 The original solution of the Hopf invariant one problem operations by J. F. Adams was very long and complicated, using secondary cohomology operations.Atiyah showed how primary operations in K-theory could be used to give a short solution taking only a few lines, and in joint work with Adams also proved analogues of the result at odd primes.The Atiyah–Hirzebruch spectral sequence relates the ordinary cohomology of a space to its generalized cohomology theory.