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[[[>50 Some of Hilbert's Problems:
| *Problem* | *Resolved?* |
| 1. The Continuum hypothesis | Partially | Independent of the axioms of arithmetic |
| 2. The axioms of arithmetic are consistent | Partially | See Godel's Theorem |
| ... | ... | ... |
| 7. Is EQN:a^b a transcendental number, for algebraic numbers EQN:a\ne{}0,1 and algebraic /b/ ? | Yes | See Gelfond-Schneider theorem |
| 8. The Riemann hypothesis | No | One of the Millennium problems |
]]]
David Hilbert at the beginning of the 20th Century formed a list of twenty-three Mathematical problems which were unsolved at the time as a challenge to Mathematicians. They have been very influential in the development of Mathematics since that time.
Many have been resolved but some including the Riemann Hypothesis await a decision.
The complete list and their status can be found on the WikiPedia page:
* http://en.wikipedia.org/wiki/Hilbert's_problems