I believe that Fefferman's disproof in 1971 of the $L^p$ boundedness of disc multiplier for any $p \neq 2$ was considered a great surprise at the time; it showed that the classical result of Bochner and Riesz establishing norm convergence of Fourier series of $L^p$ functions in one dimension failed in two and higher dimensions, if one summed the series in the order of the magnitude of the frequencies (i.e. spherically summed Fourier series). The construction was one of the first applications of Kakeya sets (also known as Besicovitch sets) to harmonic analysis (though there was an earlier paper of Stein and Weiss that also used a related idea). Nowadays, the connection is taken for granted, but it was certainly not obvious at the time of Fefferman's result. (Fefferman himself writes in his paper "... It therefore comes as a surprise, at least to me, that the disc conjecture is false.")

I believe that Fefferman's disproof in 1971 of the $L^p$ boundedness of disc multiplier for any $p \neq 2$ was considered a great surprise at the time; it showed that the classical result of Bochner and Riesz establishing norm convergence of Fourier series of $L^p$ functions in one dimension failed in two and higher dimensions, if one summed the series in the order of the magnitude of the frequencies (i.e. spherically summed Fourier series). The construction was one of the first applications of Kakeya sets (also known as Besicovitch sets) to harmonic analysis (though there was an earlier paper of Stein and Weiss that also used a related idea). Nowadays, the connection is taken for granted, but it was certainly not obvious at the time of Fefferman's result. (Fefferman himself writes in his paper "... It therefore comes as a surprise, at least to me, that the disc conjecture is false.")

I believe that Fefferman's disproof in 1971 of the L^p boundedness of disc multiplier for any $p \neq 2$ was considered a great surprise at the time; it showed that the classical result of Bochner and Riesz establishing norm convergence of Fourier series of L^p functions in one dimension failed in two and higher dimensions, if one summed the series in the order of the magnitude of the frequencies (i.e. spherically summed Fourier series). The construction was one of the first applications of Kakeya sets (also known as Besicovitch sets) to harmonic analysis (though there was an earlier paper of Stein and Weiss that also used a related idea). Nowadays, the connection is taken for granted, but it was certainly not obvious at the time of Fefferman's result. (Fefferman himself writes in his paper "... It therefore comes as a surprise, at least to me, that the disc conjecture is false.")

I believe that Fefferman's disproof in 1971 of the $L^p$ boundedness of disc multiplier for any $p \neq 2$ was considered a great surprise at the time; it showed that the classical result of Bochner and Riesz establishing norm convergence of Fourier series of $L^p$ functions in one dimension failed in two and higher dimensions, if one summed the series in the order of the magnitude of the frequencies (i.e. spherically summed Fourier series). The construction was one of the first applications of Kakeya sets (also known as Besicovitch sets) to harmonic analysis (though there was an earlier paper of Stein and Weiss that also used a related idea). Nowadays, the connection is taken for granted, but it was certainly not obvious at the time of Fefferman's result. (Fefferman himself writes in his paper "... It therefore comes as a surprise, at least to me, that the disc conjecture is false.")