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