In digital form, the year in which he was born should be written as

n_3 n_2 n_1 n_0

So, what the problem is saying is that

2017 - (1000 n_3 + 100 n_2 + 10 n_1 + n_0) = n_3 + n_2 + n_1 + n_0

or

2017 = 1001 n_3 + 101 n_2 + 11 n_1 + 2 n_0

Now, we can either have n_3 = 1 and n_2 = 9; or n_3 = 2 and n_2 = 0. In the second case we get the equality

2017 = 2002 + 11 n_1 + 2 n_0 <=> 15 = 11 n_1 + 2 n_0.

The only way to satisfy this equation within the natural numbers is with n_1 = 1 and n_2 = 2.

2017 = 1910 + 11 n_2 + 2 n_0 <=> 107 = 11n_1 + 2 n_0

This can be satisfied with n_1 = 9 and n_0 = 4. Since Bertie is in university, this has to be the answer. So, he was born in 1994.