What are some examples of big results in mathematics and or physics that took a long time to be considered groundbreaking? What was the length of time from the original publication to the recognition?
What are some examples for which this process was really quick?
There is no point in giving examples on the second question, because for most truly groundbreaking results this time is really short.
On the first question, one can mention almost all results of Archimedes and Apollonius, which had almost no development in antiquity, and during the middle age there were no people who understood them. (People read and discussed more elementary books of Euclid, but not Archnimedes or Apollonius). True recognition only came in 16th century.
In the modern times, the period is smaller. One can mention Sharkovskii's theorem (see Wikipedia) which was proved in 1964, but was not noticed by the large mathematics community until the paper by Li and Yorke (1975) who proved a special case. This special case created a lot of excitement.
Another example is Fatou-Julia theory of iteration of rational functions created around 1920. It was dormant and almost forgotten until new developments made it one of the most fashionable areas of mathematics in the middle 1980s.
Discovery of non-Euclidean geometries in 19th century, it took about 40-50 years for them to get accepted.
From an article by Freeman Dyson:
In the year 1865, Maxwell published his paper 'a dynamical theory of the electromagnetic field' ... we, with the advantage of hindsight can clearly see that his paper was the most important event in the 19th C in the history of the physical sciences ... but the importance of Maxwells work was not obvious to his contemporaries. For more than twenty years his work was largely ignored. Physicists found it hard to understand because the equations were complicated. Mathematicians found it hard to understand as he used physical language. It was regarded as an obscure speculation without much experimental support.
The physicist Michael Pupin, in his autobiography 'from immigrant to inventor' describes how he travelled from America to Europe in search of someone who understood Maxwell ... Pupin went first to Cambridge hoping to learn the theory from Maxwell himself. He did not know that Maxwell had died four years earlier (!). After learning of his death he stayed on in Cambridge and was assigned a college tutor who knew less about Maxwell than he did and was only interested in teaching him to answer questions in the Mathematical Tripos.
He was amazed to discover, as he said, 'How few the physicists were that had caught the meaning of the theory, even after twenty years after Maxwell had first stated it in 1865'.
The Michelson-Morley experiment took a very long time to be widely known, and it also took a very long time to be accepted, even by Michelson and Morley themselves. The original experiment was in 1887, but Michelson continued doing different versions of the experiment until 1929, trying to get the "right" result. Einstein may or may not have known about it in 1905, and if he did, it played no major part in his reasoning.
Special relativity also took a long time to be widely accepted. Einstein published it in 1905, but there was a lot of skepticism until around World War II. The early evidence was either uncertain or ambiguous. The more solid evidence came with Ives-Stilwell in 1938 and Rossi-Hall in 1941.
