At low pH insulin is highly prone to self-assembly into amyloid fibrils. The process has been proposed to be affected by the existence of secondary nucleation pathways, in which already formed fibrils are able to catalyze the formation of new fibrils. In this work, we studied the fibrillation process of human insulin in a wide range of protein concentrations. Thioflavin T fluorescence was used for its ability to selectively detect amyloid fibrils, by mechanisms that involve the interaction between the dye and the accessible surface of the fibrils. Our results show that the rate of fibrillation and the Thioflavin T fluorescence intensity saturate at high protein concentration and that, surprisingly, the two parameters are proportional to each other. Because Thioflavin T fluorescence is likely to depend on the accessible surface of the fibrils, we suggest that the overall fibrillation kinetics is mainly governed by the accessible surface, through secondary nucleation mechanisms. Moreover, a statistical study of the fibrillation kinetics suggests that the early stages of the process are affected by stochastic nucleation events.