This is a bit of a trick on a classic riddle!
The surgeon is the boy's **father**.
The classic version of this riddle has the surgeon say "I can't operate on this boy, he's my son!" which is in an era where people assumed surgeons were male, the answer would be "the surgeon is his mother."
However, in your version, the surgeon explicitly states, "I'm his father!" So, the surgeon is his father.
