Although it is common that many composers and arrangers don't really need to hear the music in order to compose great pieces, Mozart was unique. His first language was really music. Much of his music was almost like it was being dictated to him and all he had to do was write it down. I think there is a scene in "Amadeus" where it shows him composing, then a flash, and he knew the piece complete and just had to write it down. I think that was how it was like for him. He even wrote a few pieces without a score - wrote the first violin part from beginning to end, second violin from beginning to end, viola... Sick, just sick.
I do think Mozart's mind was on the same genius level as Einstein, Da Vinci or any other great science mind, except in music.
Beethoven was a genius too - he just had to revise a lot to get it perfect. He made the ideal Romantic Period figure since he suffered for his art. Very little of the 19th Century Western classical music was unaffected by Beethoven
I agree completely with you about Mozart and that in the field of music he ranks as an absolute genius, as great in music as da Vinci and Einstein were in theirs. It did come naturally to him, as you say, it was his natural language, his mother tongue. And the music itself is simply perfect in parts, every note is exactly right (remember his famous dialogue with the Austrian Emperor, Josef II, when the Emperor muttered, sitting at the keyboard, "Too many notes, dear Mozart. Too many notes," to which Mozart shot back that every note was exactly where it was supposed to be and that there were neither too few nor too many. Deference was not a defining characteristic of his).
Amadeus captured very well the idea that one can be an extraordinary creative genius in one field, - a field which one treats with utter dedication and a quest for perfection - and a rather earthy human being in other walks of life. It didn't touch upon Mozart's politics, which were extremely radical (he was an ardent freemason, and The Marriage of Figaro was based on a somewhat subversive radical text by the French aristocrat Beaumarchais, The Barber of Seville.)
Re the contrast with Beethoven, I have wondered what might have happened with Mozart had he been born 20 years later than he actually was; he would have been around to see the stifling and rather deferential society where composers and musicians depended on aristocratic patronage and favour, fall out of fashion. Career-wise, it was a lot easier for Beethoven to flourish, although, as you rightly say, he suffered hugely in personal and psychological terms. Josef Haydn, who knew them both, rated both very highly long before either of them had become celebrated.
Cheers
