Hit it off with American poet and Irish mathematician (8)
I believe the answer is:
hamilton
'irish mathematician' is the definition.
Although both the answer and definition are singular nouns, I cannot see how one could define the other.
'hit it off with american poet' is the wordplay.
'off' is a deletion indicator (some letters taken off).
'with' is a charade indicator (letters next to each other).
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'poet' becomes 'milton' (John Milton).
'hit' with 'it' removed is 'h'.
'h'+'a'+'milton'='HAMILTON'
'and' is the link.
Can you help me to learn more?
(Other definitions for hamilton that I've seen before include "Capital of Bermuda -- musical (opened in New York, 2015)" , "Bermudian capital" , "Port in Canada - capital of Bermuda" , "Lady . . . . . . . . was Lord Nelson's lover" , "in Scotland or Bermuda" .)