The "Ordo servundum in addiscendis disciplinis mathematicis" is a milestone in the history of the teaching of mathematics. Conceived by Christoph Clavius for the Jesuit Colleges, it was not only a syllabus for mathematical studies for the students at Jesuit colleges but also an instrument for training mathematics teachers. Its coherence and its skilful, innovative, modular format have made it a masterpiece of pedagogic technique. This marks the end of a long and arduous journey throughout which Clavius' patient and persistent persuasion convinced the Company that mathematics should be an integral part of the syllabus in Jesuit colleges.