Doctor of Philosophy

Abstract

Having completed the eight university semesters required for a doctor’s degree, Hilbert began to consider possible subjects for his dissertation. In this work he would be expected to make some sort of original contribution to mathematics. At first he thought that he might like to investigate a generalization of continued fractions; and he went to Lindemann, who was his “Doctor-Father,” with this proposal. Lindemann informed him that unfortunately such a generalization had already been given by Jacobi. Why not, Lindemann suggested, take instead a problem in the theory of algebraic invariants.