How should I deal with feeling dumb? I am a graduate student in mathematics at a top school. Most of other students achieved gold medal in International mathematics olympiad for high school and/or other similar competitions. Most did their undergraduate in the very best school.

I came from a very modest educational background but worked really hard. I did not participate in IMO or other math competitions and if I did, I do not think I would have done well. I attended a not well-known small university in Australia.

Now that I am surrounded by all these gold medalists, I just feel that they are way beyond me and I am so dumb when I compare myself to them. How should I deal with this feeling?
I have thought about this too. I am also a math grad student. I went to a liberal arts college in the US. I took lots of non-math courses, didn't take any graduate courses, and didn't do any extra math activities like the Budapest semester. At some point I made a list of the math I learned as an undergrad and what I learned in grad school and it is a huge amount more in grad school. Another thing that helped was realizing that some of the grad students who, based on impressions, would do very well, never finished the program due to various reasons. 

One thing that could help is to befriend grad students with whom you could let your guard down. There can be a lot of posturing, but much of it is quite obvious. Grad students who do that can still be helpful to talk to. It also helps to talk to faculty members whom you feel comfortable chatting with. They can really help you feel more at ease. I was at a workshop/school once and overheard a senior faculty member telling his math professor friend that by the end of a math conference, everyone feels like an idiot. So what if some grad students know more than you? At some point when you specialize you'll know a lot about quite a lot of things, and find joy in looking back at your accomplishments.