An example of an important solution to a little-known problem might be Frank P. Ramsey's "On a problem of formal logic" in Proc. London Math. Soc. 30 (1930) 264-286. The problem was in logic and not well-known even to logicians, but Ramsey's solution was taken up by combinatorialists (notably Erdős and Szekeres) and it grew into the important field now known as Ramsey theory.
John Stillwell
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