There is this sentence in a book named Shoe Dog which has confused me a lot. In what sense is the word born used here?
I'd met other accountants who knew numbers, who had a way with numbers, but Hayes was to the numbers born.
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To the numbers born is a playful use of the form "to the manner born", which is a longstanding term meaning "born into the habit". It is first documented in Shakespeare's Hamlet (1605):
HORATIO: Is it a custom?
HAMLET: Ay, marry, is't: But to my mind, though I am native here and to the manner born, it is a custom more honour'd in the breach than the observance.
A newspaper later played on this Shakespearean form by changing "manner" to "manor" to indicate a person born into a noble family, itself an metaphor for a country maintaining a longstanding occupation of another (Times of London, 1859):
"Before Solferino, Austria was only an intruder in Italy; now she is as one 'to the manor born'."
As pointed out by Fattie in the comment below, "To the Manor Born" was used as a title of an exceptionally popular UK television situation comedy series. Its entry into widespread public usage, through this, caused many of us Brits to assume that this was the original or only meaning of the phrase.
The author is making a further play on words by applying this formation a new noun: "numbers", rather than "manner". It means that Hayes was born with a skill in numbers, or with a destiny to become a skillful accountant.
BORN is an adjective:
: destined from or as if from birth
// born to succeed
In your example there is also inversion used to make the sentence more emphatic:
"Hayes was great at arithmetic as if from birth"