Fellowships at the Mellon Institute are constantly increasing in the amounts subscribed by industrialists for their maintenance and, as well, in their importance. The renewal, year after year, of such fellowships, as those on baking, petroleum and ores, goes to show the confidence which industrialists have in the Mellon Institute. Again, the large sums of money which are being spent by companies in bringing small unit plants to develop the processes which have been worked out in the laboratory, demonstrate that practical results are being secured. Where there have been sympathy and hearty cooperation between the Mellon Institute and the company concerned, the institute has been able to push through to a successful conclusion large scale experiments in the factory of the company, which in the beginning of the fellowship seemed almost impossible: it may be said that the results of the fellowships at the Mellon Institute indicate that a form of service to industry has been established, the possibilities of which no man can say. A FEW CLASSIC UNKNOWNS IN MATHEMATICS BY PROFESSOR G. A. MILLER UNIVERSITY OF ILLINOIS KING HIERO is said to have remarked, in view of the marvelous mechanical devices of Archimedes, that he would henceforth doubt nothing that had been asserted by Archimedes. This spirit of unbounded confidence in those who have exhibited unusual mathematical ability is still extant. Even our large city papers sometimes speak of a mathematical genius who could solve every mathematical problem that was proposed to him. The numerous unexpected and far-reaching results contained in the elementary mathematical text-books, and the ease with which the skilful mathematics teachers often cleared away what appeared to be great difficulties to the students have filled many with a kind of awe for unusual mathematical ability. In recent years the unbounded confidence in mathematical results has been somewhat shaken by a wave of mathematical skepticism which gained momentum through some of the popular writings of H. Poincare and Bertrand Russell. As instances of expressions which might at first tend to diminish such confidence we may refer to Poincare's contention that geometrical axioms are conventions guided by experimental facts and limited by the necessity to avoid all contradictions, and to Russell's statement that "mathematics may be defined as the subject in which we never know what we are talking about nor whether what we are saying is true."