Should I apply to my undergrad institution's graduate program?

[PieceOfPi]

I am almost done with applying to graduate schools in mathematics. My new question now is whether to apply my undergraduate institution's graduate program.

First of all, all the professors that I have talked to told me that I should go somewhere else for graduate school. And I strongly agree with them; as much as I like my current place, I feel like I would learn more if I go elsewhere. And I have already been here for four years, so I think it is time for me to go somewhere new.

On the other hand, I am relatively confident that I would get into my current school if I apply, so it would be a good safety net. Furthermore, I like the people who are in this school's math department, so it also gives me a safety net in terms of the atmosphere as well.

So I am wondering what to do about this. The deadline for this school's application is January 15th, so I am trying to make up my mind about it soon. Let me know if you have any thoughts.

Thanks

 

[Ryker]

I'd just apply if I were you. You've got nothing to lose, apart from the application fees, and you can always make the decision where to go once you've received all the offers.