, i. e., whether a finite number of such expressions can be chosen by means of which for every exponent
every other expression of that form is integrally and rationally expressible.
From the boundary region between algebra and geometry, I will mention two problems. The one concerns enumerative geometry and the other the topology of algebraic curves and surfaces.
[32] Cf. Sitzungsber. d. K. Acad. d. Wiss. zu München, 1890, and an article about to appear in the Math. Annalen.
[33] "Ueber die Erzeugung der Invarianten durch Integration," Nachrichten d. K. Geseltschaft d. Wiss. zu Göttingen, 1897.
[34] Math. Annalen, vol. 36 (1890), p. 485.
15. RIGOROUS FOUNDATION OF SCHUBERT'S ENUMERATIVE CALCULUS.
The problem consists in this: To establish rigorously and with an exact determination of the limits of their validity those geometrical numbers which Schubert[35] especially has determined on the basis of the so-called principle of special position, or conservation of number, by means of the enumerative calculus developed by him.