What's the best age to start the role of Dungeon Master where you have the maturity and the skills to run an interesting campaign for adults?
Perfection is reached, not when there is no longer anything to add, but when there is no longer anything to take away. -- Antoine de Saint-Exupery
If you are going to be playing with adults you best be an adult yourself unless of course the adults have never played and Dungeons & Dragons games. Otherwise you will find yourself trying to justify your actions against those who are knowledgeable in the rules and questioning you a lot.
Speaking generally I would be suspicious of anyone under 17 wanting to run a game. Not that someone under 17 couldnt but they would need to be exceptional in both rules of play and the ability to keep older players entertained.
I won't name a number. Because numbers are irrelevant. Dungeon Mastering is a matter of consistency, creativity, and reasoning. While older people are somewhat more likely to have developed some of those qualities, I've known forty year olds who would make worse Dungeon Masters than my 7 year old nephew.
Edited: daishain on 17th Dec, 2017 - 6:40pm
Key element is experience and knowledge. Sometimes players want to do things that aren't typical, maybe scientific or engineering wise and if you aren't on top of what they are trying to accomplish then they can take you for a ride.
I will go brave and say that I like someone 35 and older as Dungeon Master, if they are older even better. If they have a beard and glasses even better- it feels authentic. *laugh*.
I think that any age is okay to be a Dungeon Master, as long as you have the knowledge and maturity to run a game. Typically though the age should be in the same category as the players or older, so that respect and cooperation with the Dungeon Master is there and play is enjoyed by all involved.