Master Berthold Hawkeye was both the alchemist who mentored Roy Mustang and the estranged father of Riza Hawkeye. A brilliant alchemist, Hawkeye developed the complex theorems necessary to apply flame alchemy at its most powerful and efficient level. However, he refused to share his flame alchemy secrets with Roy, fearing they were too dangerous for someone so young and inexperienced.
Riza described her father as a frightening man with whom she had little connection. Concerned about his life's work being destroyed or misused, Master Hawkeye chose not to keep written notes. Instead, he tattooed a large Transmutation Array containing his findings on his daughter's back, which likely strained their already fragile relationship further.
As an independent alchemist, Master Hawkeye held disdain for the State Military, similar to Izumi Curtis. This disdain was evident in his dismissive reaction to Roy's enlistment during the Ishval Civil War and his preference for living in squalor rather than joining the State Alchemist Program.
When Roy visited his teacher's house to obtain the theory of Flame Alchemy for his own enlistment as a State Alchemist, Master Hawkeye revealed that the theory was tattooed on his daughter's back. Shortly after this revelation, he succumbed to illness and died in Roy's arms, coughing up blood.
(Source: Fullmetal Alchemist Wiki)
