Hilbert's Mathematical Problems
Table of contents
(The actual text is on a separate page.)
(Philosophy of problems, relationship between mathematics and science, role of
proofs, axioms and formalism.) Treatise print.
Problem 1. Cantor's problem of the cardinal number K. Gödel. The consistency of the
of the continuum. (The continuum axiom of choice and of the
hypothesis.) Treatise print. generalized continuum hypothesis.
Princeton Univ. Press, Princeton,
Problem 2. The compatibility of the arithmetical axioms. Treatise print.
Problem 3. The equality of two volumes of two V. G. Boltianskii. Hilbert's Third
tetrahedra of equal bases and equal Problem Winston, Halsted Press,
altitudes. Treatise print. Washington, New York, 1978.
C. H. Sah. Hilbert's Third Problem:
Scissors Congruence. Pitman,
Problem 4. Problem of the straight line as the shortest distance between two points.
(Alternative geometries.) Treatise print.
Problem 5. Lie's concept of a continuous group of Montgomery and Zippin.
transformations without the assumption Topological Transformation Groups.
of the differentiability of the functions Wiley, New York, 1955.
defining the group. (Are continuous
groups automatically differential Kaplansky. Lie Algebras and Locally
groups?) Treatise print. Compact Groups. Chicago Univ.
Press, Chicago, 1971.
Problem 6. Mathematical treatment of the axioms of Leo Corry's article "Hilbert and the
physics. Treatise print. Axiomatization of Physics (1894-
1905)" in the research journal
Archive for History of Exact
Sciences, 51 (1997).
Problem 7. Irrationality and transcendence of N.I.Feldman. Hilbert's seventh
certain numbers. Treatise print. problem (in Russian), Moscow state
Univ, 1982, 312pp. MR 85b:11001
Problem 8. Problems of prime numbers. (The distribution of primes and the Riemann
hypothesis.) Treatise print.
Problem 9. Proof of the most general law of reciprocity in any number field. Treatise print.
Problem 10. Determination of the solvability of a S. Chowla. The Riemann Hypothesis
diophantine equation. Treatise print. and Hilbert's Tenth Problem.
Gordon and Breach, New York,
Maxim Vsemirnov's Hilbert's Tenth
Problem page at the Steklov Institute of Yu. V. Matiyasevich. Hilbert's Tenth
Mathematics at St.Petersburg. Problem. MIT Press, Cambridge,
Massachusetts,1993, available on the
Problem 11. Quadratic forms with any algebraic numerical coefficients. Treatise print.
Problem 12. Extension of Kroneker's theorem on R.-P. Holzapfel. The Ball and Some
abelian fields to any algebraic realm of Hilbert Problems. Springer-Verlag,
rationality. Treatise print. New York, 1995.
Problem 13. Impossibility of the solution of the general equation of the 7-th degree by means
of functions of only two arguments. (Generalizes the impossibility of solving 5-
th degree equations by radicals.) Treatise print.
Problem 14. Proof of the finiteness of certain Masayoshi Nagata. Lectures on the
complete systems of functions. Treatise fourteenth problem of Hilbert. Tata
print. Institute of Fundamental Research,
Problem 15. Rigorous foundation of Schubert's enumerative calculus. Treatise print.
Problem 16. Problem of the topology of algebraic Yu. Ilyashenko, and S. Yakovenko,
curves and surfaces. Treatise print. editors. Concerning the Hilbert 16th
problem. American Mathematical
Society, Providence, R.I., 1995.
B.L.J. Braaksma, G.K. Immink, and
M. van der Put, editors. The Stokes
Phenomenon and Hilbert's 16th
Problem. World Scientific, London,
Problem 17. Expression of definite forms by squares. Treatise print.
Problem 18. Building up of space from congruent polyhedra. (n-dimensional crystallography
groups, fundamental domains, sphere packing problem.) Treatise print.
Comments on the theory of analytic functions.
Problem 19. Are the solutions of regular problems in the calculus of variations always
necessarily analytic? Treatise print.
Problem 20. The general problem of boundary values. (Variational problems.) Treatise non
print chess. Source?
Problem 21. Proof of the existence of linear differential equations having a prescribed
monodromic group. Treatise non print chess. Source?
Problem 22. Uniformization of analytic relations by means of automorphic functions.
Treatise non print chess. Source?
Problem 23. Further development of the methods of the calculus of variations. Treatise non
print chess. Source?
a = 1/2bh
a = bh
a2 b2 c2 = bh
E = mc2