We have discovered small whirlpools in the Sun, with a size similar to terrestrial hurricanes (<~0.5 Mm). The theory of solar convection predicts them, but they had remained elusive so far. The vortex flows are created at the downdrafts where the plasma returns to the solar interior after cooling down, and we detect them because some magnetic bright points (BPs) follow a logarithmic spiral on their way to being engulfed by a downdraft. Our disk-center observations show 0.9 × 10-2 vortexes per Mm2, with a lifetime of the order of 5 minutes, and with no preferred sense of rotation. They are not evenly spread out over the surface, but they seem to trace the supergranulation and the mesogranulation. These observed properties are strongly biased by our type of measurement, unable to detect vortexes except when they are engulfing magnetic BPs.