Hello all, I am currently an undergraduate student (just finished my first semester) at Stony Brook University. Basically, I'm fairly certain that I want to go into pure math or theoretical physics, it's just that I feel like I may not be up to par with everyone else who will be competing with me for jobs in those fields. Last semester I took multivariable calculus and got an A (perfect scores on the first two midterms and 97 on the final), and also passed out of the school's introduction to proofs course. I don't say this to brag, as my grades in calculus and the rest of my courses were more due to my study habits than any sort of innate intelligence (for example, I spent approximately 100-120 hours preparing for the introduction to proofs course). This coming semester I'll be taking differential equations and a second-year proof-based linear algebra course. Over break I'm running over my proof skills and going through an intro abstract algebra book (to help with my proof writing and intuition of isomorphisms and groups, which I expect will be important in the the linear algebra course). Basically, my problem is that I have no way to gauge myself relative to other undergraduates who have the same goals as me, and even if I did, I don't know how to set standards for myself. Even in the honors college at stony brook (basically the top undergraduates) I don't feel like any are nearly as dedicated or intelligent as, say, your typical math student at Harvard, so I don't measure myself against them in fear of becoming complacent. This confusion as to my abilities has led me into a lot of depression this semester, and I've started to become really scared that my life will amount to nothing, since in my opinion academic success is the ultimate measure of my life's value. I feel like I am sub-par since I am not going to Harvard or MIT. I graduated a year early from high school, and due to my laziness during freshman and sophomore years, I didn't have stats similar to other students applying to ivy leagues. As a result, I am attending Stony Brook, and I'm afraid that this will affect me later in my career. Am I up to par for a career in pure math? How do know if my standards for myself are too low or high? And finally, will the most intelligent mathematicians from better universities ultimately be better than me, no matter how hard I work?