  Mahowald's conjecture arose as part of a program attempting to view chromatic
phenomena in stable homotopy theory through the lens of the classical Adams
spectral sequence. The conjecture predicts the existence of nonzero classes in
the cohomology of the finite sub-Hopf algebras $A(n)$ of the mod 2 Steenrod
algebra that correspond to generators in the homotopy rings of certain periodic
spectra. The purpose of this note is to present a proof of the conjecture.
