Only dead mathematics can be taught where competition prevails: living mathematics must always be a communal possession.
— Mary Everest Boole
CREDITS: Today’s quote is from Mary Everest Boole. Background photo courtesy of State Library of Queensland, Australia (no known copyright) via Flickr.
Denise Gaskins' Let's Play Math 
What does the first part if the sentence mean.
Competition prevails when we stress the importance of performance — when we value grades and standardized test scores. In such an environment, the only math most students will learn is a series of step-by-step recipes and rote-memory rules. That is dead mathematics.
But when we collaborate, play with ideas, and compare different solutions, then we build a community of creative thinkers. Math becomes alive. And as life grows and produces more life, so living math grows in understanding and begets new concepts.
For a good introduction to living classroom math, see Annie Fetter’s talk on YouTube. https://youtu.be/a-Fth6sOaRA