Harald became the first of the two Bohr brothers to earn a master's degree, which he earned for mathematics in April 1909. Niels took another nine months to earn his on the electron theory of metals, a topic assigned by his supervisor, Christiansen. Bohr subsequently elaborated his master's thesis into his much-larger Doctor of Philosophy (dr. phil.) thesis. He surveyed the literature on the subject, settling on a model postulated by Paul Drude and elaborated by Hendrik Lorentz, in which the electrons in a metal are considered to behave like a gas. Bohr extended Lorentz's model, but was still unable to account for phenomena like the Hall effect, and concluded that electron theory could not fully explain the magnetic properties of metals. The thesis was accepted in April 1911, and Bohr conducted his formal defence on 13 May. Harald had received his doctorate the previous year. Bohr's thesis was groundbreaking, but attracted little interest outside Scandinavia because it was written in Danish, a Copenhagen University requirement at the time. In 1921, the Dutch physicist Hendrika Johanna van Leeuwen would independently derive a theorem in Bohr's thesis that is today known as the Bohr–Van Leeuwen theorem.