The presidents of the society have been J. H. Van Amringe, 1888-90; Emory McClintock,. 1890-94; G. W. Hill, 1894-96; Simon Newcomb, 1896-98; R. S. Woodward, 1898-1900; E. H. Moore, 1900-02; Thomas S. Fiske, 1902-04; W. F. Osgood, 1904-06; Henry S. White, 1906 08; Maxime Bocher, 1908-10; H. B. Fine, 1910 12; E. B. Van Vleck, 1912-14; E. W. Brown, 1914-16; L. E. Dickson, 1916-. The secretaries have been Thomas S. Fiske, 1888-95, and F. N. Cole, 1895-. The business of the society is transacted by a council composed of the officers, ex-presidents, editorial committee of the (Transactions,' secretary of the Chicago Sec tion and 12 other members elected for a term of three years.
While the society is more especially devoted to the advancement of the higher branches of mathematics, it exerts a considerable influence both directly and through its members on the teaching of the subject in the schools and uni versities. The report of a committee of the society on college entrance requirements in mathematics has been adopted by the College Entrance Examination Board. A report on the requirements for the master's degree, pre sented to the Chicago Section, has been favor ably recognized by several of the Western uni versities. The society has also contributed materially to bring about the organization of associations of teachers of mathematics throughout the country, a movement especially stimulated by Professor Moore's presidential address in 1902.
Historical notices of the society may be found in the presidential addresses of Dr. Mc Clintock ((Bulletin,' January 1895) and Profes sor Fiske (ib., February 1905). Other notices are scattered through the secretary's reports. The society, which has increased its member ship by 50 per cent in the last 12 years, serves to-day to bring together in a harmonious whole all the mathematical activities of America. It is a centre not only of scientific activity but also of professional good feeling and agree able personal relations.
The British Mathematical Association, for merly known as the Association for the Im provement of Geometrical Teaching, is devoted to improved instruction in elementary mathe matics.
The Mathematical Association of America, organized in 1915 to represent the field of col legiate mathematics, has now over 1,100 mem bers. It has adopted as its official organ the American Mathematical Monthly. The presi dents of the Association have been E. R. Hedrick, 1915-17, and Florian Cajori, 1917- ). The secretary-treasurer is W. D. Cairns. Meet ings are held twice a year, usually in connec tion with those of the American Mathematical Society. Nine local societies have thus far been organized, holding meetings usually twice a year.
The international congresses of mathema ticians have been mentioned above. While these are individually hut temporary gather ings, they had come, before the war, to be an established institution of great and permanent value. Their sequence of time and place is: Paris, 1889; Chicago, 1893; Zurich, 1897; Paris, 1900; Heidelberg, 1904; Rome, 1908; Cam bridge, 1912.
The exchanges of the American Mathemat ical Society include about 140 journals which regularly publish mathematical papers of ap preciable value. In the notices appended to his collection of abbreviated titles of journals Jahresbericht der Deutschen Mathematiker Vereinigung,' Vol. XII, 1903, pp. 426 414) Felix Muller sets the grand total ever published of all journals of a fairly mathematical complexion at about 1,200, of which over 600 now survive. More than 300 journals are cited in the refer ences of the early numbers of the 'Encyclopedia of Mathematics.) The 'Revue
reports the contents of some 250 journals; the (Fortschritte) list is about 170.
The oldest journals in Miiller's list are the 'Philosophical Transactions' and the 'Journal des Savants,' both dating from the year 1665. Following these are the publications of the academies of Paris (1666) and Bologna (1690). From the 18th century there still survive, be side the journals of the academies (Berlin 1700; Petersburg, 1724; Gottingen, 1751; and others), also the 'Memorie di Matematica e di Fisica> (1782) of the Sodeti Italian, the 'Bulletin) (1789) of the Society Philomatioue of Paris, and the de l'Ecole Poly technique) (1794). Among the extinct jour nals may be mentioned the 'Ladies' Diary' (1704), 'Gentlemen's Diary) (1741), these two uniting in the 'Lady's and Gentlemens (1841-71) ; the 'Cambridge Mathematical Jour nal) (1839-45), the forerunner of (Sylvester's Quarterly Gergonne's 'Annales de Mathematique) (1810-31); Tortolini's (1850-57), superseded by the present 'Annali di Mathematica); and the various journals (1786 '825) of Hindenburg, Breithaupt, Besse!, Kretschmar. In America the ephemeral exist ences are chronicled of the 'Mathematical Cor (1804-06), ( Adrain's (1808) and 'Mathematical Diary) (1825-32), 'Mathe matical Companion) (1828-31) , Mathematical Miscellany) (1836-39), 'Cambridge Miscellany of Mathematics, Physics and Astronomy' (1842-43), 'Runkle's Mathematical (1858-61). The publication of the 'Analyst' (1874-83) marked a substantial advance. Mar tin's 'Mathematical (1877) and 'Mathematical Magazine) (1882), the matical (1882) and 'Mathematical Messenger) (1884) are extinct.
The following list gives the date of founda tion, the title and the present place of publica tion of the strictly mathematical journals now in existence and not already cited in connec tion with the list of mathematical societies above: 1826. ' Create Journal far die mine and angewandts Maths rnatik, 1836. ' Liouville's Journal de Mathematiques pures et alt pliqules: Pans.
1842. ' Nouvelles Annales de Mathematiques.' 1855. ' Quarterly Journal of Pure and Applied Mathematics: London.
1858. Annali di Matematica pure ed applicata: Milan. 1863. ' Giornale di Maternatiche di Battaglia': Naples. 1868. ' Mathematische Annalen,' Leipsic.
1870. ' Bulletin des Sciences Mathernatiques: Paris.
1871. Jahrbuch fiber die Port.chritte der methemaa: Berlin.
1872. ' Messenger of Mathematics,' London.
1878. ' American Journal of Mathematics,' Baltimore. 1881. Mathes's,' Ghent.
1882. ' Acta Mathematic..' Stockholm.
1884. ' Annals of Mathematics.' Cambridge, Masa. 1884. ' Bibliotheca Mathematics,' Leipsic.
1886. ' Periodico di Mathematics ' (Supplemento WM. horn.
1890. ' Tidsskrift for Matematik: Copenhagen. 1891. ' Revue de Mathematiques spftiales: Pans.
1894. American Mathematical Monthly,' SpringEekL 1.10. 1894. ' L'Interrpediaire des Mathematicians, Pans.
1895. ' Gaseta Matetnatica: Bucharest.
1896. ' Il Pitagora,' Palermo.
1896. ' Revue de Mathematiques,' Turin.
1807. Wiadomoaci Maternatyczne: Warsaw.
1898. ' Formulaire Mathematique: Turin.
1898. L' Education Mathematique: Paris.
1898. ' Bolletino di Bibliografia e Storks dells Sciense Mato =fiche.' Turin.
1899. ' L' Enseignmcnt Mathematique: Paris.
1900. ' Bolletino di Matematica,' Bologna.
1906. Sphinx Oedipe, Nancy.
1909. Mathematics Teacher, Syracuse, N. Y.
1912. Tohokn Mathematical Journal. Sondai, Japan.