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Alexander Macfarlane in Chicago, 1893
The Columbia Exhibition included both the International Electrical Congress and the International Congress of Mathematicians. What brought about these congresses?

According to a popular history of chemistry, "chemistry played a pioneering role in the organization of the sciences, since it was the first discipline for which an international congress of specialists was organized (at Karlsruhe in 1860)." The same history goes on to explain the marketing manifesto:

international rivalry was encouraged by a series of World Expositions that took place almost every four years between 1862 and 1900, allowing the public to compare dyes displayed by various companies
The Columbia Exposition in Chicago, Illinois in 1893 attracted the curious from around the world. The occasion was also an opportunity for scientists to assemble and discuss the advances in their fields. The International Electrical Congress included Nichola Tesla, Charles Steinmetz, and Alexander Macfarlane as presentors and Hermann Helmholtz as guest. As one of Steinmetz' biographers explains, his complex number methods for motor research took hold because of his presentation, in the same section with Macfarlane, at the International Electrical Congress.

The University of Chicago opened its doors in October 1892, and the Department of Mathematics organized a Congress of Mathematicians to be held in connection with the Columbia Exposition. The German government commissioned Felix Klein as its official representative. The conference had a stimulating effect on the scientists. Subsequently there has been a sequence of International Congresses of Mathematicians with the first official ICM in 1897 in Zurich. Sometimes the Chicago Congress is called the zero-th ICM for its primordial role in the instituted sequence. The proceedings of this conference (see references) have Library of Congress call number QA1 I8, and are shelved just to the left of the sequence of proceedings from the subsequent ICMs.

Transformation Zeitgeist
The publication of Sophus Lie's Transformation Groups in 1888 was an important event. It developed some tools needed to advance the transformation geometry proposed by Felix Klein at Erlangen some years before. Further, Alexander MacFarlane had started a dialogue on the most suitable quaternion-allied system for doing electromagnetic theory. And coincidentally, Oliver Heaviside delivered his Electromagnetic Theory in 1893, a book that started with a complete chapter devoted to mathematical method.

Chicago Congress of Mathematicians, 1993:
Alexander Macfarlane joined the mathematicians and entered his name on the Official Register. He read papers on the definitions of the trigonometric functions and on the principles of elliptic and hyperbolic analysis. The mathematical papers of the Chicago Congress were published in 1896 under the editorial guidance of E.H.Moore, Henry S. White, Oskar Bolza, and Heinrich Mashke, but MacFarlane's contributions were not included, even though acknowledged.

The official photograph includes but half of the 45 registrants at the Chicago Congress and excluded Macfarlane. Though he participated in later ICM's, his bid for inclusion in 1893 was blunted. We see Felix Klein front and center and facing the camera in the official photo. It is Eduard Study, also representing Germany, positioned over his right shoulder, slouching in his seat, head slightly tilted. The other photograph has Macfarlane facing the camera, Henry Clew looking on.

Official Register:
Charlotte C. Barnum, New Haven, Connecticut
Wooster W. Beman A.M. professor of mathematics, University of Michigan, Ann Arbor, Michigan
E.M. Blake, Ph.D. instructor in mathematics, Columbia College, New York
T.M. Blakslee, Ph.D. professor of mathematics, Des Moines College, Des Moines, Iowa
Oskar Bolza, Ph.D. associate professor of mathematics, University of Chicago
Ellery W. Davis, Ph.D. professor of mathematics, University of Nebraska, Lincoln, Nebraska
Henry T. Eddy, Ph.D., C.E., President of Rose Polytechnic Institute, Terre Haute, Indiana
Achsah M. Ely, B.A. professor of mathematics, Vassar College, Poughkeepsie, New York
Rufus L. Green, M.A. associate professor of mathematics, Leland Stanford Junior University, Palo Alto, California
George Bruce Halsted, Ph.D. professor of mathematics, University of Texas, Austin, Texas
Norbert Hertz, Ph.D., Vienna, Austria
Thomas F. Holgate, Ph.D. instructor in mathematics, Northwestern University, Evanston, Illinois
Lorrain S. Hulburt, M.A. instructor in mathematics, Johns Hopkins University, Baltimore, Maryland
John W. Johnson, M.A. associate professor of physics and astronomy, University of Mississippi
H.G. Keppel, fellow in mathematics, Clark University, Worcester, Massachusetts
Felix Klein Ph.D., professor of mathematics, University of Gottingen, Germany
John H. Kleinheksel, M.A. professor of mathematics, Hope College, Holland, Michigan
Frank H. Loud B.A. professor of mathematics and astronomy, Colorado College, Colorado Springs, Colorado
Alexander Macfarlane, Sc.D., LL.D., professor of physics, University of Texas, Austin, Texas
James McMahon M.A. assistant professor of mathematics, Cornell University, Ithaca, New York
Heinrich Maschke Ph.D. assistant professor of mathematics, University of Chicago
Mansfield Merriman Ph.D., C.E. professor of civil engineering, Lehigh University, Bethlehem, Pennsylvania
John A. Miller, M.A. instructor in mathematics, Leland Stanford Junior University, Palo Alto, California
E. Hastings Moore, Ph.D. professor of mathematics, University of Chicago
James E. Oliver M.A. professor of mathematics, Cornell University, Ithaca, New York
Max Osterberg, Columbia College, New York
Bernard Paladini Ph.D. University of Pisa, Italy
John E. Purdon M.D. Cullman, Alabama
Edward D. Roe Jr. associate professor of mathematics, Oberlin College, Oberlin, Ohio
Ida M. Schottenfels, A.B., Chicago, Illinois
Montague R. Severson M.D. Charlottesville, Virginia
James B. Shaw Jr. Ph.D. professor of mathematics, Illinois College, Jacksonville, Illinois
William B. Smith Ph.D. professor of mathematics and astronomy, University of Missouri, Columbia, Missouri
William E. Story Ph.D. professor of mathematics, Clark University, Worcester, Massachusetts
E. Study Ph.D. professor extraordinarius of mathematics, University of Marburg, Germany
Henry Taber Ph.D. assistant professor of mathematics, Clark University, Worcester, Massachusetts
Harry W. Tyler Ph.D. professor of mathematics, Massachusetts Institute of Technology, Boston, Massachusetts
Charles A. Van Velzer Ph.D. professor of mathematics, University of Wisconsin, Madison, Wisconsin
John M. Van Vleck, M.A., LL.D. professor of mathematics and astronomy, Wesleyan University, Middletown, Connecticut
Clarence A. Waldo M.A. professor of Mathematics, De Pauw University, Greencastle, Indiana
Arthur G. Webster Ph.D. assistant professor of mathematical physics, Clark University, Evanston Illinois
Henry S. White Ph.D. associate professor of mathematics, Northwestern University, Evanston Illinois
Mary F. Winton A.B. honorary fellow in mathematics, University of Chicago
M.J. Yantzyn, San Francisco, California
Alexander Ziwet, assistant professor of mathematics, University of Michigan, Ann Arbor, Michigan

References:
1. Mathematical Papers read at the International Mathematical Congress held in Connection with the World's Columbia Exposition, Chicago 1893 , MacMillan Co./ American Mathematical Society, 1906. Includes Official Register and editor's statement on page 167 concerning Alexander Macfarlane's pamphlets. Keynote lecture: " The Present State of Mathematics" by Felix Klein, pp.133-5.
2. History of Chemistry (1995) Bensaude-Vincent & Stengers,
translated by Deborah van Dam from the 1993 French original, published by Harvard, pages 95 & 182
3. Official "Klein" photo: A Century of Mathematics in America, Part III, page four, Peter Duren editor, AMS, 1988.
4. Ronald R. Klein (1992) Steinmetz : engineer and socialist,page 90, Johns Hopkins University Press.
5. History of University of Chicago Department of Mathematics
6. Photo with Henry Clew in Chicago: from Emilio Segre Visual Archive which has 25,000 images!
7. David E Rowe & Karen Hunger Parshall "Come to the Fair: The Chicago Mathematical Congress of 1893", see pp. 61-69 of A Century of Mathematical Meetings Bettye Anne Case editor, AMS.
8. Herman Weyl "Relativity as a Stimulus in Mathematical Research" Proceedings of the American Philosophical Society 93:535-41. There is a brief reference to antipathy between Study and Klein in this paper's opening. Available on JSTOR.

Read the Alexander Macfarlane Homepage to learn about his contributions to science.
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