Prestige and Education
There has been much discussion, both in talk radio and newspapers, about the supposed overemphasis of national rankings when choosing a college or university. Contrary to what many may say, national rank and prestige does matter, especially in a competitive environment.
Rank matters more when there exist objective or at least partially objective measures/metrics by which to categorize people, this holds particularly true in the sciences, engineering, and law. Rank is not as important in fields where such metrics either don't exist or are not important, you can always argue that since objective measures don't exist objective categorization is not possible.
Rank is most important when applying for jobs and in choosing post-undergraduate education. What is most important is the rank of the school's PhD program. In the sciences rank offers significant advantages; peers within your own field take you more seriously, there are more and better research opportunities along with more funding for research, you interact with people at the top of your field on a daily basis, and you have more/better access to equipment for experiments. In addition rank helps you obtain professorships in universities with good research programs.
The ultimate measure of talent for a theoretical scientist is the quality of his/her published papers and that of an experimental scientist, the quality/results of his/her experiments. After a certain level, the quality of performance matters much more than the rank of your schooling, though the rank of your schooling may in some part determine the quality of performance. Also, the rank of your schooling may determine the opportunities available by which you can perform in the first place. Though you can get a job, even a good job, and do good research with degrees from lower ranked schools, you will have to prove yourself much more and with less opportunities to be considered equal.
Though rank is not everything, it does count for much, especially if you desire to be at the top of your field. In my opinion I would say, go for it, aim for the number one school. Even if you aren't accepted into the number one school, the time and dedication you put into becoming competitive will take you much farther than if you didn't aim for the top school.
Here are the rankings:
Phyiscs
Physics Elementary Particles/Fields/String Theory
Mathematics
I will leave you with a quote from Arthur Miller's play "Death of a Salesman"
He [in reference to Willy Loman] had a good dream. It's the only dream you can have - to come out number-one man.
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