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Graduate Studies Texas Tech University 77 75 G-7S 74 GRADUATE STUDIES TEXAS TECH UNIVERSITY Men and Institutions in American Mathematics Edited by J. Dalton Tarwater, John T. White, and John D. Miller K C- r j 21 lye No. 13 October 1976 TEXAS TECH UNIVERSITY Cecil Mackey, President Glenn E. Barnett, Executive Vice President Regents.-Judson F. Williams (Chairman), J. Fred Bucy, Jr., Bill E. Collins, Clint Form- by, John J. Hinchey, A. J. Kemp, Jr., Robert L. Pfluger, Charles G. Scruggs, and Don R. Workman. Academic Publications Policy Committee.-J. Knox Jones, Jr. (Chairman), Dilford C. Carter (Executive Director and Managing Editor), C. Leonard Ainsworth, Harold E. Dregne, Charles S. Hardwick, Richard W. Hemingway, Ray C. Janeway, S. M. Kennedy, Thomas A. Langford, George F. Meenaghan, Marion C. Michael, Grover E. Murray, Robert L. Packard, James V. Reese, Charles W. Sargent, and Henry A. Wright. Graduate Studies No. 13 136 pp. 8 October 1976 $5.00 Graduate Studies are numbered separately and published on an irregular basis under the auspices of the Dean of the Graduate School and Director of Academic Publications, and in cooperation with the International Center for Arid and Semi-Arid Land Studies. Copies may be obtained on an exchange basis from, or purchased through, the Exchange Librarian, Texas Tech University, Lubbock, Texas 79409. * Texas Tech Press, Lubbock, Texas 16 1976 I A I GRADUATE STUDIES TEXAS TECH UNIVERSITY Men and Institutions in American Mathematics Edited by J. Dalton Tarwater, John T. White, and John D. Miller No. 13 October 1976 TEXAS TECH UNIVERSITY Cecil Mackey, President Glenn E. Barnett, Executive Vice President Regents.-Judson F. Williams (Chairman), J. Fred Bucy, Jr., Bill E. Collins, Clint Form- by, John J. Hinchey, A. J. Kemp, Jr., Robert L. Pfluger, Charles G. Scruggs, and Don R. Workman. Academic Publications Policy Committee.-J. Knox Jones, Jr. (Chairman), Dilford C. Carter (Executive Director and Managing Editor), C. Leonard Ainsworth, Harold E. Dregne, Charles S. Hardwick, Richard W. Hemingway, Ray C. Janeway, S. M. Kennedy, Thomas A. Langford, George F. Meenaghan, Marion C. Michael, Grover E. Murray, Robert L. Packard, James V. Reese, Charles W. Sargent, and Henry A. Wright. Graduate Studies No. 13 136 pp. 8 October 1976 $5.00 Graduate Studies are numbered separately and published on an irregular basis under the auspices of the Dean of the Graduate School and Director of Academic Publications, and in cooperation with the International Center for Arid and Semi-Arid Land Studies. Copies may be obtained on an exchange basis from, or purchased through, the Exchange Librarian, Texas Tech University, Lubbock, Texas 79409. Texas Tech Press, Lubbock, Texas 1976 CONTENTS PR EFAC E. .. .. ... .. .. .. .. ... ... .. .. .. ... .. .. .. .. .. 5 MEN AND INSTITUTIONS IN AMERICAN MATHEMATICS . 7 Marshall H. Stone. University of Massachusetts, Amherst, 01002 INTERNATIONAL RELATIONS IN MATHEMATICS . 31 Marshall H. Stone. University of Massachusetts, Amherst, 01002 THE RISE OF MODERN ALGEBRA TO 1936 . 41 Garrett Birkhoff. Harvard University, Cambridge, Massachusetts 02138 THE RISE OF MODERN ALGEBRA, 1936-1950 . 65 Garrett Birkhoff. Harvard University, Cambridge, Massachusetts 02138 MATHEMATICAL AMERICANA . 87 Salomon Bochner. Rice University, Houston, Texas 77001 MATHEMATICS IN COLONIAL AND EARLY REPUBLICAN AMERICA . 99 Dirk J. Struik. Massachusetts Institute of Technology, Cambridge, 02139 SOME EARLY AMERICAN MATHEMATICIANS . 107 Philip S. Jones. University of Michigan, Ann Arbor, 48104 THE NEW ELEMENTS OF MATHEMATICS BY CHARLES S. PEIRCE . 111 Carolyn Eisele. Hunter College CUYN, New York, 10021 GEORGE BRUCE HALSTED AND THE DEVELOPMENT OF AMERICAN MATHEMATICS . .. 123 Albert C. Lewis. University of Texas, Austin, 78712 A BRIEF HISTORY OF GRAPHICAL ENUMERATION . .. 131 Robert W. Robinson. University of Michigan, Ann Arbor, 48104 CONFERENCE PROGRAM......................................... 133 PARTICIPANTS AT THE CONFERENCE................................135 PREFACE This collection of papers represents the proceedings of the conference on the History of American Mathematics held at Texas Tech University on 28, 29, and 30 May 1973. This conference was the first in a series of six conferences to be held at various universities in the State of Texas under the general title: American Mathematical Heritage. The series has received partial support from the Texas College and University Bicentennial Program. The second conference was the American Mathematical Heritage Symposium on the History of Statistics and Probability held at Southern Methodist Univer- sity, 27, 28, and 29 May 1974; and the proceedings of this conference will be forthcoming. The third conference in Algebra was held at The University of Texas at El Paso in 1975. Other conferences in Topology, Complex Analysis and Applied Mathematics are planned for The University of Texas at Austin, Rice University, and The University of Texas at Arlington, respectively. The three main articles presented at this conference were by Marshall Stone, Salomon Bochner, and Garrett Birkhoff. Illness prevented Professor Bochner from attending; his papers were read by Professor R. 0. Wells, Jr. The theme of the conference was appropriately the title of Professor Marshall Stone's paper, "Men and Institutions in American Mathematics," and for this reason, it appears as the title article. With the exception of papers by Kenneth May and Robert Thrall, these proceedings contain the papers presented at the conference. Some are faithful copies, others have been shortened to achieve spatial and conceptual balance. Robert Thrall's paper has appeared elsewhere, and Kenneth May's paper is, unfortunately, unobtainable. Bochner's paper appeared in the American Mathematical Monthly in a more complete version. This conference was funded by Texas Tech University, and the proceedings were audiotaped and are reposited in the Texas Tech.University Southwest Collection. We gratefully acknowledge permission to use in the essay Mathematical Americana material from the article "Continuity and Discontinuity in Nature and Knowledge," Dictionary of the History of Ideas, copyright 1973 by Charles Scribner's Sons. J. Dalton Tarwater John T. White John D. Miller 5 MEN AND INSTITUTIONS IN AMERICAN MATHEMATICS MARSHALL H. STONE History serves several purposes. First of all, it aims to preserve a record, necessarily incomplete and hence selective, of significant events of the past. It serves to create and embody traditions that play an important part in our social thinking. More important than this, however, is the hope that from well-written history one can draw some lessons for the future, finding in the record of past behavior indications of how people are likely to behave in the future or guides as to what their behavior should be in complex situations. In our concern for the future of mathematics, the chief problem is to create circumstances propitious for the study and discovery of mathematical truths. This seems to be a compel- ling reason for reviewing the history of American mathematics on this and other occasions. I am not a historian and am in no position to offer a paper that meets the criteria of adequacy and precision properly applied to historical writing. What I can do and what I propose to do is merely to supply future historians with evidence drawn from a rich experience dating from the autumn of 1919, the year when I first came in contact with some of the leading figures in American mathematics. It has been my good fortune to know a great many of those who conceived and carried out the ambitious plans that have resulted in putting America in the forefront of world mathematics. It has been my privilege to work closely with many of them in the development of mathematics at several leading universities and in some of the most effective mathematical and scientific organizations. In choosing the title "Men and Institutions in American Mathematics" for a paper based largely on personal recollections, I seek to suggest a theme that will give some unity to these reminiscences. Indeed, I firmly believe that the principal problem for mathematical historians is to examine the men who were prominent or influential at different stages and to investigate the institutions in and through which they worked. Men create institutions with certain purposes in view but are in turn confined by the very institutions they create. It is this interaction between men and institutions that is one of the major concerns of history. The chief and most stable institution in the world of mathematics has been for at least a hundred years the department of mathematics in a college or university. For teaching or creating mathematics, it is the department that provides the milieu in which a mathematician does his daily work and finds many of his most intimate associations. This was not always the case, inasmuch as in earlier times many famous mathematicians were supported by private sponsors or by learned academies in posts designed for consultation and research rather than for teach- ing. The careers of Euler and Lagrange furnish well-known examples. However, when science had won a place in the university curriculum, increasing the demand for courses in mathematics, the department of mathematics began to take the form we know and eventually assumed responsibility not only for 7 8 GRADUATE STUDIES TEXAS TECH UNIVERSITY teaching but also for research. Historically, departments of mathematics have provided nuclei around which have grown other institutions,
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