Gleason's theorem has a constructive proof

Gleason's theorem for R-3 says that if f is a nonnegative function on the u nit sphere with the property that f(x) + f(y) + f(z) is a fixed constant fo r each triple x, y, z of mutually orthogonal unit vectors, then f is a quad ratic form. We examine the issues raised by discussions in this journal reg arding the possibility of constructive proof of Gleason's theorem in light of the recent publication of such a proof.