minimum GPA for top math phd programs
At that level, the only value for which there will be no issue is perfect marks, usually 4.0. But admissions, especially for top students to top schools doesn't work like that. More is considered than just GPA. Otherwise there would be no need for admissions committees.
You need a good, but balanced, application. And at the level you are speaking of, once you make the initial cut the non-quantitative things ae probably most important. What do your letters say about you? What research in field have you done? How is the quality of your insight? Do people actually like working with you. What do they predict will be your trajectory.
But &quot;near perfect&quot; is probably fine as long as the rest of it is here. At the margins, in selecting between a couple of candidates, it won't be GPA.
And coming from a good school doesn't hurt, but you need to do well there, just as you would at a &quot;lesser&quot; place. A &quot;C&quot; student from Yale isn't very impressive, I've been told. And lots of students are admitted from those lesser schools.

Actually, if you want better advice than you are likely to find here, ask any of your upper division professors whether you'd be likely to admitted to Columbia if you chose to continue there. Especially someone who has been involved in doctoral admissions in the past several years.