Hilbert's fifteenth problem [SEP] named after
Hilbert's fifteenth problem
Hilbert's fifteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. The problem is to put Schubert's enumerative calculus on a rigorous foundation.
Introduction.
Splitting the question, as now it would be understood, into Schubert calculus and enumerative geometry, the former is well-founded on the basis of the topology of Grassmannians, and intersection theory. The latter has status that is less clear, if clarified with respect to the position
Hilbert's axioms as exemplary, by Hilbert's third problem as solved by Dehn, one of the actors, by Hilbert's fifteenth problem from the needs of 19th century geometry. The subject matter of manifolds is a strand common to algebraic topology, differential topology and geometric topology.
1945 to 1960.
Terminology: By this period manifolds are generally assumed to be those of Veblen-Whitehead, so locally Euclidean Hausdorff spaces, but the application of countability axioms was also becoming standard. Veblen-Whitehead did not assume,