 After serving in the army, Guidobaldo returned to his estate of (Monte Baroccio) Mombaroccio in the Marche, where he was able to spend his time doing research into mathematics, mechanics, astronomy and optics.He studied mathematics under Federico Commandino during this period and became one of his most staunch disciples.He also became a friend of Bernardino Baldi, who was also a student of Commandino around the same time.