1.
"Math poses difficulties. There's little room for eyewitness testimony, seasoned judgement, a skeptical eye or transcendental rhetoric."

The function of the second sentence is to:

2.
"To the degree that Audubon's prose has the
shapely feel of a novel, it's because he was deft at
crafting his observations into the stuff of story; the
birds that he chronicles became not merely objects of
scientific data, but characters in a dramatic narrative."

The segment before the semicolon ("it's...story") primarily serves to:

3.
"Why is the connection between smells and memories so strong? The reason for these associations is that the brain's olfactory bulb is connected to both the amygdala (an emotion center) and to the hippocampus, which is involved in memory. And, because smells serve a survival function (odors can keep us from eating spoiled or poisonous foods), some of these associations are made very quickly, and may even involve a one-time association."

The primary purpose of the passage is to: