Beethoven was only sixteen when he travelled from Bonn to Vienna in 1787 to meet Mozart. He had a letter of introduction from a mutual acquaintance and went to see Mozart at his house. When Beethoven met Mozart, he asked Beethoven to play something of his own creation. It impressed Mozart so much that he decided to take on Beethoven as a student.
However, after the meeting when Beethoven went back to his accommodation there was an urgent message from his father saying his mother was seriously ill. Beethoven had to return to Bonn only two weeks after being in Vienna to be with his family without any lessons from Mozart. But when he went back to Vienna in November 1792, Mozart passed away.
It was unfair that Mozart and Beethoven did not get to play together or learn from each other. Yet, Beethoven always remained a fan of Mozart’s work like The Magic Flute.