Is Kate tamed or pretending to be tamed? Is her obeisance to Petruchio sincere or ironic? The Taming of the Shrew has been controversial at least since 1897, when George Bernard Shaw called Shakespeare’s play an “insult to womanhood and manhood.” Which is why modern productions find ways to rethink it. Jean-Christophe Maillot recasts his ballet as the eternal search for one’s ideal other half. —L.J.