From the Middle Ages onwards, the Mibu family held the positions of repair section chief of Todai-ji-Temple Great Buddha, the chief of Tonomonoryo (Palace Custodians and Supply Bureau), and also, from when the Omiya family was discontinued at the end of Muromachi period, sanhakase (a position teaching mathematics and growing mathematicians) after the era of Takasuke MIBU.
中世以降壬生家は官務に加え修理東大寺大仏長官（または造東大寺次官）・主殿頭、のち室町時代末期に大宮家が断絶したため、壬生孝亮以降は算博士も世襲することとなった。