<p>I went to Yale for undergrad and Penn for grad school and I honestly can’t imagine passing up Yale for Penn undergrad (except maybe for Wharton if you absolutely know you want to go to Wall Street). </p>
<p>As JHS said, unless you are a true prodigy, you won’t find all that much difference in the quality of math/science instruction at these 3 top schools. All will suit you well for a job search or further study in a top grad school</p>
<p>The differences are in other areas. I have less exposure to UChicago, so I will limit my comments to Yale v. UPenn:</p>
<ul>
<li><p>Though I do like Philly as a city, I never really liked the campus at UPenn very much. A few nice buildings, but basically kind of depressing. I personally always found myself quite in love with Yale’s campus and architecture and libraries, even inspired by it, but I suppose that’s just personal taste.</p></li>
<li><p>On a day-to-day basis, the area around Yale just had much more in the way of accessible, casual, student oriented places to eat, grab coffee, or drinks if you’re old enough. I found the area around Penn’s Campus just absolutely devoid of good places to hang. Maybe things have gotten better in the last few years.</p></li>
<li><p>The housing system at Yale, and the physical plant now that renovations are nearing completion, are vastly better than Penn’s from what I saw. I would never trade Yale’s fabulous college system for Penn’s frat oriented culture.</p></li>
<li><p>Student’s at Penn are smart, obviously, but extremely career focused and on the competitive side. The culture at Yale is more laid back and intellectual – knowledge for knowledge’s sake to a much greater degree. The students seem much more diverse in terms of interests.</p></li>
<li><p>Except for sports, there is a vastly greater array of high quality extra-curriculars at Yale, and students really go all out for them, much more so than at Penn.</p></li>
<li><p>Yale’s got a $17billion endowment to serve 11,000 students; Penn’s got a $6 billion endowment to serve 20,000 students. There’s just more money around to fund special programs, summer projects, research ideas, etc. </p></li>
</ul>
<p>Just my thoughts. Visit Yale and Penn again and take a look at Chicago and go with your gut. At the end of the day, there is no bad outcome here.</p>