"Do you have a son, professor?"
Translation:A bheil mac agaibh ollaimh?
Agaibh.. agad would be rather impolite in this case, just like with grandfather.
Agaibh means 'at you' and is used for plural as well as formal singular, where agad is used informal/singular, same meaning. https://duome.eu/tips/en/gd
According to Faclair.com agaidh is the gen sing of agadh meaning hesitation/hesitating, so you've learned a new word that way. :)