Chances of Getting into a Top PhD Math Program I know many people have asked similar questions and admissions can sometimes be a crapshoot. But, I am currently a sophomore mathematics major at a non-target top 25 public school. If I can maintain a 3.8+ GPA and major GPA, is that a respectable range for a top grad program? I know GRE scores are a factor too, but have not taken them yet. But I am currently doing undergrad research with a professor (maybe will get my name on a paper) and plan to do departmental honors, which requires me to write a thesis by the time I graduate. Struggling with trying to decide if I want to do industry or grad school. My advisor of course is pushing me towards grad school and tells me if I maintain my grades I will have a good shot. I also plan to take hopefully 2-3 grad courses by the time I graduate. What realistically are my chances? I know it is hard to say without GRE's and no answer is definite, but is it even worth me looking at top tier programs?

Thanks.
It depends on the definition of "a top grad program".

I think your GPA is good. GRE is usually not a (big) factor. I would expect most applicants to have >85/90%. If you are worried take the test as soon as possible. You can choose to send only your best result at the end.

Graduate courses are good only if you get good grades from them.

Try to make sure you get at least 3 strong recommendation letters by the time of the application. You want them to be from your field of interest. At least one should be from a more experienced faculty.

Also if it is possible try to get some undergraduate research experience. It helps, but it is not necessary.