EDIT: My question in the title was motivated by the following situation.
A mathematician from my field has solved a problem in this field which was considered to be important. In fact he even was awarded an international prize for this work. To solve this problem he has used methods from a completely different field of math which are not known to experts in his original field.
He managed to use these methods to solve few other open problems in the field, although less known than the first one. However he has failed to get other people to be interested in these tools since they require a really different education. For the same reason he cannot suggest such kind of problems to his students since they also would need to spend a lot of time to master the background from different fields, but even if they do, they would probably feel isolated.
Thus I am wondering to what extend this situation is typical, and whether there are other examples of mathematical works whose interdisciplinary character played a negative role in one's career.