Hey! I’m an incoming freshman at Yale, not a current student, so my words should be taken with a grain salt. But I figured I could offer a few insights I garnered along my own application path.
Regarding the whole STEM-humanities cross-pollination quest – I feel you, 110% percent. I’m passionate about physics and math and cosmological symmetries and all but equally inspired by linguistics, literature, philology, theories of aesthetic impulse and artistic interpretation. At the end of the day, I felt Yale offered the best climate for that kind of multi-pronged intellectual immersion. Research opportunities in the sciences appeared to be wide-spread, given the undergraduate focus, and the curriculum seemed geared to accommodate breadth as well as depth (as reflected in the expectation of taking more classes per semester and the abundance of double-majoring). Plus, through whatever intangible cues, I got the sense that exploration was an established campus presence, a thing to be encouraged and cultivated.
I got a similar feeling from Brown. I think the difference there is the sheer degree of the freedom – Brown kids truly engineer their own curriculum, without distribution requirements and all. This can be both a good and bad thing. The upside is taking whatever you want; the downside is, well, taking whatever you want, and ending up imprisoned in your comfort zone. The dangers of not being pushed a little are there: I talked to some people who had, rather myopically, decided to take all four courses in the same department and simply skip over classes that involved weaknesses of theirs. That, and a kind of happy-go-lucky outlook on grade inflation that I perceived in Brown’s social arena, made me feel like the school probably wasn’t for me.
I didn’t apply to UChicago, but it’s worth noting that their science and math departments are objectively the strongest out of the three schools you listed. To me, research-rooted rankings like that are more relevant to graduate students than undergraduate ones, but hey, something to consider. Culturally, I’ve heard that UChicago is more competitive than Yale or Brown. One financial bonus is that Chicago offers merit scholarships, a nice feature that the Ivies, traditionally, avoid.
If possible, I’d recommend you visit all three and feel it out for yourself. That’s really the only way to get an authentic glimpse at what life’ll be like, beyond brochures and websites and advice from (admittedly biased, haha) college confidential users 