In 1960, at just 47 years old, Matheson became the first Vice-Chancellor of Monash University, a position he held until 1976. Given only 12 months to prepare for the opening of the University, Matheson worked with exceptional speed and effectiveness. He assembled staff, established courses, and set up faculties, teaching and research facilities. When Monash opened, Matheson led and oversaw rapid development, from an empty site in Clayton, to a university recognised internationally for excellence in research and teaching. When the University opened in 1961, it had just 347 students; but 11 years into Matheson's term, it had expanded to over 12,000. Matheson managed the tumultuous years of student activism at Monash in the late 1960s and early 1970s. He was often criticised by some of the more radical students, but succeeded in maintaining strong academic standards throughout. His responsiveness to student ideas and demands meant the unrest was contained as successfully as possible.