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Religious Bearings in the Development of Mathematics

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Religious Bearings in the Development of Mathematics This dissertation has been 65—3869 microfilmed exactly as received HUMBERD, Jesse David, 1921- RELIGIOUS BEARINGS IN THE DEVELOPMENT OF MATHEMATICS. The Ohio State University, Ph.D., 1964 Education, history University Microfilms, Inc., Ann Arbor, Michigan Copyright by Jesse David Humberd 1965 RELIGIOUS BEARINGS IN THE DEVELOPMENT OP MATHEMATICS DISSERTATION Presented In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of the Ohio State University By Jesse David Humberd, B.S., B.A., M*A., B.D, - 5 ;- - i s - # - j t The Ohio State University 1964 Approved by A d v ise r Department of Education ACKNOWLEDGMENTS The author wishes to express his sincere thanks and appreciation to Dr, Harold P, Fawcett, teacher and adviser, for his inspiring personality in the classroom, and for his enthusiastic support in the preparation of this study. The author was first challenged by Dr, Fawcett in 1947, when in his first graduate course, Education 687, he was challenged to read more than twenty basic works in mathematics education. From that day to the present, he has known and valued greatly the ready enthusiasm and wise counsel of this master teacher. It is with deep gratitude that the author recognizes the cooperation and encouragement of his wife, Laura, during the preparation of this study. Much of the inconvenience resulting from moving the family several times, for graduate work; and most of the extra effort at home caused by periods of the w riter’s absence, has been borne by her. And to Lenora and Margaret, (or as they would have it, Lee and Meg), the author expresses thanks for their loyalty, during what must have seemed to be most of their lives. If they ever doubted that the study would ever be completed, at least they always hoped It would be. ii VITA December 21, 1921 Bom - Roann, Indiana 1943 B.S., Bryan University, Dayton, Tenn, 1942-1945 U. S . Navy 1947 B.A., Wittenberg College, Springfield, Ohio 1947 Teacher, Springfield, Ohio 1947-1948 Instructor, Wittenberg College 1948-1951 Teacher, Miami County Schools, Ohio 1950 M.A*, The Ohio State University 1954 B.D., C-race Theological Seminary Winona Lake, Indiana 1954-1958 Assistant Professor, Grace College Winona Lake, Indiana 1958-1959 Instructor, The Ohio State University School 1959-1964 Professor, Grace College Winona Lake, Indiana FIELDS OF STUDY Major Field: Mathematics Education Mathematics Education: Professors Harold P. Fawcett, Nathan Lazar, and John Kinsella Science Education: Professors John S. Richardson and G. P. Cahoon Higher Education: Professors Everett Kircher and Earl Anderson iii CONTENTS Chapter Page I . INTRODUCTION ............................................................. 1 Background for the study Need for the study Assumptions PART I . RELIGIOUS BEARINGS IN THE DEVELOPMENT OP MATHEMATICS I I . EARLIEST TIMES TO THALES (600 B .C .) . 25 III. THE GREEK AGE 600 B.C. to A.D. 641 . 45 IV. THE MIDDLE A G E S ........................................................ 83 V. THE SEVENTEENTH CENTURY.................................... 110 V I. THE MODERN A G E ............................................................. 163 PART I I . RELIGIOUS BEARINGS IN THE CONTENT OP MATHEMATICS V II. NUMBER................................................................................. 193 V I I I . MATHEMATICS— RELATIVE OR ABSOLUTE TRUTH? 218 IX. MATHEMATICS— INVENTION OR DISCOVERY? . 236 PART I I I . RELIGIOUS BEARINGS IN THE TEACHING OP MATHEMATICS X. PRESENT PRACTICES IN THETEACHING OP MATHEMATICS................................................... 250 X I. SUGGESTED PRACTICES IN THE TEACHING OP MATHEMATICS.................................................. 263 BIBLIOGRAPHY ..................................................................................... 295 iv CHAPTER I INTRODUCTION Background for the study The object of this study is to advance the thesis that religion has been an influential force in the history and development of mathematics. A review of the literature dealing with the progress of mathematics throughout the history of man disclosed a dearth of information relating to the role which religious influences have played in that development. The w riter’s responsibility for the teaching of mathematics in a Christian institution of higher learning, and his concern for Christian education at all levels, led to this study. In a previous study, he was concerned with the place of mathematics in the education of m inisterial stu d en ts.A t that time evidence was found that mathematics could contribute to the education of the minister in several ways. Its study could provide certain tools essential to an educated man in his understanding of the quantitative aspects of life. Mathematics could assist him in developing the !j. D. Humberd, ”A Proposed Program in General Mathematics for the M inisterial Student” (unpublished Master's thesis, The Ohio State University, 1950). 1 ability to think clearly, and could contribute toward his acquaintance with the world of men and ideas, as well as with the world of nature and science. Subsequent experience has confirmed this evidence, and the writer has since that time completed theological training. He is now teaching in a Christian college in which all teachers are expected to be theologically trained, as well as academi­ cally prepared in one of the usual disciplines. Religious bearings in mathematics. There is little provision in the usual college mathematics curriculum for presentation of much of the historical and cultural back­ ground information which could enrich the study of the facts and principles of mathematics. The demands of the usual courses are such that any dilution dare not be excessive. Yet in the Christian school, there is an expressed desire and intent on the part of the faculty, and on the part of the constituency, to integrate all parts of the curriculum with the Christian philosophy under which the school o p e r a te s . Different schools operate under different sets of aims and objectives. Accrediting agencies recognize the validity of this procedure by placing as the first criter­ ion in any self-study the clearly defined statement of the purposes of the institution. All additional criteria of evaluation relate to these clearly defined purposes. The purposes of a mathematics department In a Christian school are similar to those in the mathematics department of any school. Almost everyone knows that mathematics serves very practical purposes in the market place, and in the office of the engineer. Most educated people would agree that mathematics carries the major burden of scientific reasoning, and permeates the major theories of physical science. Many are aware that mathematics has played a major role in the development of philosophy, has influenced the fine arts, and has provided models for logical thinking. Some have found in mathematics aesthetic values. In short, mathematics has been a major cultural force in civilization. But in all these aspects, mathematics is generally viewed as a secular science, devoid of religious overtones. Such a gap in the literature may be of little moment to a student studying to pass a course, or to complete the requirements for a degree. Mathematics may become merely the science of calculating correct answers from certain available data, for the one studying for a career in science and engineering. Yet even such students recognize differences between good and poor teaching, and realize that a good mathematics teacher is one who teaches in such a way that "the whole is a great deal more than the sum of its parts." It is no secret that many educated people avoid the study of mathematics as an intellectual interest* Unless forced by some external requirement to ’’take" some mathematics, most people have been satisfied to get by with a minimum of knowledge secured by the end of the first or second year of high school* It has not even been necessary for future teachers of arithmetic in elementary schools to be acquainted with mathematics beyond the minimum required for entrance into college. Many have returned to elementary classrooms after a six- or seven-year period in which they had no formal contact with mathematics. In recent years, the demand for more mathematical competency on the part of teachers at all levels has been widely made. A strong emphasis upon something called modern mathematics has aroused much comment, if not consternation, among teachers in America. Millions of dollars have been spent in a multitude of efforts to improve the mathematics curriculum, and to provide special courses of Instruction in mathematics for teachers to help them upgrade their understanding and facility. In some of these efforts, provision has been made for the inclusion of historical and cultural aspects of the background of some of the mathematical content. This has been included to increase interest, and to make more meaningful the operations and concepts presented. The writer favors such efforts, and believes that in a • Christian school, these historical and cultural contri­ butions should be joined with the religious bearings in the development of mathematics wherever practicable. There are areas in the mathematics curriculum in which such integration finds natural expression. There are many areas in which such attempts would be artificial and strained. The cultural and religious bearings of some aspect of mathematics may appeal to one teacher, and another may not judge them worth inclusion. In the usual sequence
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