I'm about to finish my undergraduates studies; I majored in mathematics and minored in physics, and I always intended on going to grad school to pursue a PhD in mathematics, but I've been having doubts recently. I did well in all my courses (3.92 GPA), but I'm trying to seriously consider if my background is strong enough now and if I'd truly have the motivation to stick it out. I've also been thinking even if I decided to give it a shot, it might be nice to take some time off for rest and to improve on some of my weaker areas. But I've been told by a few people that if you want to do a PhD in mathematics, you have to go pretty much right after undergrad, mainly because recent letters of recommendation are so important, and professors forget you after a time. So I wanted to know if this is true, and also thought I'd ask for advice if anyone has been in a similar situation.
Answer
The other answers don't really address the issue of recommendations, so let me, at least briefly. I've been on our math PhD admission committee several times and we get many applications from people who've gotten their undergrad some time ago.
First, yes there is some truth to it being easier to get in right after your undergrad degree. The letters of recommendation are important. If your professors know you quite well, and the department is relatively small, they should still be able to write you decent letters after a year or two hiatus, but if it gets to 5-10 years, they may not, and with that kind of time lapse, their letters won't count for as much anyway.
My advice would be to consider what else you want to do. Is there something else you really want to do for awhile (peace corps, travel, interesting job opportunity)? If so, it won't kill your chances for grad school, but you may have to apply to more backup schools. If you're out for longer, it might be best to do a masters first before getting into a PhD program.
If you don't have any definite ideas, why don't you try applying to a few masters programs (Vladhagan's suggestion of trying a masters first is a good idea to give you a sense of what you want to do and give yourself a better background) and a few PhD programs that seem interesting to you? At the same time, maybe go to a career fair and send out a few job applications in the spring? The PhD programs that accept you (at least if you're in the US) at least should give you an opportunity to visit, so even if you're undecided about a PhD in the spring, visiting these schools (and similarly any job interview impressions) may help you make a decision.
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