I was in a math PhD program for one year during the 2009-2010 year in US (with funding by school). I was expelled due to low grades (nothing related to violence/cheating). During the Fall of 2010, I took some classes at a local university and applied to Master's programs during that time. I went to a Master's program in math in Canada from 2011-2013 (currently there).
My plan is to apply to top PhD programs in the US in math this Fall and enter at the Fall of 2013. I have a 4.0 Masters GPA, >95% GRE math scores, publications, and excellent relations with Master's advisors. I have developed great focus and motivation and have rid myself of procrastination which plagued me the past. I am also sure I want to continue doing mathematical research.
I am sure that when applying to PhDs, mentioning the expulsion from years ago will only hurt me so I intend to not mention it (I have not told anyone about this either). My question is if PhD programs will discover this hidden information when I apply? What if when I apply for fellowships?
I would strongly recommend mentioning it briefly somewhere in your application, with a very short explanation of why it is irrelevant (for example: you were less mature and motivated, so you procrastinated and your grades suffered, but your performance over the last few years proves that these issues are no longer a problem). Don't emphasize it too much, but your best strategy is not to hide anything.
You are right that it might hurt your chances, but I do not think it will hurt them much. If it came up in a committee I was on, I would argue against worrying about it, if the rest of your application was compelling. If you do not mention it, then you'll have an unexplained gap of a year in your CV, and that will also raise suspicions, since such a gap is usually a sign of something that did not work well. If you don't want to mention it or have a gap, then the alternative is lying.
You should definitely not lie, by giving an incomplete list of previous schools attended if asked for a complete list, or by giving a different explanation of what you were doing during that year. You might get away with the lie, since it can be difficult to detect missing information or disprove vague excuses, but if the lie is detected then it will ruin your chances of admission. (And committee members might even mention it to friends at other schools, if they are irritated enough about the lie.) Even if you get admitted, the lie may also come up again to haunt you in the future. For example, a faculty member from your old school may someday visit to give a talk, recognize you, and mention the connection to your advisor. Or you and your advisor may someday end up attending a conference at that university. You probably won't get kicked out of grad school if the lie is discovered later, but it's technically possible (at least at some universities), and in any case you do not want to be known among the faculty as someone who lied about his/her past.
You've already done the hard part of moving beyond this issue and demonstrating that it is no longer a problem, and that will minimize the risks of honesty. By contrast, the risks of dishonesty may follow you for years.