Returning to Scotland in 1905, Wedderburn worked for four years at the University of Edinburgh as an assistant to George Chrystal, who supervised his D.Sc, awarded in 1908 for a thesis titled "On Hypercomplex Numbers". He gained a PhD in algebra from the University of Edinburgh in 1908. From 1906 to 1908, Wedderburn edited the "Proceedings of the Edinburgh Mathematical Society". In 1909, he returned to the United States to become a Preceptor in Mathematics at Princeton University; his colleagues included Luther P. Eisenhart, Oswald Veblen, Gilbert Ames Bliss, and George Birkhoff.