On Saturday, November 24, 2018 at 8:03:43 AM UTC-8, Jim wrote:
I have read many FARs that describe the requirements for obtaining a pilot certificate but I have not found an FAR that states a pilot certificate is required in order to fly an aircraft - without passengers and not for compensation or hire. 14 CFR 61.3 details the requirements for a "required pilot flight crewmember" but I do not see that it states a person may not fly an aircraft unless that person has a pilot certificate.

What am I missing?

Maybe 14 CFR 61.56 Flight Review covers this. It states that no person may act as pilot-in-command of an aircraft unless that person has fulfilled the flight review requirements. Since a person flying an aircraft alone (solo) is the pilot-in-command during that flight maybe the flight review requirement, in what seems to me to be a rather indirect fashion, defines such a flight as against the rules. I really don't know. I think it would be useful to have a clear (?) statement that a pilot certificate is required for a person to fly an aircraft.