Hilbert's fifteenth problem

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Hilbert's fifteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails a rigorous foundation of Schubert's enumerative calculus.

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 in 1900.