Hermann the Lame, also known as Hermannus Contractus and Hermann of Reichenau, was born in 1013. When he was seven, his father, Wolfrad von Altshausen, and his mother, Hiltrud, sent him to the monastery at Reichenau, where he spent the rest of his life. Unable to walk and confined to a chair that had to be carried around by his fellow monks, Hermann also had difficulty in speaking, but these disabilities did not prevent him from having a brilliant career as a teacher. Although there are legends that he visited more illustrious schools, such as the one at Augsburg, Hermann's own testimony indicates that he acquired information by borrowing works from other libraries and holding discussions with visitors. Many students came to the monastery to learn the subjects of the quadrivium from him.

Hermann's study of music went far beyond the requirements of the liturgy, and of mathematics far...