TITLE: Is it common to decide not to go to graduate school after extensive undergraduate research experience?
QUESTION [5 upvotes]: At the beginning of my undergraduate career, I was almost sure I would want to apply to graduate programs in pure mathematics. Is it common to make such drastic change at the end of one's undergraduate career?

REPLY [3 votes]: I think it's very common. Oxford and Cambridge produce about 400 mathematics graduates a year, only a small fraction do PhDs.
The whole point of undergraduate research opportunities is to give you a feel for what research is. This then allows you to make a more informed choice of whether it's for you. Realizing now that it's not right for you is much better than deciding that three years down the track. 
Many math PhD students are disappointed that it's not more like undergraduates maths where nice well-developed closed theories are studied. Instead a lot of it is trying to understand and make sense of strange examples in order to build a theory.
In terms of your experiences, these things happen. Sometimes only after it's written up does a student discover it's already been done. Research is very hard to plan and progression rate is generally very unclear. 
Do a PhD if you love maths and can't imagine doing anything else.