Then yesterday afternoon, I was wondering. Paul in 1Cor 11:4 encourages women to pray with a covering on their head, but says men should pray without a covering. I was wondering, how this squared with Jewish tradition that says that men should wear a cap when praying? Was Paul upholding a Greek tradition to this Gentile church, and not the Jewish tradition?
I had a chance in the evening to do some research, and it appears that the answer is the Jewish tradition of men covering their heads is newer than Paul.
This Jewish page cites as the authority for the practice a 3rd century (BCE) rabbi. So presumably in Paul's time this tradition hadn't started yet.
