Master Berthold Hawkeye was both the alchemist who mentored Roy Mustang as well as the estranged father of Riza Hawkeye.
A brilliant alchemist, Hawkeye postulated the complex and intricate theorems necessary to apply flame alchemy at its most powerful and efficient level, but refused to pass on his flame alchemy secrets to his pupil, thinking them too dangerous for young and naive Roy. Riza describes her father as a frightening man with whom she did not generally associate and could not at all relate. Afraid of his life’s work being destroyed and what his Flame Alchemy knowledge could do if it fell into the wrong hands, Master Hawkeye refrained from keeping notes in the normal fashion and, instead, tattooed a large Transmutation Array containing the culmination of his craft and findings on his daughter’s back, perhaps further straining - or serving as an indication of - the Hawkeyes’ already shaky relationship.
Master Hawkeye, as an independent alchemist, appears to hold some disdain for the State Military (much like Izumi Curtis), as revealed by his flippant reaction to Roy’s enlistment during the Ishval Civil War as well as his preference of living in squalor with all his genius over joining the State Alchemist Program.
As Roy returned to his teacher’s house in an attempt to get hold of the theory of Flame Alchemy to enlist as a State Alchemist (he was just a regular soldier at that time), Master Hawkeye revealed to him his daughter possessed the theory and succumbed to illness, coughing up blood as he died in Roy’s arms.