What is your favorite example of a celebrated mathematical fact that had a hard time to become accepted by the community, but after overcoming some initial "resistance" quickly took on?
It can be a theorem, a proof method, an algorithm or a definition, that is
- widely known and
- very useful in the present day,
- less than 99 years old; this is in order to avoid examples from the very distant past, such the difficulties Grassmann's work had being accepted
but which at the time of its inception was not appreciated, misunderstood or ignored by the mathematical community, before it became mainstream or inspired other research which in turn became mainstream. This is a partial converse question to this one that asks for mathematical facts that were quickly accepted but then discarded by the community. This and this question are somewhat related, but former focuses on people (resp. their entire works, see Grassmann) not being accepted, rather then individual results, whereas the latter solely on famous articles rejected by journal; also, the results that are being mentioned in these links are often rather old and do not fit this question.
Example. Numerical optimization: The first quasi-Newton algorithm was discovered in 1959 and "was not accepted for publication; it
remained as a technical report for more than thirty years until it appeared in the ﬁrst issue of the SIAM Journal on Optimization in 1991" (Nocedal & Wright, Numerical Optimization).
But the algorithm inspired a slew of other variants, has been cited over 2000 times to this day and quasi-Newton type algorithms are still state-of-the-art in for certain optimization problems.