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Since 'Ad Hoc' solutions are not generalizable, this may mean that Adderall could not cast outside of Mathamancy, or that his spells were idiosyncratically unique to his assigned tasks.
Real World References
Ad Hoc is Latin for "For This" and refers to a solution designed for a specific task, and not applicable to other purposes.
Adderall is an amphetamine used to treat attention-deficit hyperactivity disorder (ADHD) and narcolepsy. Many people also take it (unprescribed and usually illegal) to help focus on work, training, or study.
His nickname, "Add," is a reference to being a practitioner of Mathamancy.
Hawk is a type of bird, tying into his Flight special.