Summary
Of the cleanly-formulated Hilbert problems, problems 3, 7, 10, 11, 13, 14, 17, 19, 20, and 21 have a resolution that is accepted by consensus. On the other hand, problems 1, 2, 5, 9, 15, 18+, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether it resolves the problem.
The + on 18 denotes that the Kepler conjecture solution is a computer-assisted proof, a notion anachronistic for a Hilbert problem and to some extent controversial because of its lack of verifiability by a human reader in a reasonable time.
That leaves 16, 8 (the Riemann hypothesis) and 12 unresolved. On this classification 4, 16, and 23 are too vague to ever be described as solved. The withdrawn 24 would also be in this class. 6 is considered as a problem in physics rather than in mathematics.
Read more about this topic: Hilbert's Problems
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