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First off, when people describe Yale as "weak" in science, they are referring to it being only, say top 10 in the US in overall research/graduate programs in the physical and biological sciences, rather that among the top two or three as it is in the humanities and social sciences. As an undergraduate, this will basically not matter (except perhaps as an engineer, where Yale is considered significantly worse than some of its peer institutions). The quality of undergraduate science instruction is as good at Yale as at any of its major competitors, and there are plenty of research opportunities available. Even freshmen can get involved in research - 2 of the 11 people on my floor will be spending this summer at Yale working with faculty on research. If you are accepted, you might want to consider applying to the Perspectives on Science program, which is a great way to be exposed to the wide variety of cutting edge research done by Yale faculty, and guarantees you support for research in the summer after your freshman year.
I can't claim to be able to compare Yale's culture to MIT's (since all I know about MIT is what I hear from my friends there) but I can guarantee that you will find that most people at Yale are not at all snobby. The math and science majors I know are a good mix of geeky and cool; though they are generally passionately dedicated to their area of interest, they are just as involved in campus social life as everyone else.
To be fair, you will find a lower percentage of science majors among the student body at Yale than at Harvard, Princeton or Stanford (and certainly lower than at MIT), but you will by no means be alone. Yale is a healthy mix of students with a wide variety of interests, with plenty of resources for everyone.
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