From Halopedia, the Halo wiki
Hilbert was built during the golden age of human colonial expansion and later refit for long-range sensing in the Outer Colonies. Dr. Catherine Halsey arranged to have her daughter, Miranda Keyes, assigned to serve on the ship, believing it to be the safest place for a UNSC officer to be stationed. However, around 2550, the ship became involved in the Battle of Gamma Pavonis VII. Having no weapons capable of breaching a Covenant destroyer's energy shield, Keyes ordered Hilbert to ram into the enemy vessel. The resulting collision damaged the shield, allowing Hilbert to continue onwards and crash into the vessel proper. As the crew abandoned ship, which was now falling into Gamma Pavonis VII's gravity well, Hilbert's fusion core went critical. Only two of the crew members survived – Miranda included.
The ship was likely named after renowned German mathematician David Hilbert.
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