The Old Ashmolean Building on Broad Street in Oxford claims to be the
"oldest surviving purpose-built museum building in the world". The
building was built in 1683 for the museum of Elias Ashmole, which was
open to the public.

The claim could be that the building is the "oldest purpose-built museum
building in the world" were it not for the museum in the library of
Alexandria. But this no longer survives, and many not qualify as a
'public museum' anyway.

Clearly there are many museums around now that are in buildings that
were built before 1683, but none of these were originally built to be
museums; they have since been converted to that purpose. Other buildings
may have been built to house private collections, but none were built
expressly to be public museums.

Does anyone dispute these claims?

Quizically,

Giles Hudson,
Curatorial Assistant,
Museum of the History of Science,
Old Ashmolean Building,
Oxford.