Cantor ya gabatar da karatunsa a kan ka'idar lambobi a Jami'ar Berlin a 1867. Bayan ya koyar a takaice a makarantar 'yan mata ta Berlin, Cantor ya dauki matsayi a Jami'ar Halle, inda ya shafe dukan aikinsa. An ba shi habilitation da ake buƙata don karatunsa, kuma a kan ka'idar lambobi, wanda ya gabatar a 1869 a lokacin da aka nada shi a Jami'ar Halle.A 1874, Cantor ya auri Vally Guttmann. Suna da 'ya'ya shida, na ƙarshe (Rudolph) wanda aka haifa a 1886. Cantor ya iya tallafawa iyali duk da biyan kuɗi na ilimi, godiya ga gadonsa daga mahaifinsa. A lokacin hutun amarci a cikin tsaunukan Harz, Cantor ya shafe lokaci mai yawa a cikin tattaunawar lissafi tare da Richard Dedindek, wanda ya sadu da shi shekaru biyu da suka gabata yayin hutu a Switzerland. Tambaya: Menene Cantor yake yi a lokacin hutun amarcinsa?
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