You don’t need permission to photograph a work that is not protected by copyright (in “the public domain”). Works fall into the public domain for several reasons, one of which is expiration of the copyright term. In 1997, works created before January 1, 1922 are in the public domain. Also, works created by federal government officers and employees as part of their official duties are not protected by copyright. (This rule does not apply to works created by state or local government officers and employees).
You don’t need permission to use a copyrighted work in two circumstances: (1) if you are only copying facts or ideas from the work; or (2) if your use is “fair use”.
You are free to copy facts from a protected work or to copy ideas from a protected work. The copyright on a work does not extend to the work’s facts. This is because copyright protection is limited to original works of authorship, and no one can claim originality or authorship for facts. Anyone can use ideas.

Fair Use

It may be that your photograph is “fair use” of the art works you photograph. If so, you don’t need permission. Whether a use of a copyrighted work is fair use is decided on a case-by-case basis by considering the purpose and character of the use, the nature of the copyrighted work, the amount and substantiality of the portion used, and the effect on the potential market for or value of the protected work.
There is no simple rule to determine when an unauthorized use is “fair use”. You are more likely to be able to rely on fair use for photographing copyrighted items if your work serves a traditional fair use purpose (educational, research, news reporting, criticism, or public interest). Fair use is always subject to interpretation.