Gil Kalai quotes:

Counting pairs is the oldest trick in combinatorics... Every time we count pairs, we learn something from it.

As for explaining mathematical phenomena it opens the question: explaining to whom? humans?, other computers?

Like musicians who can read and write complicated scores in a world without sounds, for us mathematics is a source of delight, excitement, and even controversy which are hard to share with non mathematicians. In our small micro-cosmos we should ever seek the right balance between competition and solidarity, criticism and empathy, exclusion and inclusion.

The book is so rich and yet it is well done. A rare achievement indeed!