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31 History of the American Mathematical Society 1888 19391 HISTORY OF THE SOCIETY 31 HISTORY OF THE AMERICAN MATHEMATICAL SOCIETY 1888-1938* RAYMOND CLARE ARCHIBALD At the present time, throughout the world, there are many mathe­ matical societies, but if we limit our consideration to those which have been in existence at least twenty-five years there are but twenty. This number is reduced to eleven if the minimum age is set at fifty years. Let us then recall who our ten elder sisters may be. The Ham­ burg Mathematical Society, founded in 1690, with publications is­ sued almost continuously during the past two hundred years, started out as "A Society for Lovers of the Art of Calculation." The Amster­ dam Mathematical Society is only 160 years old, but it has been issuing substantial volumes since 1782. The other eight societies are very much younger. The forerunner of the Czechoslovakian Society for Mathematics and Physics, organized in 1869, was the Society for Free Lectures on Mathematics and Physics, founded 76 years ago. This Society with nearly 2000 members is the most affluent of all mathematical organizations, owning its own press and buildings where it transacts an extensive business in texts used throughout the country. The important Moscow Mathematical Society developed in 1867 from a Circle of Lovers of Mathematics, started in 1864. The fifth member of this family of societies, The London Mathematical Society, was born a year later, and its kinship with our own organiza­ tion will presently be indicated. After two seven-year intervals the Mathematical Society of France arrived in 1872 and the Kharkov Mathematical Society in 1879. The group of ten was completed in 1884 by the delivery of triplets, the Edinburgh Mathematical Soci­ ety, the Mathematical Circle of Palermo, and the Physico-Mathe- matical Society of Japan. These ten societies are in eight countries, and in five of these coun­ tries during the nineteenth century great mathematical discoverers were flourishing. France had, for example, Laplace, Legendre, Ponce- let, Cauchy, Hermite, and Poincaré; Germany had Gauss, Weier- strass, Riemann, Jacobi, Steiner, and Kronecker; Great Britain had Hamilton, Smith, Cayley, Sylvester, Stokes, and Maxwell; Italy * This was the first of the ten invited addresses for the Semicentennial Celebra­ tion; the other nine have been published as Volume 2 of the American Mathematical Society Semicentennial Publications. Twenty-two portraits on lantern slides, here listed at the end of the address, were used to illustrate this lecture. License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use 32 R. C. ARCHIBALD [J anuary had Cremona, Brioschi, Beltrami, Betti, and Dini; Russia had Che- byshev, Lobachevskïï, and Liapunov. It was probably while thinking of the work of such men that Maxime Bôcher wrote in January, 1895 : "In my opinion there is no American mathematics worth speaking of as yet." If facts now common property had been known to Bôcher, he might well have cast his statement into different form. Only the briefest suggestion as to such facts may now be indicated. There was certainly no real mathematical research in the United States before the beginning of the nineteenth century. Robert Adrain was then formulating and answering questions involving elliptic in­ tegrals and the calculus of variations. Also Nathaniel Bowditch, famed for his American Practical Navigatory prepared a monumental English edition of most of Laplace's Mécanique Céleste with very elaborate commentary, and he published an interesting memoir on the motion of a pendulum suspended from two points, and thus initiated the study of curves much later to become famous also in connection with certain acoustical phenomena as Lissajous's curves. Next in chronological order is Benjamin Peirce, of Harvard Univer­ sity, an extraordinarily inspiring teacher and a man of great abilities, whose notable Analytical Mechanics is to be found in nearly all the great libraries of Europe. But of prime importance was his epoch- making Linear Associative Algebra, first published privately in 1870, and anticipating a good deal of the work of Study and Scheffers in connection with the theory of hypercomplex numbers. George Wil­ liam Hill, born about a generation later than Peirce, was the greatest master of mathematical astronomy in the last quarter of the nine­ teenth century. His extraordinary memoir in the first number of the American Journal of Mathematics, in 1878, was fundamental in the development of celestial mechanics in three different directions, throughout the next generation. But his privately printed memoir of 1877, with the introduction of infinite determinants and the differ­ ential equation now generally known as "Hill's equation", is even more famous. Simon Newcomb was slightly older than Hill and wrote interesting and valuable theoretical papers on hyperspace and the general integrals of planetary motion. The great contributions of Josiah Willard Gibbs in thermodynamics and vector analysis and part of his work in statistical mechanics seem to have been developed before 1888. From the founding of The Johns Hopkins University to the end of 1883 Sylvester was the enormously inspiring professor of mathematics, and the editor-in-chief of the American Journal of Mathematics from its foundation in 1878. Thus this notable journal had been published for ten years before our Society was founded, and License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use 1939] HISTORY OF THE SOCIETY 33 contained many important papers by such men as Sylvester, Cayley, and H. A. Rowland, as well as others less significant by such authors as Fabian Franklin, W. I. Stringham, and Henry Taber, who had re­ ceived their doctor's degrees at The Johns Hopkins; by F. N. Cole, awarded his doctorate at Harvard, although the work for it was mainly done in Leipzig under Klein's direction; and by E. H. Moore, whose A.B. and Ph.D. degrees came from Yale University. These suggestions must suffice to indicate that in the United States before the founding of our Society there was already an inspiring mathematical center, and that a considerable body of mathematical work, some of it of first importance, had certainly been already achieved. Many people scattered over the country were then engaged in mathematical pursuits, and among them were not a few who had obtained their doctor's degrees either here or in Europe. Hence the time was opportune for drawing them together in a mathematical or­ ganization. In the spring of 1887, when Thomas Scott Fiske was in his second year as a graduate student and assistant in mathematics at Columbia College, he decided that six months of the following year should be spent in study at the University of Cambridge. Coming with high credentials he was received as a guest. Among his rich experiences was the establishment of an intimate friendship with J. W. L. Glai- sher who took him to the meetings of the London Mathematical Society. These meetings deeply impressed Fiske, and on returning to New York he was imbued with the idea that in America there should be a stronger feeling of comradeship among those interested in mathematics. And thus it came about that upon the call of Fiske, and two friends in the graduate school, Edward Lincoln Stabler and Harold Jacoby—three young men all born in the same year, 1865— six persons assembled at Columbia College on Thanksgiving Day, 1888, to organize a local mathematical society. A constitution was adopted at the second meeting on December 29, 1888, and the New York Mathematical Society came into being. John Howard Van Am- ringe, professor of mathematics in the School of Arts at Columbia College, was elected as its first president, and Dr. Fiske as secretary. "Van Am," as the president was universally called, was a unique fig­ ure in Columbia College and University, and probably no other teacher there of his day was so loved and revered. As M. H. Thomas has told us, "his boys" have delighted to perpetuate his memory at Columbia in song and stone and bronze and oils. One of Columbia's most popular songs is the adaptation to Van Am of "John Peel," the fine old English hunting song, commencing License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use 34 R. C. ARCHIBALD [January D'ye ken Van Am, with his snowy hair, D'ye ken Van Am, with his whiskers rare, D'ye ken Van Am, with his martial air, As he crosses the Quad in the morning? And then the refrain: For the sight of Van Am raised my hat from my head, And the sound of his voice often filled me with dread, Oh! I shook in my boots at the things that he said, When he asked me to call in the morning. The little Society met monthly during the college year, and the sixteen members at the end of 1889 included: J. K. Rees, professor of geodesy and practical astronomy and director of the Observatory at Columbia; I. C. Pierson, secretary of the Actuarial Society of America; J. E. McClintock, vice president of the Actuarial Society of America and actuary of the Mutual Life Insurance Company of New York, later to serve the Society so notably; M. I. Pupin, in­ structor in mathematical physics at Columbia and throughout life one of the Society's finest friends. In December, 1890, when the new president, Dr. McClintock, was in the chair, a letter from an American who had attended a meeting of the London Mathematical Society was read. It described the meeting and made reference to its Pro­ ceedings. Resulting discussion led to the motion that our Society publish a bulletin, the details to be worked out by the Council which had been established in June, 1889.
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