Robert was born in the year $n^{2}$. On his birthday in the year $(n+1)^{2}$, he will be 89 years old. In what year was he born?
Robert was born in the year $n^{2}$ and will be 89 years old in the year $(n+1)^{2}$.

Therefore, $(n+1)^{2}-n^{2}=89$ or $n^{2}+2 n+1-n^{2}=89$ and so $2 n+1=89$ or $n=44$.

Thus, $n^{2}=1936$, so Robert was born in the year 1936 .

ANSWER: 1936