Woody Allen once said that Mozart's Symphony 41 proved the existence of God. Certainly, a symphony of such grandness and scale had, until the summer of 1788, never before been seen in the musical universe. Its implications for the direction of music in the future, and its influence on future composers is immeasurable. What makes Mozart's Jupiter symphony worthy to share the name of the most powerful god of the Roman world?
The answer to this question comes in the Molto Allegro, and more specifically in its coda, (8:09-8:36). In the coda, Mozart takes the five musical themes or melodies that had been developed throughout the final movement, and does something that no one has ever achieved to the extent that he did, not even the illustrious Beethoven.
What Mozart does is take these five themes and combines them to create a fugato in five-part counterpoint. That is, he takes the five melodies and simultaneously plays them in a variety of combinations and permutations. Imagine five separate melodies, all with their own notes, being played simultaneously, but each constantly changing. It's impossible for the human ear to focus on the enormous amount of notes that this simultaneous playing and constant changing entails. The effect is that the music seems to encompass an infinite amount of sound. With lesser two or three-part fugues, it is occasionally possible to sense everything that is going on. Once you get to four voices, it's nearly impossible to detect all of the nuances of the melodies. With five, well, only God could completely grasp its profundity.