Translation:My mom was born in nineteen fifty-two.
Второй means 'second' (2nd)
Два means just 'two' (2)
Here the construction implies '52nd'
I don't get the cases for the year. пятьдесят seems to be in accusative, and втором should be prepositional. Am I right and what is the logic here, in general?
IIRC, ordinal numbers (1st, 2nd, etc) in Russian only have the last word of the number declined, the others are in dictionary form.
In the US, we often truncate the date in this kind of context to, e.g., '52 - but with the apostrophe in front of the number.
Couldn't have been born in 1852 or 2152, so 1952 is the only possible date. In the US, we often truncate dates in this context to, e.g., '52.