By the age of 22 he had been awarded his doctorate, been appointed to a professorship at the Gymnasium at Erlangen and had published an extremely important mathematics paper.
Sa edad na 22 niya ay iginawad sa kanyang titulo ng doktor, ay hihirangin upang angkinin ang isang pagkapropesor sa himnasyo sa Erlangen at nagkaroon na-publish ng isang lubhang mahalagang papel sa matematika.