gs without incurring the
expense of long trips. Its first four presidents were E. R. Hedrick,
Florian Cajori, E. V. Huntington, and H. E. Slaught.

An event which has perhaps affected the very vitals of mathematical
teaching in America still more is the founding of the American
Mathematical Society in 1888, called the New York Mathematical Society
until 1894. Through its _Bulletin_ and _Transactions_, as well as
through its meetings and colloquia lectures, this society has stood
for inspiration and deep mathematical interest without which college
teaching will degenerate into an art. During the first thirty years of
its history it has had as presidents the following: J. H. Van Amringe,
Emory McClintock, G. W. Hill, Simon Newcomb, R. S. Woodward, E. H.
Moore, T. S. Fiske, W. F. Osgood, H. S. White, Maxime Boecher, H. B.
Fine, E. B. Van Vleck, E. W. Brown, L. E. Dickson, and Frank Morley.

=Aims of college mathematics: methods of teaching=

The aims of college mathematics can perhaps be most clearly understood
by recalling the fact that mathematics constitutes a kind of
intellectual shorthand and that many of the newer developments in a
large number of the sciences tend toward pure mathematics. In
particular, "there is a constant tendency for mathematical physics to
be absorbed in pure mathematics."[8] As sciences grow, they tend to
require more and more the strong methods of intellectual penetration
provided by pure mathematics.

The principal modern aim of college mathematics is not the training of
the mind, but the providing of information which is absolutely
necessary to those who seek to work most efficiently along various
scientific lines. Mathematical knowledge rather than mathematical
discipline is the main modern objective in the college courses in
mathematics. As this knowledge must be in a usable form, its
acquisition is naturally attended by mental discipline, but the
knowledge is absolutely needed and would have to be acquired even if
the process of acquisition were not attended by a development of
intellectual power.

The fact that practically all of the college mathematics of the
eighteenth century has been gradually taken over by the secondary
schools of today might lead some to question the wisdom of replacing
this earlier mathematics by more advanced subjects. In particular, the
question might arise whether the college mathematics of today is not
superfluous. This question has been partially answer