Schouten was an effective university administrator and leader of mathematical societies. During his tenure as professor and as institute head he was involved in various controversies with the topologist and intuitionist mathematician L. E. J. Brouwer. He was a shrewd investor as well as mathematician and successfully managed the budget of the institute and Dutch mathematical society. He hosted the International Congress of Mathematicians in Amsterdam in early 1954, and gave the opening address. Schouten was one of the founders of the Mathematisch Centrum in Amsterdam.