Do you have research experience (summer research programs that led to a paper)? Have you taken a large number of graduate level courses (on topics like functional analysis, algebraic topology, differential geometry, analytic number theory etc. that aren't necessarily seen in undergraduate levels courses)? Will you get a high mathematics GRE score (>75%)? Do you have extremely positive letters of recommendation from professors well-known in their field?
You don't need to tick all of these boxes, but I think it's very difficult to get into a top-10 program without ticking most of them, so be realistic in which schools you apply to.