This lecture: 'Some Milestones in the Life and Work of Mathematical Chemist J.J. van Laar (1860-1938)' discusses his life and three important examples of his work. Insufficient schooling meant that Van Laar was not permitted to take academic examinations and this lack of recognized qualifications led to problems in establishing his scientific career. These difficulties brought him close to mental collapse in 1896 and 1911. At the University of Amsterdam he was opposed by J.D. Van der Waals (1837-1923) but was highly appreciated by H.W. Bakhuis Roozeboom (1854-1907). This lecture focuses on some of his achievements and describes his recognition as a scientist. H.A. Lorentz (1853-1928) played an important part in Van Laar's development as a mathematical chemist. Van Laar is said to have endowed him with 'the father role' and it is certain that Lorentz encouraged and supported him. The study of mathematical chemistry as Van Laar practiced it no longer exists. Together with Bakhuis Roozeboom, Van Laar is the founder of phase theory. Examples of his work are discussed in the sections of the melting point line of tin amalgam (1902), the spinodal (1905) and retrograde solubility (1908). The lecture concludes with a description of the final years of his life and includes the kind letter of condolence by L.S. Ornstein (1880-1941). Throughout the lecture reference is made to fragments of letters and to photographs.