Here is a really smart passage by Jamie James from his 1993 book The Music of the Spheres: Music, Science, and the Natural Order of the Universe, that could help you appreciate what Beethoven did, apart from writing some music that we find stirring and fun to listen to today. Beethoven in music, and Romanticism in general, overturned the Pythagorean view of the orderly cosmos that had persisted from ancient Greece till around 1800. But that may yet turn out to be more of a temporary aberration than we realize.

Picture to yourself, if you can, a universe in which everything makes sense. A serene order presides over the earth around you, and the heavens above revolve in sublime harmony. Everything you can see and hear and know is an aspect of the ultimate truth: the noble simplicity of a geometric theorem, the predictability of the movements of heavenly bodies, the harmonious beauty of a well-proportioned fugue — all are reflections of the essential perfection of the universe. And here on earth, too, no less than in the heavens and in the world of ideas, order prevails: every creature from the oyster to the emperor has its place, preordained and eternal. It is not simply a matter of faith: the best philosophical and scientific minds have proved that it is so.

This is no New Age fantasy but our own world as scientists, philosophers, and artists knew it until the advent of the Industrial Revolution and its companion in the arts, the Romantic movement. Those ideals are gone forever.

...Two hundred years ago the world was turned upside down. The social order abruptly tumbled, a phenomenon symbolized by the falling stones of the Bastille, and simultaneously a revolution took place in what came to be called the humanities. The pious moralism of Samuel Richardson and Samuel Johnson, the dominant literary personalities of eighteenth-century London, was supplanted by the idiosyncratic, even bizarre visions of Blake and Coleridge. In painting, the serene, sheltering arcadias of Watteau and Gainsborough were displaced by Goya’s horrific allegories, Fuseli’s nightmares, Delacroix’s patriotic gore.

And in music there was Beethoven. Between the finale of Mozart's Così fan tutte, which in 1790 proclaimed, “Happy is the man who makes reason his guide,” and the willful, majestic melancholy of Beethoven's late string quartets, thirty-five years later, we may trace a profound alteration in temperament. Gloated the German critic Ludwig Borne in 1830, writing about the young generation so profoundly influenced by Beethoven, “It is a joy to see how the industrious Romantics light a match to everything and tear it down, and push great wheelbarrowfuls of rules and Classical rubbish away from the scene of the conflagration.” Of course the rules and rubbish he refers to are precisely the concepts of the orderly cosmos and the Great Chain of Being that had served as the cornerstones of Western thought since its inception.

Thus how supremely ironic it is that this revolutionary school of music, Romanticism, should today be enshrined as the official culture, marginalizing what preceded it and what was to come after. Works that literally incited revolution in Wagner’s Dresden, in Verdi’s Milan, are now considered to be the stately theme music of established authority. Pieces that modern audiences listen to in hushed reverence sometimes provoked outrage at their premieres. Christoph von Dohnanyi recently made this comment in a private conversation: “Everyone thinks that he understands Beethoven better than contemporary music. In fact, it is much more difficult to understand Beethoven than any modern composer you can name, without a great deal of study.” We may interpret that to mean that unless we understand the musical world order that Beethoven was overturning, we shall never understand the meaning of his achievement. Yes, it is great music — but why? Not because it has lovely melodies, nor because its stirring rhythms stimulate nervous excitement. It is great music because it pointed the way to a new direction.

...Paradoxically, modern concertgoers brought up on a steady diet of Beethoven, Mendelssohn, and Brahms (and, as we have noted, Bach and Handel, who until recently were made to sound as much like them as possible) often find themselves perplexed when they hear the music of their own time. They have been conditioned to expect, and thus they demand, a thrilling emotional impact, what might be called the Romantic buzz, from music. When they hear the music of their contemporaries they are puzzled, because it does not sound like music from the [19th] century. That might seem to contradict Christoph von Dohnanyi’s comment, but what he was driving at is that a sensitive modern concertgoer is more likely to arrive at a true, intuitive understanding of music composed in his lifetime, however enigmatic it might be, than of Beethoven’s works; yet a simplistic misunderstanding of Beethoven is nonetheless the most common interpretive attitude of all.

...Until we understand the sublime cosmic order that Beethoven and his progeny overturned... he will remain as remote from us as the ancien régime itself.

The complete first chapter is available at http://jamiejamesauthor.com/music-spheres/excerpt.html and has a bit more to say about the parallel evolution of science and music and our attitudes toward each.