He had a special feeling for what he called the ‘correct miscalculation,’ for he believed that mistakes were often as revealing as the right answers.
-- The Housekeeper (Chapter 1 paragraph 4)

Importance: As the Housekeeper comes to work for the Professor, the Professor teaches her and Root about mathematics. The Housekeeper explains that the Professor even loves wrong answers, because wrong answers can be as revealing as the right answers. This has much more to do than with just math. While the wrong answer in math can lead to the right answer in math, the wrong answers in life can sometimes ultimately lead to the right place in life.

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.
-- The Professor (Chapter 1 paragraph 82)

Importance: Here, the Professor speaks to the Housekeeper about math and creating proofs to solve mathematical problems. He explains that a proof can...