“It wasn’t immediately clear to me why my phone number was so interesting, but his enthusiasm seemed genuine. And he wasn’t showing off […] It nearly convinced me that there was something special about my phone number, and that I was somehow special for having it.”

One of the Professor’s gifts is his ability to make the mundane feel extraordinary; mostly he does this through numbers, as he does here, but he also expresses wonder, despite his brilliance, in the many things other people can do that he cannot.

“And yet, the room was filled by a kind of stillness. Not simply an absence of noise, but an accumulation of layers of silence, untouched by fallen hair or mold, silence that the Professor left behind as he wandered through the numbers, silence like a clear lake hidden in the depths of the forest.”

This contrast reflects the Professor’s rich inner life, which can seem ugly or boring to outsiders—even before his accident, he describes himself as spending most of his life in his own mind. But this is also a bit of misdirection; the narrator feels as if there is nothing of sentimental value here, but in fact she later finds some of his most valuable memories.

“The truly correct proof is one that strikes a harmonious balance between strength and flexibility. There are plenty of proofs that are technically correct but are messy and inelegant or counterintuitive. But it’s not something you can put into words—explaining why a formula is beautiful is like trying to explain why the stars are beautiful.”

This is one of many points where the novel bridges mathematics and art, the technical with the sublime. The narrator is used to thinking of mathematics as being about the right answer; the Professor surprisingly rejects that, explaining that it is as much about the beauty in the proof.