The self-assembly of the protein tau into neurofibrillary tangles is one of the hallmarks of Alzheimer's disease and related tauopathies. Still, the molecular mechanism of tau aggregation is largely unknown. This problem may be addressed by systematically obtaining reproducible in vitro kinetics measurements under quiescent conditions in the absence of triggering substances. Here, we implement this strategy by developing protocols for obtaining an ultrapure tau fragment (residues 304-380 of tau441) and for performing spontaneous aggregation assays with reproducible kinetics under quiescent conditions. We are thus able to identify the mechanism of fibril formation of the tau 304-380 fragment at physiological pH using fluorescence spectroscopy and mass spectrometry. We find that primary nucleation is slow, and that secondary processes dominate the aggregation process once the initial aggregates are formed. Moreover, our results further show that secondary nucleation of monomers on fibril surfaces dominates over fragmentation of fibrils. Using separate isotopes in monomers and fibrils, through mass spectroscopy measurements, we verify the isotope composition of the intermediate oligomeric species, which reveals that these small aggregates are generated from monomer through secondary nucleation. Our results provide a framework for understanding the processes leading to tau aggregation in disease and for selecting possible tau forms as targets in the development of therapeutic interventions in Alzheimer's disease.