I think neither of you is right, but I am not certain...
The date-of-birth idea is by the way very interesting because I
am 19 though I was not born on 30 Jan 1991

And in my little world the day is the first number, not the month. Usually I would write that date as 30.1.1991 or as 1991-01-30 (when naming files on the computer, for example), not as 01-30-1991.
The next poster usually writes dates like "year-day-month"