*AMERICAN MATHEMATICS*

459

AMERICAN MATHEMATICS |

By Professor G. A. MILLER

UNIVERSITY OF ILLINOIS

ABOUT a dozen years ago a well-known French mathematician wrote as follows in reference to our mathematical situation:^{[1]} "Mathematics in all its forms and in all its parts is taught in numerous [American] universities, treated in a multitude of publications, and cultivated by scholars who are in no respect inferior to their fellow mathematicians of Europe. It is no longer an object of import from the old world but it has become an essential article of national production, and this production increases each day both in importance and in quantity."

Taken by itself this assertion looks good and it is doubtless more nearly true to-day than it was at the time of publication. If we turn our eyes away from this statement and rest them upon the mathematical book shelves of a good library, we can not fail to notice that our accomplishments do not seem to be in accord with the complimentary statement noted above. This disaccord will become still more evident if we look through the pages of some of the standard works of reference, such as the great mathematical encyclopedias which are now in the course of publication.

If a student of the history of mathematics would make a list of the leading mathematicians of the world during the last two or three centuries, arranging the names in order of eminence, he would have a fairly long list before reaching the name of an American. Such names as those of Euler, Cauchy, Gauss, Lagrange, Galois, Abel and Cayley have no equals in the history of American mathematics; and, among living mathematicians, probably all students would agree that there are no American names which should be placed on a mathematical equality with those of Poincaré, Klein, Hilbert, Frobenius, Jordan, Picard and Darboux. Both of these lists of names could be considerably extended without any danger of being unfair to the mathematicians of this country, but they suffice to establish the fact that our mathematical situation is not yet satisfactory, notwithstanding our remarkable progress during recent decades.

This unsatisfactory situation is reflected in many of our standard books of reference. For instance, under such an important word as "matrix" one finds in Webster's New International Dictionary (1910)

- ↑ Laisant, "La Mathematique, Philosophie-enseignement," 1898, p. 143.