Quaternion Society

A scientific society, the Quaternion Society was an "International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics". At its peak it consisted of about 60 mathematicians spread throughout the academic world that were experimenting with quaternions and other hypercomplex number systems. The guiding light was Alexander Macfarlane who served as its Secretary initially, and became President in 1909. The Association published a Bibliography in 1904 and a Bulletin (annual report) from 1900 to 1913.

The Bulletin became a review journal for topics in vector analysis and abstract algebra such as the theory of equipollence. The mathematical work reviewed pertained largely to matrices and linear algebra as the methods were in rapid development at the time.

In 1895, Professor P. Molenbroek of The Hague, Holland, and Shinkichi Kimura studying at Yale put out a call for scholars to form the society in widely circulated journals: Nature, Science, and the Bulletin of the American Mathematical Society (see references). Giuseppe Peano also announced the society formation in his Rivista di Matematica.

The call to form an Association was encouraged by Macfarlane in 1896:

In 1897 the British Association met in Toronto where vector products were discussed:

A system of national secretaries was announced in the AMS Bulletin in 1899: Alexander MacAulay for Australasia, Victor Schlegel for Germany, Joly for Great Britain and Ireland, Giuseppe Peano for Italy, Kimura for Japan, Aleksandr Kotelnikov for Russia, F. Kraft for Switzerland, and Arthur Stafford Hathaway for the USA. For France the national secretary was Paul Genty, an engineer with the division of Ponts et Chaussees, and a quaternion collaborator with Charles-Ange Laisant, author of Methode des Quaterniones (1881).

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