Tage Gills Torsten Carleman was born in the parish of Visseltofta, county of Kristianstad, in southern Sweden, where his father Karl Johan Carleman was a school teacher and precentor of the local church; his mother was Alma Linnéa Jungbeck. He finished his gymnasium studies in Växjö and was awarded his baccalaureate following the final high school graduation examination on 30 May 1910. In the same year he became a student at Uppsala University. He was awarded his Master of Science degree on 14 December 1912, Licentiate on 29 May 1915, and he defended his Ph.D. thesis On the Neumann-Poincaré problem for a region with corners on 20 January 1917 (undertaken with the supervision of Erik Holmgren), and became Doctor of Philosophy on 31 May 1917.