<p>The math/science programs at Yale are definitely top notch. The reason that Yale may not be as "known" among the popular consciousness for science is only because Yale absolutely dominates in the areas of arts, humanities, undergraduate education (generally) and politics, which generally get much more "press" than science does. For example, Yale has the best art, architecture, drama, and music programs in the country, if not the world. No other universities in the United States have four professional arts schools, certainly none that are even close to the caliber of Yale's. Yale is now investing $600 million just in its arts facilities alone, which will move Yale even farther ahead of the rest of the pack. In the case of politics, the last election was Yalie versus Yalie; the 2000 election featured 3 of the 4 major candidates as Yalies, and 4 of the past 6 Presidents went to Yale. In the case of undergraduate education, last year Yale not only has the lowest acceptance rate of any college in the country and by far the greatest number of Rhodes and Marshall Scholars of any university (even though it is relatively quite small), but if you consider the most popular undergraduate majors -- biological sciences, English, history, psychology, political science, economics -- and take their average departmental rankings in the Gourman or NRC rankings, for example, Yale comes out at the top.</p>
<p>In terms of strict science and math, Yale is just one of several great research universities in the world. It isn't the clear #1 like in so many other fields. UC-San Diego, Berkeley, Yale, Caltech, MIT, Cambridge, Stanford, Harvard are all incredible science powerhouses. According to <a href="http://www.sciencewatch.com/sept-oct2002/sw_sept-oct2002_page1.htm%5B/url%5D">http://www.sciencewatch.com/sept-oct2002/sw_sept-oct2002_page1.htm</a>, the highest rated science departments by average placement are at Caltech, Harvard and Yale. The alternative ranking has HSYM and UCSD as the top five.</p>
<p>Aside from that, at the undergraduate level, Yale offers more opportunities for undergraduates for several reasons: </p>
<p>First, Yale's science facilities are concentrated on the central campus. At a school like Cornell or Harvard, the medical facilities are in different cities altogether. This makes it easier for students to take full advantage of the research going on on the campus. In the case of Princeton, it does not even have any major medical research facilities, which is part of the reason why Yale receives over $400 million in total federal research funding each year while Princeton gets less than $100 million.</p>
<p>Second, Yale has more research on the central campus per science student than any other school except Caltech and possibly MIT (depending how you measure). This means laboratory work is incredibly accessible to undergrads.</p>
<p>All this means Yale science majors do very well - from what I've seen, Yale students have the highest acceptance rate into the very top medical schools, doing incredibly well, and also do very well at getting into the top Ph.D. programs (and earning ultra-prestigious post-bac NIH / NSF fellowships and the like that typically lead to the very top Ph.D. program after a year or two of work). Talk to students there and ask them what they think.</p>
<p>Good luck!</p>