Do people actually name-drop university programs/classes/professors in their supplemental essays?

Ive written about my current research in time scales and desire to dive deeper into that research as i continue it at MIT, as well as my plan to broaden my research topics to include applied mathematics (for example, computational biology, something i’ve been wanting to do since working with marine biologists on turtles in costa rica). MIT has many opportunities for this kind of thing (UROP, etc) and I know the math department and I would be able to work to reach my goals. generally, the point is that i’m someone who wishes to specialize in both pure and applied math as a researcher, and i feel like it fits MITs desire for an explorer type of person who has specific passions.

My question is, does this fit what you’ve been saying about “knowing what MIT wants?” and if so, how would i fit all of this and answer the question”why major” portion properly as well in 100 words? i feel like an adequate explanation of either would just make the essay lean towards answering one question more than the other. Like, i have to talk about math too, and i find a lot of value in my perspective of the subject as well.