From the Super Mario Wiki
“Uh, hum! This, my good man, is the Royal Society. We are a collection of learned men of science who meet to promote scientific discussion. I cannot imagine your business here.”
The Royal Society of London for Improving Natural Knowledge, more commonly known as merely the Royal Society and also known as London's Royal Academy of Sciences, is a group that Mario interacted with in Mario's Time Machine. They fund and otherwise support scientific research and discussion. Having taking himself back to Cambridge University in 1687, seeking to return an apple Bowser had stolen, Mario speaks with members of this society to try and ascertain its historical significance. From them, he construes that the apple is the one that Isaac Newton, a member of the society himself, would have observed falling to spark his thoughts into gravity, and returns it to him.