The word I have translated “beaming” is karan, linked with keren, which usually means a horn but in this context means a beam of light.
Michelangelo was not the first to get the wrong idea; early Greek and Latin translators made the same mistake. The commentator Rashbam went so far as to call these translators idiots.
However, more important than attacking Michelangelo is to ask what the verse is actually telling us. That Moses’ face was beaming must have been noticed by everyone else in the Israelite camp; we have all had the experience of seeing a beam on someone’s face at a moment of exhilaration. The crucial thing is probably not so much that Moses’ face shone but that he was unaware of it: the verse says, “Moses did not know”. How is this possible? Did Moses not realise how ecstatic he looked?
But remember that Moses was a modest man: “The man Moses was very modest” (Num. 12:3). The odds are that he simply could not believe that he had been privileged to have such a great experience. If he did notice an aura of brightness, he thought it emanated from the tablets of the Ten Commandments which he was carrying.
The truly great person never boasts or even thinks that he or she is special but is certain that the cause has an elevating effect.