  One can hardly believe that there is still something to be said about cubic
equations. To dodge this doubt, we will instead try and say something about
Sylvester. He doubtless found a way of solving cubic equations. As mentioned by
Rota, it was the only method in this vein that he could remember. We realize
that in the generic case Sylvester's magnificent approach aimed at reduced
cubic equations boils down to an easy identity expressing a cubic polynomial as
a sum of two third powers of linear forms. This leads to Cardano's formula for
cubic equations involving the third roots of unity.
