Applying to grad school for mathematics with low GPA, but reluctant to bring up the health issues that caused it I'm currently a 3rd year undergrad majoring in math/physics. I was admitted to my university through an honors program due to outstanding high school achievement (my university is a large public one, moderately well known in the US) with several scholarships. 

But after my first semester, I fell back into a recurring bout of severe depression, and did not get help. My grades ended up tanking that next semester (C average). I thought I had overcome it by my second year, but soon developed psychosis and could no longer focus on studying; I neglected my health and hygiene, and I couldn't even get up some mornings to get to class. None of my professors are aware of my situation. 

I finally sought help last spring and I've been doing better (keeping up with work, getting better grades, etc), but I feel like nothing will ever make up for those two years of mediocre grades. My overall GPA right now is sitting around a 2.5. I feel like while this is possible to explain away, I'm reluctant to divulge information about my severe mental illness to admissions because there is still a lot of stigma associated with it. I've seen mixed answers as to whether or not it's a good idea to do.

My question is, is there still a way for me to pursue applied mathematics in graduate school? Is graduate school aiming too high? And if so, do I talk about my limitations as far as my health is concerned? 

I love math, and love learning. I've done a few practice Math Subject GRE exams, and they were fairly easy (as long as I study for the parts I'm not 100% on, of course). I've also done a few small math projects with grad students and I've worked in a lab since I was a freshman; I feel like I'm passionate enough about the subject to succeed but I'm afraid admission committees will not look past my GPA to see that and wouldn't risk having someone like me in their program.
You certainly have no obligation to mention your depression when applying.  You can say nothing about the subject and let your recently improved work stand for itself, or you can allude to personal issues and reassure the committee that they are no longer troubling you.  If you do well in your last two years of college, then difficulties in your first two will matter far less.

On the other hand, I think it could be worth mentioning.  In mathematics there's less stigma surrounding depression than you might expect (at least in the U.S.).  Compared with the rest of society, the mathematical community is unusually tolerant of various forms of psychological variation, provided that you can do good mathematics.  A number of famous mathematicians have suffered from depression, so it would be foolish to dismiss an applicant for that reason, and many mathematicians know colleagues who have been depressed.  The key question is whether you have found treatment that keeps it under control.  If you leave your situation vague, then you leave open the possibility that whatever was causing the bad grades might return.  If you explain that you sought treatment for depression and found it successful, then that will reassure the committee that your recent improvements are likely to be long lasting.

If you do mention this issue, I'd keep it brief.  A single sentence in your personal statement would be enough (the committee doesn't need or want any details about your health or treatment).  And, as I said above, there's no need to say anything at all if you aren't comfortable with it.  However, I don't believe doing so could hurt your application, and it might help explain your grades.