The Immortal Triangle - How Compact History Can Be!

While musing over the birthday of Mozart, I was struck at how music was transmogrified in such a short period. The three giants, Haydn, Mozart and Beethoven knew one another. Both Mozart and Beethoven had Haydn as a teacher for a short period.
By gazing at certain dates, one can easily see the compactness of those times:
Haydn was born in 1743.
Mozart in 1756.
Beethoven in 1770.
Most interesting is the reality that at the beginning, Haydn was Mozart's mentor, but the process reversed due to Haydn's surviving Mozart by many years, and becoming ultimately a kind of student of his former student by being witness to the miracle that Mozart became, and influenced by the language that emerged from this unprecedented genius.
And Beethoven, as a teen-ager, met Mozart once. At that meeting Mozart prophetically uttered "one day Beethoven will make a big noise in the world."
And so, from 1743 to 1827 (the passing of Beethoven), the world of music received, arguably, its most important transfusion.