E, as the youngest male, must be $8$ or $11$.
J is $6$ or $3$ (if we allow 'brother-in-law' to describe her husband's sister's husband).
F has exactly one brother, so must be $5$, $7$, $8$ or $10$.
C has a husband, and says her father is a mathematician, so C is $5$. Therefore $1$ is a mathematician, and as the oldest mathematician in the family can be identified as I. F can no longer be $5$.
D, having cousins in the tree, must be one of the third generation.
There is now no option but to assume that J is $6$. [Michael hasn't quite explained why: he probably noticed that $6$ is C's husband, and therefore not a mathematician, and so J can't be $3$.] From here we can deduce that $4$ is a mathematician, and that E and B are his children, since they have each said that their father is a mathematician.
We can now rule out F being $7$ or $8$, and so F is $10$. F tells us that her parents (C and J) are not mathematicians, and her brother ($11$) is.
H is a mother of two mathematicians, so she is $3$, and either $7$ or $9$ is a mathematician (we were told that E is). This means that for D to have just one mathematician cousin, D must be $7$ and F must be a non-mathematician.
Finally, A must be $11$, as his father is a mathematician, so K is $11$. We still haven't said which of $7$ and $9$ is the mathematician, but since we haven't yet got a female mathematician, it must be B.
