Charles Fefferman proves in 1971, in Annals of Mathematics, that the multiplier operator associated with the unit ball in two or more dimensions is not bounded on the Lp spaces for p different from 2 — thereby refuting a natural conjecture about the convergence of Fourier sums in multiple dimensions that had seemed plausible by analogy with the one-dimensional case. The result, known as "the ball multiplier problem", reveals a fundamental qualitative difference between Fourier analysis in one dimension and in several, and redirects much of the subsequent research in multidimensional harmonic analysis. Fefferman received the Fields Medal in 1978, at age 29.