Mathematical Developments Arising from Hilbert Problems

Abstract

Part 1: Hilbert's first problem: The continuum hypothesis by D. A. Martin What have we learnt from Hilbert's second problem? by G. Kreisel Problem IV: Desarguesian spaces by H. Busemann Hilbert's fifth problem and related problems on transformation groups by C. T. Yang Hilbert's sixth problem: Mathematical treatment of the axioms of physics by A. S. Wightman Hilbert's seventh problem: On the Gelfond-Baker method and its applications by R. Tijdeman Hilbert's 8th problem: An analogue by E. Bombieri An overview of Deligne's proof of the Riemann hypothesis for varieties over finite fields (Hilbert's problem 8) by N. M. Katz Problems concerning prime numbers (Hilbert's problem 8) by H. L. Montgomery Part 2: Problem 9: The general reciprocity law by J. Tate Hilbert's tenth problem. Diophantine equations: Positive aspects of a negative solution by M. Davis, Y. Matijasevic, and J. Robinson Hilbert's eleventh problem: The arithmetic theory of quadratic forms by O. T. O'Meara Some contemporary problems with origins in the Jugendtraum (Hilbert's problem 12) by R. P. Langlands The 13-th problem of Hilbert by G. G. Lorentz Hilbert's fourteenth problem--the finite generation of subrings such as rings of invariants by D. Mumford Problem 15. Rigorous foundation of Schubert's enumerative calculus by S. L. Kleiman Hilbert's seventeenth problem and related problems on definite forms by A. Pfister Hilbert's problem 18: On crystalographic groups, fundamental domains, and on sphere packing by J. Milnor The solvability of boundary value problems (Hilbert's problem 19) by J. Serrin Variational problems and elliptic equations (Hilbert's problem 20) by E. Bombieri An overview of Deligne's work on Hilbert's twenty-first problem by N. M. Katz Hilbert's twenty-third problem: Extensions of the calculus of variations by G. Stampacchia.