The only example I know is Charlie Fefferman and his first student. 

*Advisor*: Fefferman, born April 18, 1949.  Year of PhD 1969.   
*Student*: [Antonio Córdoba Barba](http://www.genealogy.math.ndsu.nodak.edu/id.php?id=6690), born January 12, 1949. Year of PhD 1974. 

Difference in age: 3 months and change. 

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Trivia: that is the only example I know also where both father and [son](http://www.genealogy.math.ndsu.nodak.edu/id.php?id=83675) studied under the same PhD advisor.