Undergraduate / "The master of mathematics" - yale short answer [4]

Your short answer about your father is touching, but try to be a little more specific. for example, "I would take him to our favorite restaurant, _____" or "I'd take up a hammer and start working on the roof right beside him"

Tell us about the most significant challenge that you have faced throughout your school years.
this is a pretty generic question; perhaps add a twist to it that would make it uniquely yours?

Undergraduate / A Discerning Sleepless Night - common app essay. [2]

Very unique!
Just some ideas - maybe bring out the symbolism of night = unknown, day = knowledge a little more. Sometimes with college essays you have to be blunt with your artistic devices because these guys aren't exactly going to be literary critics with your essays; they read many a day.

also, maybe a bit more imagery would be nice. late at night you start to see things you usually don't notice, and if you got to the heart of that I'm sure the readers would really relate. the little things are sometimes the most impactful.

overall great job!