Is is grammatically right to leave out the definite article in the following sentence?
what would change if the word about were not added?
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As a native speaker of British English, I would use either "around aged 30", or "around the age of 30" instead of "at about age 30".
The related things to know here are:
I would never say "at about the age 30" or "at about age 30", as it seems grammatically confused. Instead, I might say "At about aged 30", or "at about the age of 30", because they are grammatically correct. I would normally replace 'at about' with 'around' though.
EDIT. Without 'about', the correct phrases would be "at aged 30", or "at the age of 30".
EDIT EDIT. I would use "around aged 30", even if we were talking in present simple tense.