He received his doctorate from Göttingen in 1852 and he was to be the last pupil of Gauss . However he was not well trained in advanced mathematics and fully realised the deficiencies in his mathematical education.
Niya natapos ang kanyang titulo ng doktor mula sa Gottingen sa 1852 at siya ay ang huling mag-aaral ng gauss. Gayunman siya ay hindi mabuti sanay na sa mga advanced na matematika at ganap na realised ang deficiencies sa kanyang matematiko edukasyon.