensions" will be held at the Pascal history of mathematics is the influence Centre for Advanced Studies in Faith and that religious positions or theological Science, Redeemer College, Ancaster, factors have played in the formation and Ontario from July 21 to 25. The theme is interpretation of theories. Conversely, "an analysis and evaluation of the internal mathematics has played a role in aspects role of theistic religious beliefs in the of the content of various religious natural sciences 3.ild mathematics", aLld positions. This lecture will view exarnples the conference is "intended for those with of influence in both directions, but confLne an interest in the relationship between itself largely to Christianity and to science and religious belief'. The developments since the early modem deadline for submission of papers was period." April 1. F or more information on the conference, Of par"1:icular interest to CSHPM members contact Dr. Jitse van der Meer, Redeemer will be a workshop on "Religion and College, 777 Gamer Road, Ancaster, ON Mathematics" chaired by Ivor Grattan L9K 1J4 (Canada), phone 905-648-2131, Guinness, who needs no introduction, and fax 905-648-2134, e-mail who will speak on "Manifestations of [email protected], or visit Christianity in Mathematical Theories - www.redeemer.on.calpascal.
23 UBI (Cont.) Futuro, a sort of think-tank on the state of the These two new directions of involvement, the world, at which I preside. There, together with studies of the future and of health, culminated many academic and non-academic thinkers, we in the organization of two very ambitious deal with all sort of problems affecting the events, which proved very successful. These planet. Related to this, I regularly lecture to were (1) an international conference in 1992 on groups dealing with peace, the rise of "Education for the FuturelEducation for consciousness, and educational innovation. Peace", and the founding of the "Instituto de And I am active in academic societies, Estudos do Futuro", and later on, (ii) another conferences, congresses in many places of the major international symposium on the world and I continue to write on several topics encounters and conflicts of traditional and -- much more than I publish! high-technology medical practices. In my long journey, I have realized that much My involvement with Pugwash and with the of the unhappy and disgraceful state of the "Science and Culture" forum of UNESCO world can be traced to a narrow vision of man, were also important in broadening my views of as an individual and as a social, planetary and man as a reality in itself, a social reality, a cosmic reality. Lack of an ethics of respect, planeta.ry and a cosmic reality. The solidarity and cooperation in human, dichotomies that still persist between matter individual and social behavior is a major and mind, intellectual and manual labor, space problem. This kind of moralist discourse and time, good and bad behavior became my follows naturally from a broad look into main focus of concern. I embraced studies of history -- and particularly the history of consciousness, which synthesize all this. science and mathematics, which are part of the essence of Western civilization. This is not WHERE DO I STAND NOW? HOW DO I revisionism but recognition of the mistakes SEE MYSELF? WHAT AM I DOING? and of the nonadjustment of systems of knowledge to the ideal of a planetary It is difficult to say how I place myself civilization. Of course, the ideals of a professionally. I continue to be a teacher. planetary civilization, of equity and of Now, I teach smaller groups, only occasionally solidarity are not shared by all. I have been children and mostly graduate students. I have instilling these ideals in my academic and students doing research and writing theses in pedagogical practices and in my behavior. very diverse areas, from Ethnomathematics and History of Mathematics through ABOUT THE BULLETIN Philosophy. The Bulletin is published each May and November, and is co-edited by Hardy Grant I have part-time academic appointments in ([email protected]) and Sharon graduate programs of Education (Universidade Kunoff ([email protected]). Material Regional de Blumenau), Mathematics without a byline or other attribution has been Education (Universidade Estadual Paulista / written by the editors. Les pages sont UNESP, Rio Claro), Ethnomathematics chaleureusement ouvertes aux textes soumis (Pontificia Universidade Cat6lica at en franyais. Comments and suggestions are C amp inas ) and History of Science (Pontificia welcome, and can be directed to either of the Universidade Cat6lica at Sao Paulo). There I editors; submissions should be sent to Hardy have my students working for masters degrees Grant, at the above e-mail address or by post and doctorates. to 539 Highland Avenue, Ottawa, ON K2A 2J8 (Canada). I am also active in the Instituto de Estudos do
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