convincing evidence for the existence of galaxies with $M_{\rm star}>3\times10^{11}$ M$_{\sun}$ at $z>4$ is still missing (e.g., @dunlop07).

Closely related to this issue is the very intriguing finding that the number density of the most massive galaxies ($M_{\rm star}> 3\times 10^{11}$ M$_{\sun}$) seems to evolve very little from $z\sim4$ to $z\sim1.5$ [@marchesini09], suggesting that the most massive galaxies in the universe were mostly in place already at $z\sim3.5$, and implying potentially severe disagreements with the predictions from the latest generations of semi-analytic models of galaxy formation.

However, uncertainties on the observed SMF are still large, especially at the high-mass end and at high redshifts [@marchesini09]. At $z\lesssim3$, the SMF error budget is now almost entirely dominated by systematic uncertainties caused by the different SED-modeling assumptions adopted to derive stellar masses (e.g., stellar population synthesis models or initial mass function (IMF)). Progress in reducing the impact of these systematic uncertainties necessarily requires better calibrations of the stellar mass estimates (e.g., through measurements of the dynamical masses from studies of their kinematics). At $3<z<4$, instead, the contributions of photometric redshift errors, small-number statistics, and sample variance (due to the relatively small probed volumes) are still significant, and dominate the total error budget 