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Marin Mersenne: Educator of Scientists INFORMATION TO USERS The most advanced technology has been used to photograph and reproduce this manuscript from the microhlm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI University Microfilms International A Bell & Howell Information Com pany 300 Norlfi Zeeb Road. Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9027883 Marin Mersenne: Educator of scientists Boria, Vittorio, Ph.D. The American University, 1989 Copyright ©1989 by Boria, Vittorio. All rights reserved. UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106 MARIN MERSENNE: EDUCATOR OF SCIENTISTS by Vittorio Boria ofm cap. submitted to the College of Arts in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematics Education Signature of Committee Chair: ^cL.oC Dean of t|he College 6 October 1989_________ Date 1989 The American University Washington, D.C. a n AMERICAN UNiVERSITY LIBRARY 0 COPYRIGHT by VITTORIO BORIA 1989 ALL RIGHTS RESERVED Pro Pace et Prosperitate MARIN MERSENNE; EDUCATOR OF SCIENTISTS BY Vittorio Boria ABSTRACT The teaching of mathematics in the sixteenth and early seventeenth century France was reduced to a bare minimum. Lack of enthusiasm in the teachers, lack of motivation in the students, and absence of creativity in researchers relegated mathematics to an insignificant role in education. Marin Mersenne (1588-1648), a French monk, spent about forty years promoting a greater interest in science. A scientist himself, he made contributions in music, in number theory, the study of functions, and physics. He corresponded with many scholars of his time, and motivated them to search for the solution of many specific problems. He had correspondents in France, Spain, England, Germany, Holland, Belgium, Czechoslovakia, Poland, Italy, Egypt, and Turkey. Thanks to his mediation, many scholars could communicate among themselves, sharing the results of their studies. He was able to bring scholars together at regular meetings, where scientific papers were read, national and international publications were reviewed, correspondence with ii and from the most remote corners of Europe were exchanged, experiments were designed and discussed, and quarrels among scientists were settled. Eventually such regular meetings gave birth to the French Academy of Sciences. From Italy he brought to France Torricelli's barometric experiment, which led to the discovery of the atmospheric pressure, against the established Aristotelian philosophy. As a consequence, long established principles were brought under closer scrutiny: modern science was born. Mersenne was especially able to motivate young gifted students to pursue mathematical careers. He did this by proposing to them some problems in line with their interests and their level of preparation, suggesting relevant reading material, introducing them to well known scientists, involving them in his experiments, and sharing the credit with them. By the third decade of the seventeenth century the curriculum of the schools in France was beginning to be challenged, the teaching of mathematics became a noble profession, and the sciences started to attract the attention of every educated person. For his efforts in popularizing science and involving great scholars in scientific research and publication, Mersenne today can be a model for mentors. Ill ACKNOWLEDGEMENTS It is with a heart full of gratitude to the Father, the source of all knowledge, to the Son, the Alfa and Omega, and to the Holy Spirit, the Paraclete, that I present this work. I am happy to acknowledge the contribution of my Franciscan Capuchin confreres of the St. Francis Friary, in Washington, D.C., and of the beloved Province of St. Francis, and the MISEREOR Bischoflischen E. V. for their fraternal and financial support during the past three years. I am indebted to the faculty of the Mathematics and Statistics and the Education Departments of The American University. I am very grateful to Dr. Mary Gray and Dr. David Sadker, members of my committee, for their advice, patience, and consent to serve. Dr. Steven Schot, the chair of the committee, besides being a valuable teacher in the classroom, inspired and directed the research with necessary advice. I am specially indebted to him. "Rétribuât vobis Dominus retributionem suam!" IV TABLE OF CONTENTS ABSTRACT ............................................ Ü ACKNOWLEDGEMENTS .................................. iv CHAPTER ONE. INTRODUCTION ......................... 1 Relevance of the Research................... 5 Biographical Notes ............................. 8 Description of C o n t e n t ..................... 17 Limitations .................................. 18 CHAPTER TWO. STATUS OF MATHEMATICS AND PHYSICS IN THE XVIth AND XVIIth CENTURIES AND MERSENNE'S EDUCATION .... 20 The Curriculum of Mathematics at La Flèche . 33 Education in the Order of the Minims .... 46 CHAPTER THREE. MERSENNE AND HIS CONTACTS WITH OTHER SCHOLARS ......................... 53 Mersenne's Editorial Activity ................ 58 Correspondence ............................... 91 Academies .............................123 CHAPTER FOUR. MERSENNE, THE EDUCATOR AND THE M E N T O R ....................................143 Mersenne's Scientific Methodology ............ 150 Christiaan Huygens ............................ 168 Mersenne and his Young Correspondents: an A n a l y s i s ............................. 184 CHAPTER FIVE. SOME MATHEMATICAL AND GEOMETRICAL RESULTS BY M E R S E N N E ..................................194 Mersenne's Philosophical Approach to Mathematics ..................... 195 Number T h e o r y .................................. .206 Multiply Perfect Numbers ...................... 221 The Cycloid ..................................... 226 Mersenne and the C y c l o i d ........................ 232 CONCLUSION ..................... 256 SELECTED BIBLIOGRAPHY.................................273 VI CHAPTER ONE INTRODUCTION Today the teaching of mathematics in many of the technically most advanced countries is the topic of much research. Although various studies differ on the aims and goals and the suggested recommendations regarding the problem of numeracy, all of them agree with the findings: the learning of mathematics is dangerously inefficient. Analyzing the situation in the United States, Izaak Wirszup, of the University of Chicago, says that this is "one of the earnest challenges" in the history of the country.' One of the commonly voiced complaints is that The vast majority of our high school graduates have not studied physics, chemistry, geography, or a foreign language ... they cannot even apply basic mathematics and science to simple jobs. This results in a personal tragedy of shattered hopes for countless of young Americans. It is also a national tragedy.: The situation becomes even more critical when one compares the results of tests administered to sample groups 'I. Wirzup. "Education and National Survival," Educational Leadership 41 (January 1984): 4-11. 'Ibid., 7; see B. Vobedja, "Student Improve Basic Skills, but Few Can Apply Them Well," Washington Post. 58, (February 1 1989), 2. 2 in various countries of the world. Students from American and Canadian schools often ranked much lower not only than those from Japan and from Eastern European countries, but even from some of the emerging nations such as Korea and Taiwan.: Students' and parents' attitudes about the academic achievement as well as the difference between the intended and the implemented curricula were also analyzed. It was found that on the average, students in the Western Hemisphere were less motivated than students in the other above-mentioned countries. Some of the factors that have been blamed for the present crisis are: I. The lack of competency, heavy work load, low salary, and stressful conditions of the teachers, coupled with the public's indifference to the quality and status of educators; II. The quality of the curriculum. A recent article in the Washington Post quotes a study by an "ad hoc" committee on the present situation: Math education is an enterprise rooted in antiquity, with some of today's curricula ^Besides the above mentioned study by I. Wirszup, see also Hiroshi Kida, David W. Shwalb and Barbara J. Shwalb, Evaluation in Education: An International Review Series. (London,
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