The PHENIX experiment presents results from the Relativistic Heavy Ion Collider 2005 run with polarized proton collisions at root s=200 GeV, for inclusive pi(0) production at midrapidity. Unpolarized cross section results are given for transverse momenta p(T)=0.5 to 20 GeV/c, extending the range of published data to both lower and higher p(T). The cross section is described well for p(T)< 1 GeV/c by an exponential in p(T), and, for p(T)> 2 GeV/c, by perturbative QCD. Double helicity asymmetries A(LL) are presented based on a factor of 5 improvement in uncertainties as compared to previously published results, due to both an improved beam polarization of 50%, and to higher integrated luminosity. These measurements are sensitive to the gluon polarization in the proton. Using one representative model of gluon polarization it is demonstrated that the gluon spin contribution to the proton spin is significantly constrained.