Whenever a (major) new result is proved, it is typically only understood only by a handful of experts, then by people who work in close vicinity, gradually understood by everyone in the general subject area, and then by a broad mathematical audience, and if the result is particularly important, eventually trickle down to mainstream science. This process is a more realistic version of the adage "there are only two kinds of mathematical problems: trivial and impossible. It is impossible until you solve it and then it becomes trivial."
I am asking what is the expected amount of time (in a modern sense) before a major breakthrough in mathematics is 'digested'. For instance, the invention of calculus was no doubt at the time a tour de force, but by now it is understood by almost all professional mathematicians and is taught to a broad audience at a relatively low level. Doron Zeilberger once remarked, on his opinion page, that eventually the proof of Fermat's Last Theorem can be understood by undergraduates.
Of course, I am asking for the average time, as there are great many examples of variances. I believe that the proof that there exist infinitely many bounded gaps between primes will be digested far faster than, say, the proof of Weil's conjectures, due to the relatively simple principles and machinery that goes into the former. Thus a discussion on the variance and the reliance on particular subject matters might be enlightening as well.