Mathematical Developments Arising from Hilbert Problems, Part 1

algebraic numbers Amer analogue analysis analytic arith arithmetic axiomatic axioms Banach space cardinal coefficients cohomology commutation compact complete conjecture consistency consistency proof construction curvature curve defined Deligne derived differential equation dimension diophantine elementary equivalent euclidean example existence f.c. proofs finite fields finite number formal foundations Gel'fond geometry given Green's functions Hamiltonian hidden variables theory Hilbert space Hilbert's program independent infinite integral L-functions lattice linear logical manifold mappings Math mathematical method metric modular Neumann number field number theory operators p-adic Phys physical Piron points polynomial prime numbers problem Proc properties proved quantum field theory quantum mechanics question rational real numbers relations representation Riemann Hypothesis satisfying Segal set theory singular solution structure subsets subspaces theorem tions topology transcendental numbers transformation group vacuum vacuum expectation values values vector zero zeta function