The Smith conjecture; Morgan and Bass could write in 1984 that "the Smith conjecture stands in the first rank of mathematical problems when measured by the amount and depth of new mathematics required to solve it." See https://en.wikipedia.org/wiki/Smith_conjecture for the statement. You get convinced of the huge variety of techniques used in the proof, just by looking at the table of contents of the book: Morgan, J. W. and Bass, H. (Eds.). The Smith Conjecture (Papers Presented at the Symposium Held at Columbia University, New York, 1979. Orlando, FL: Academic Press, 1984)